Monsieur Baozhu Ning

Keywords: LoRaWAN, Wireless networks, Internet of Things, Quality of Service, LPWAN, Capacity

This thesis focuses on Low Power Wide Area Networks (LPWAN), a new class of wireless networks which aim to provide massive connectivity at a low cost in the context of the Internet of Things (IoT). This thesis focuses more particularly on the LoRaWAN technology, which is an open protocol based on the LoRa proprietary modulation. LoRaWAN knows a significant popularity among both the academic and industry communities. It is now established as one of the major players in LPWAN networks.

A typical LoRaWAN network is composed of a massive number of end devices (ED), i.e. connected objects, a set of gateways (GW) acting as bridges between the LoRa network and the Internet Protocol (IP) network and finally a network server (NS). EDs transmit their data via LoRa modulation with an random channel access method (unslotted Aloha-like), i.e. without any form of coordination. The GWs transmit to the NS via the IP network all the data captured on their LoRa interface. The NS is responsible for processing the received data. LoRaWAN is an uplink oriented network, meaning that the overwhelming majority of the traffic is expected to be from the EDs to the NS. However, LoRaWAN also allows rare downlink transmissions, from the NS to the EDs.

Due to the massive number of EDs, the low transmission power and the random channel access method, data is sometimes lost by the LoRa link. This thesis proposes solutions to make LoRaWAN communication more reliable, i.e. to deliver more than 99% of the application data. The reliability gain must be achieved in a realistic manner with respect to the capacity of the network, i.e. the number of EDs that can be served by the network in the same area. The consequence of this constraint is twofold: on the one hand the Time On Air (TOA) for the uplink transmissions must be kept as low as possible in order to avoid network congestion as much as possible, and on the other hand the TOA for downlink transmissions must be kept extremely low due to the limited downstream capability of LoRaWAN.

With the goal of a reliable LoRaWAN communication, this thesis firstly proposes an in-depth study of the characteristics of the LoRaWAN link, based on experimental measurements in a public urban network. Our characterization of the LoRaWAN link leads us to conclude that the reliability mechanisms currently existing in the LoRaWAN protocol are unfit to provide a highly reliable link. We therefore propose adaptations to make the LoRaWAN protocol reliable while conserving the technology scalability.

The thesis proposes two types of adaptations: The first adaptation consists in adding an error recovery protocol overlay, transparent for LoRaWAN, based on error correcting codes applied transversely to the packet flow. This approach makes it possible to reconstitute all of the data transmitted despite packet losses. The thesis proposes two distinct algorithms for this error recovery aspect, one based on the Reed-Solomon correcting code, and the other based on a correcting code derived from Low Density Parity Check (LDPC) codes. This thesis evaluates the performance of the two proposed error recovery algorithms.

The second proposed adaptation consists in reviewing the distribution of the transmission parameters of the EDs in the network. It is based both on the characterization of the LoRaWAN channel and on the observation that the proposed error recovery overlay makes it possible to obtain high reliability while making it possible to be tolerant to a certain threshold of packet losses. This thesis therefore proposes to review the LoRaWAN's Adaptive Data Rate (ADR) algorithm. The ADR is an algorithm which supports over-the-air and dynamic configuration of the EDs transmission parameters. We propose in this thesis, to optimize the ADR in order to reduce the TOA of the EDs to the minimum required.

Résumé

Cette thèse concerne les réseaux dit "Faible Puissance et Longue Portée" (Low Power Wide Area Networks LPWAN), une nouvelle classe de réseaux sans fils qui visent à fournir une connectivité massive à un faible coût dans le contexte de l'Internet des Objets (Internet of Things IoT). Cette thèse se focalise sur la technologie LoRaWAN, un protocole ouvert, basé sur la modulation LoRa, qui connait un succès important et s'est imposé comme l'un des acteurs majeurs des réseaux LP-WAN.

Un réseau LoRaWAN typique est composé d'un nombre massif de noeuds terminaux (i.e. les objets connectés), d'un ensemble de passerelles entre le réseau LoRa et le réseau IP et enfin d'un serveur central. Les noeuds émettent leurs données via la modulation LoRa avec une méthode d'accès au canal radio de type Aloha non slotée (i.e sans aucune forme de coordination). Les passerelles transmettent au serveur via le réseau IP toutes les données captées sur leur interface du réseau LoRa. Le serveur à la charge de traiter les données reçues. LoRaWAN est un réseau structuré essentiellement pour le sens montant, i.e. des noeuds vers le serveur mais permet également de rares transmissions dans le sens descendant, du serveur vers les noeuds.

Du fait du nombre massif de noeuds, des faibles puissances d'émission et du mode d'accès au canal basé sur Aloha, des données sont parfois perdues sur le lien LoRa.

Cette thèse propose des solutions pour fiabiliser la communication LoRaWAN, i.e. de délivrer plus de 99% des données applicatives. Le gain de fiabilité doit se faire de manière réaliste vis à vis de la capacité du réseau, i.e. le nombre de noeuds pouvants être servis par le réseau dans une même zone. La conséquence de cette contrainte est double: d'une part le temps d'émission dans le sens montant doit être maintenu le plus bas possible afin de repousser au maximum la congestion du réseau, et d'autre part le nombre de transmissions dans le sens descendant doit être maintenu extrêmement bas du fait de la capacité descendante restreinte.

Pour atteindre l'objectif d'une communication LoRaWAN fiabilisée, cette thèse propose dans un premier temps une étude en profondeur des caractéristiques du lien LoRaWAN, basée sur des mesures expérimentales dans un réseau urbain public. Notre caractérisation du lien LoRaWAN nous amène à conclure que les mécanismes de fiabilité existants à l'heure actuelle dans LoRaWAN sont inadaptés pour fournir un lien hautement fiable. Nous proposons donc des adaptations pour fiabiliser LoRaWAN tout en conservant au mieux la capacité de la technologie en terme de nombre de noeuds sur le réseau.

La thèse propose deux types d'adaptations: La première adaptation proposée consiste à ajouter une sur-couche protocolaire de recouvrement d'erreurs, transparente pour LoRaWAN, basée sur des codes correcteurs d'erreurs appliqués de manières transversales sur le flux de paquets. Cette approche permet de reconstituer l'intégralité des données transmises malgré des pertes de paquets. La thèse propose pour cet aspect récupération d'erreurs, deux algorithmes distincts, l'un basé sur le code correcteur Reed-Solomon, et l'autre basé sur un code correcteur dérivé des codes Low Density Parity Check (LDPC). Cette thèse évalue les performances des deux algorithmes de récupération d'erreurs proposés.

La seconde adaptation proposée consiste à revoir la distribution des paramètres de transmission des noeuds du réseau. Elle se base à la fois sur la caractérisation du canal LoRaWAN et sur le constat que la sur-couche de recouvrement d'erreurs proposée permet d'obtenir une haute fiabilité tout en permettant d'être tolérant à un certain seuil de pertes de paquets. Cette thèse propose donc de revoir l'algorithme de LoRaWAN: l'Adaptive Data Rate, qui prend en charge à la volée et de manière dynamique la configuration des paramètres de transmission des noeuds du réseau afin de réduire au minimum requis le temps de transmission des noeuds.

Mots-clefs

LoRaWAN; Réseaux sans-fils; Internet des Objets; Qualité de Service; LPWAN; Capacité;

Introduction

Research issue The growth of the Internet Of Things (IoT) brings legacy wireless networks technologies to their limits. The scalability, energy consumption, deployment cost and operating cost of the legacy conventional cellular technologies make them unsuitable for the massive deployments required by applications for smart city, smart farm, smart factory, wide scale asset tracking, etc. To address these challenges, Low Power Area Networks (LPWAN) promise to provide long range and large scale connectivity for the IoT, at low cost and low power consumption.

LoRaWAN ® is one of the leading LPWAN technologies, it is a networking protocol specification developed by the open LoRa Alliance ® on top of Semtech's proprietary modulation LoRa ® .

Thanks to the robust LoRa modulation and its wide range of physical and MAC parameters, Lo-RaWAN has the potential to successfully provide low cost connectivity to a wide variety of application, with various, and sometimes contradictory, strongly constrained requirements. Typically, these requirements are in terms of energy consumption, communication range, reliability, throughput or scalability. So, LoRaWAN claims the ability to provide connectivity to thousands of battery-powered autonomous devices into a single cell of up to ten kilometers of radius with throughput up to a kilobyte per second, for a decade.

But versatility comes at the cost that LoRaWAN requires careful and sharp engineering of the network parameters to get the best of the technology, or the performance might quickly falls below expectations.

The typical use case of LoRaWAN is to provide connectivity where "traditional" communications technologies are unable to meet the needs. It is therefore expected that LoRaWAN networks will be confronted with challenging radio conditions: very low transmission power, long range, obstructed radio propagation path, high interference levels due to co-located LoRaWAN networks, or other technologies using the same free-to-use frequency bands, etc. Under these conditions, it is expected that some of the transmissions are not received successfully. It is therefore necessary to provide mechanisms to recover these losses in order to ensure a reliable communication.

Moreover, the radio channel random access (ALOHA type) which is a key feature to lighten the embedded device side of the protocol, open a double challenge to LoRaWAN. On the one hand, an inadequate parameterization of the network will drastically increase the collision rate and cause the data loss rate to explode. On the other hand, a fraction of the transmitted frames will inevitably suffer collisions and risk of being lost, thus reinforcing the need for an adequate reliability mechanism.

CONTENTS

Our approach and contributions In this thesis we analyze in depth the characteristics of the LoRaWAN link with a particular attention on the conditions of frame losses, and to losses distribution. We show in particular through a large scale field experiment in an urban environment, that the LoRaWAN link follows a quasi-static Rayleigh channel model. This in-depth analysis of the LoRaWAN link and the more precise knowledge of the losses pattern, allows us to conclude that the current reliability mechanism of LoRaWAN are inadequate. Thus, we provide a tailored solution to make the LoRaWAN link more reliable. It consists in the use of error recovery protocols based on error correcting codes. We describe two reliability protocols built from this basis. The first, based on the Reed-Solomon correction code, keeps the data loss rate below 1% despite a frame loss rate up to 92%. The second, based on pseudo-random combinations of data fragments, can correct residual frame losses up to a loss rate of 40%, without any downlink acknowledgment (which is a scarce resource in LoRaWAN).

Finally, rooting from the observation our loss recovery protocols modify the transmission parameter adjustment paradigm, we develop a solution to optimize the LoRaWAN dynamic parameterization algorithm. The combination of our dynamic parameterization algorithm and our erasure correction layer provide highly reliable LoRaWAN communication while keeping the network load as low as possible. As a result, our solution can recover the LoRaWAN typical 10% data loss floor while reducing the network load by up to half.

Thesis content The thesis is organized as follow:

In chapter 1 we lay down the scientific basis of the thesis matters with the fundamentals of wireless networks, channel coding, IoT and LPWAN networks.

In chapter 2 we present in detail the LoRaWAN technology. Beyond describing the technology in detail, with its strengths and weaknesses, we highlight the intrinsic trade off of LoRaWAN that must be handle.

In chapter 4 we present the experimental field measurement campaigns that we carried out, and we dissect the results in order to define an accurate and truthful model.

In chapter 5 we describe and analyze the performance of two error recovery algorithms based on error correcting codes applied transversely over the LoRaWAN packets.

In chapter 6 we optimize the LoRaWAN dynamic parameterization algorithm to make the Lo-RaWAN link reliable while keeping the network load as low as possible.

Finally, in chapter 7, we conclude this thesis by emphasizing the main finding and their consequences. We also sketch the potential follow-up to this work.

Thesis context This thesis was carried out under a Cifre convention in partnership with the Semtech company and the Drakkar research team from the Grenoble Informatics Laboratory (LIG). Semtech owns and develops the physical layer of LoRaWAN: the LoRa modulation. Semtech also plays a major role in the LoRa alliance which develop the LoRaWAN protocol. LIG's DRAKKAR team is a research team that focus on various aspects related to networks, especially wireless networks and IoT, as well as their security. The team is made up of 8 permanent staff and around as many PhD students.

Chapter 1

Context Chapter Introduction

In this chapter we lay down the scientific basis of the thesis matter. In section 1.1 we recall the fundamental of the wireless networks which will serve as a basis in the rest of the thesis. In section 1.2 we describe the various coding techniques used in information theory. We make a special focus on the ECC since it is one of the keystones of our solution for reliability in LoRaWAN. In section 1.3 we describe the Internet Of Things (IoT) paradigm and explain why the legacy wireless network technologies are unable to fill these new requirements. In section 1.4 we focus on a sub-category of IoT: the Low Power Area Networkss (LPWANs). First, we define the needs and constraints to which the LPWANs respond. Then we detail the levers used by LPWAN technologies to achieve long ranges despite low transmission power. Finally, we provide an overview of the different LPWAN technologies.

Wireless Networks

Since the early radio-communication experiments at the end of the 19th century, wireless communication technologies have been widely developed and diversified, whether in scientific, industrial or military fields Thus, the uses of radio-communications are many and varied. We can distinguish some examples of typical technologies: AM/FM radio and terrestrial television use a model of unidirectional broadcasting of audio and/or video data: the relay stations (transmitters) broadcast the data to all user stations (receivers) within reach. Modulations, initially analog as for AM/FM radio or analogue terrestrial television, are now supplemented or replaced by digital modulation technologies (DAB, DTT, DVB-S, ...).

Walkie-talkies and amateur radios carry out the bidirectional broadcasting of the users' voices, in analog (PMR446) or digital (dPMR446) modulation in which each station is successively a transmitter and a receiver.

Radio guidance which requires point-to-point bidirectional ad-hoc data communication (without architecture) for remote device control.

Mobile telephony (GSM, UMTS, LTE, ...) which allows long-distance bidirectional point-to-point communication via an architecture between users. Communication is performed both by the radio communications between each of the terminals and their respective associated relays (terrestrial or satellite antenna), and by the back-end communication between relays via a secondary network.

Wireless Local Area Network (WLAN), such as Wi-Fi 802.11, or Wireless Personal Area Network (WPAN) such as Bluetooth 802.15 allow point-to-point bidirectional communications over short distances, either ad-hoc or with infrastructure. The terminals use the radio link to communicate either on the personal/local network, or in interconnection with a long distance network to communicate on the Internet.

Technological and industrial breakthroughs, particularly in the precision of silicon etching and in the transistors size reduction, have made it possible to integrate processors, memories, and radios in many objects: measuring and sensors devices, street furniture, household appliances ... The proliferation of uses, the diversity and novelty of constraints as well as the mass of these newly connected objects gave birth to the concept of the IoT which brings together these new fields of wireless networks development.

Physical Layer of Wireless Networks

Radio Transmission of Information

The radio transmission of information consists of transmitting an information signal over an electromagnetic wave. In the case of wired communication, the information signal can be sent directly, i.e. without frequency transposition, to the medium in the form of an electrical signal. This is referred to as baseband transmission. In the case of wireless communication, baseband transmission isn't possible, thus the information signal must be modulated to a higher frequency sinusoidal signal. We then speak respectively of modulating signal and carrier. The result of the modulation of the carrier by the modulating signal is the modulated signal. The information signal is then represented by variations of one -or a combination -of the physical characteristics of the carrier: amplitude, frequency and phase. On reception, the receiver performs the reverse operation -demodulation -to extract the modulated signal, the information, from the received signal.

In analog modulation, the modulating signal, the data, is directly the input signal. In digital modulation, discrete values are assigned to different physical states of the carrier: symbols which then make it possible to represent bits. Each of the distinct states that the signal coding represent is a symbol. The number of symbols is called the signal valence V . The figure 1.2 illustrates the basic digital modulation of valence V = 2. This thesis focuses on the performance of digital communications and therefore uses digital modulations and analog modulations are out of scope. The Bandwidth (BW) is the difference between the lowest and highest frequencies used by the signal. The BW limits the rate at which symbols can be modulated onto the signal, thus this limit the modulation data rate (DR mod ). Nyquist's theorem thus gives DR mod -Nyquist , the maximum DR mod (in bits/s) of a signal transmitted on a channel according to the BW (in Hz) and the number of distinct symbols V :

DR mod -N y qui st (BW ) = 2 × BW × log 2 (V) (1.1)
However, a real channel is noisy, i.e. the signal of interest is mixed with electromagnetic noises which deteriorates the signal transmission. For instance, there is always at least, the thermal noise: an Additive White Gaussian Noise (AWGN) noise due to thermal agitation in the radio equipment.

The sum of all noise sources is the noise floor, with P N its power. In the following, unless stated otherwise, we will refer to the noise floor simply as the noise. For convenience, the noise is often normalized as the noise spectral density N 0 : the P N per unit of BW. As it deteriorate the signal, the noise makes it more difficult for the receiver to discriminate between different symbols. Thus the noise limits V the valence of the signal that the receiver is able to distinguish. Therefore over a real channel, thus in presence of noise, DR mod that can be reached over a given BW is bounded. Also, to be successfully demodulated, the received signal power P Rx must be strong enough, both in absolute value and relatively to the P N . We call this minimal P Rx for correct reception the sensitivity. Therefore the ratio P Rx P N , called Signal-to-Noise Ratio (SNR), is often used to characterize the strength of a received signal. We define the physical data rate (DR ph y ) as the rate at which the physical layer transmits, taking into account the overhead from any physical layer error recovery scheme, i.e. the overhead of channel coding at the physical layer (see sec. 1.1.1.3). In short, DR ph y is the DR mod multiplied by the physical coding rate.

The formulation of the maximal DR ph y has been extended from equation 1.1 by Shannon [START_REF] Elwood | Communication in the presence of noise[END_REF] in the case of AWGN noise. This maximal DR ph y -Shannon (in bits/s) is the maximal capacity of a real channel. It is expressed as a function of the BW and SNR:

DR ph y -Shannon (BW , SNR) = BW × log 2 (1 + SNR) (1.2)
DR ph y is to be distinguish from the physical net data rate (DR net ) that we define as the data rate provided to the upper layer, i.e. the data rate of the effective payload thus excluding both any redundant data and also any protocol overhead. Notice that by definition DR net ≤ DR ph y ≤ DR mod .

Figure 1.3 plots the Shannon equation for a signal received with P Rx to N 0 ratio : P Rx N 0 = 1. The core consequence of the Shannon equation is the possibility, for a given P Rx , to trade BW for DR ph y and vice versa. The extremities of the curve are particularly interesting: when the BW is narrow, it is the main factor limiting the DR ph y . This is called Bandwidth Limited Regime. Conversely, when the BW is wide enough, widening it further does not improve achievable DR ph y significantly and P Rx is the main limiting factor in this case. This is referred to as Power Limited Regime. The Shannon equation can then be approximated when SNR is small (≤ 1) and BW is wide:

DR ph y ≈ 1.44 × P Rx N 0 .
Bandwidth in the radio spectrum is a relatively scarce resource in view of the number of technologies and users who share it. This pressure on the radio spectrum tends to make it particularly expensive for operators and manufacturers. It is therefore essential to be able to scale and for the viability of deployments of radio technologies, to use it effectively. For this, we speak of spectral efficiency η, which we define as the DR net per Hz:

η = DR net BW (1.3)
Spectral Efficiency can be measured for a single transmitter and receiver -we then speak of link spectral efficiency-in which case it measures the physical layer efficiency. Spectral Efficiency can also be measured for the entire system with multiple transmitters and receivers -we then speak Multiple Access (CDMA). This makes it possible to greatly attenuate the additional BW cost of the spreading. However, because spreading codes have usually either low auto-correlation (against interference and multipath) or low cross-correlation properties (against collisions) [START_REF] Goldsmith | Wireless communications[END_REF]Chapter 13], and so the design of the spreading codes is subject to a trade off.

Radios Waves Propagation

The signal can be transmitted either on a guided medium (on an electric cable or an optical fiber for instance), we then speak of wired communication, or on a non-guided medium in which case we speak of wireless communication. In wireless communication the signal is then diffused through the environment. This thesis focuses on wireless communications, wired communications are out of scope.

Path Loss (PL) Definition

The PL is the attenuation of the signal power between the transmitter and the receiver. I.e. it is the ratio between the transmitted power P Tx and the P Rx . In linear units, the PL is expressed:

P L linéaire = P Tx P Rx (1.5)
PL is generally expressed in logarithmic units:

P L = 10 log 10 P Tx P Rx dB (1.6)
The PL is due to various phenomena which degrade an electromagnetic wave during its propagation: absorption, dispersion, diffraction , reflection, refraction ... The PL determines whether the transmitter and receiver are within communication range, as well as the quality of the link: the probability to receive or lose the transmitted data.

Path Loss (PL) Models

The exact calculation of the PL requires the computation of the exhaustive Radar Cross Section of the environment around and between the transmitter and the receiver. Such a calculation is most often impossible because it is too complex and too expensive. Simplified approximations and models are therefore used to estimate the PL. We break down the PL into 3 components:Large Scale Fading (LSF), Shadow Fading (ShF) and Small Scale Fading (SSF):

Large Scale Fading (LSF)

The LSF depends on the distance between the radios, and on the Path Loss Exponent γof the propagation medium.

Because the electromagnetic wave is not guided, it diffuses in space. The energy emitted at the source is therefore distributed over a portion of a sphere. The sphere portion depends on the opening of the transmitting antenna: the energy is distributed over a complete sphere with an isotropic antenna and over a portion of a sphere with a directional antenna. This distribution of the energy radiated at the source in space is S the power density per unit area in W/m 2 :

S = G T x × P Tx 4 × π × D 2 (1.7)
with P Tx in W, G T x the transmitter antenna gain which depends on the antenna technology, and D the distance between the transmitter and the receiver in m.

The ability to receive the signal also depends on the effective area of the antenna, the received power P Rx (in W) is:

P Rx = G R x × S × λ 2 4 × π (1.8)
with G R x the receiver antenna gain which depends on the antenna technology, and λ the wavelength.

The combination of the equations 1.7 and 1.8 gives the formula for the Free Space Path Loss (FSPL) for isotropic antennas:

LSF F SP L = P Rx P Tx = G T x ×G R x × λ 4 × π × D 2 (1.9)
This equation is known as the Friis transmission formula.

In the real world, the electromagnetic wave does not pass through void. It passes through an environment with complex geometry and part of the energy is deflected and lost. The proportion of energy lost per distance traveled depends on the environment (urban, forest, plain, indoor, etc.). The equation to compute the LSF of the Lossy Medium Path Loss (LMPL) can be derived from the equation 1.9:

LSF LM P L = G T x ×G R x × λ 4 × π × D γ (1.10) with γ > 2.
Other models exist to compute and predict LSF.

• The deterministic techniques of Ray Tracing which reduce the complexity by considering a limited number of propagation paths. The number of paths taken into account can vary in order to simplify the model as for example the two-ray ground-reflection model, or to improve the precision as for the model ten-ray dielectric canyon. Ray Tracing techniques remain difficult to apply due to the complexity and variability of the environment.

• Models based on empirical measurements in specific environments which allow an estimate of PL for deployments in similar environments. Some can be configured to take into account, for example, the height of the antennas, etc. Among these empirical models, the most commonly used are the Okumura model, the Hata model, the COST231 model or even the linear piece-wise with several slopes models . These models can also be supplemented with additional mitigating factors to account for specific obstacles, such as floors and partitions for indoor propagation.

• Statistical models which can be parameterized and refined as needed from experimental data. A classic and generic model is the log-distance model:

PL(d ) = PL 0 + 10γ log 10 D d 0
Where PL 0 is the PL at the reference distance d 0 .

Shadow Fading (ShF)

The ShF corresponds to the potential obstructions on the main wave propagation path, such as the presence of trees, buildings, walls, shutters, etc. The resulting received signal can be destructive or constructive depending on the effects of diffraction and reflection. Also, the phenomenon being dependent on the entire geometry of the environment on the path of the wave, it is widely variable. Especially in the case of mobile radios of course, but it might also be true for fixed radios if the environment is changing, for instance with the opening and closing of doors, depending on whether a tree has foliage or not depending on the season, if a vehicle parks etc. This phenomenon is therefore generally represented in the PL calculation as a random variable X which varies the attenuation around the average at a given distance. The most common model is log-normal shadowing: X ∼ l og -N (µ, σ 2 ) with parameters Μand σ 2 respectively the average and variance of the variable's natural logarithm.

Small Scale Fading (SSF)

The SSF phenomena come from multiple paths propagation. All the various multi-path components of the wave arrive at the receiver and their addition can have a destructive or constructive effect. SSF varies over very short travel distances of radios and moves of the environment, and therefore on a shorter timescale than ShF. Thus, due to SSF, the received power can vary between each successive transmissions. The SSF determines the distribution of the PL of multiple transmissions around the mean for the entire communication.

The SSF is a key element in determining on the one hand the proportion of transmissions which reach the receiver with sufficient power for demodulation, but also on the other hand to determine the power differences between several simultaneous transmissions which collide. The SSF is also taken into account in the calculation of the PL as a random variable Y which varies the strength of the received signal. The most common models of multipath channels are the Rayleigh channel and Rice channel model.

Error Recovery at the Physical Layer

Since the radio link of wireless networks is therefore by definition subject to attenuation and confronted with an unstable environment, the frames received are largely susceptible to binary errors. The modulation is therefore often supplemented by an ECC at the physical layer in an attempt to repair the erroneous bits. For instance 802.11a, 802.11g or even Bluetooth LE Coded PHY standards use a convolutional ECC, the 802.11ad standard uses an Low Density Parity Check (LDPC) code. The ECC basics are detailed in section 1.2.2.

Link Layer

Medium Access Control Sublayer

The Medium Access Control (MAC), is fundamental in shared channel systems such as wireless networks as it handles the multiplexing of over the physical transmission medium. Unlike wired networks, wireless networks cannot carry out the Carrier Sense Multiple Access with Collision Detection (CSMA/CD) algorithm which consists on the one hand in the Carrier Sense Multiple Access (CSMA) part: listen to the channel before beginning and transmit only if the channel is free, and on the other hand the CD part: listen while transmitting and stop if a collision is detected. Indeed, the transmission of a radio frame makes it impossible to listen to the channel simultaneously to detect a third-party transmission.

The MAC sub-layer of wireless networks are either:

• Methods based on explicit allocation, i.e. based on coordination and reservation of subchannels.

The principle is to split the shared channel into logical sub-channels and to assign one (or more) sub-channel to each transmitters. The division of the channel can be done:

in time (Time Division Multiple Access (TDMA)),

in frequency (Frequency Division Multiple Access (FDMA)),

by spread spectrum with orthogonal codes (CDMA).

These algorithms require synchronization between the transmitters for the allocation of the subchannels. This preliminary phase of resource reservation must be carried out by an access control algorithm without a priori knowledge, i.e. a contention type algorithm.

• Methods relying on contention, i.e. based on randomized competitive access to the shared channel.

The principle is to let the transmitters have a competitive decentralized access to the channel. A fraction of the transmissions will necessarily undergo collisions. The losses of the collided frames must be repaired by an error recovery mechanism otherwise if reliability is required... and if possible. Two subcategories of contention multiple access algorithms exist: CSMA methods -also called Listen-Befor-Talk (LBT)-and ALOHA methods.

With CSMA methods: a node communicates on the channel only if it detects the radio channel as currently free from any transmission. This solves the problem only partially due to propagation delay and the hidden terminal problem [2]. The hidden terminal problem arises when terminals within range of the same base station are not in range of each others. As a consequence, each terminal is unable to detect the activity of the other ones and thus is unable to prevent the collision despite the use of CSMA. In LPWAN (described in sec-tion1.4), the channel gain between the terminals is often several orders of magnitude worse than between the terminals and the base station. This strongly favors the problem of hidden terminals. Moreover, with the CSMA method, the nodes can spend a significant amount of time listening before getting access to the channel. It might represents unacceptable energy consumption overhead for systems with high energy constraints such as LPWAN networks.

With the ALOHA access methods, each node can transmit at any time without coordination either with the other nodes or with the base station. This is the preferred method in LPWAN networks and in particular used by LoRaWAN technology because there is no additional work nor any energy consumption.

ALOHA Access Methods Variants

The ALOHA Access Methods [3] variants are based on a simplistic principle: in its most basic version, called Pure-Aloha, each transmitter can transmit at any time without any coordination neither with the other transmitters nor with a base station. Fatally, part of the transmissions may suffer a collision but another part of the transmissions on the other hand may be transmitted successfully. We consider Probability of error (P e ) to be the probability of collision. Thus P e is the probability that there is a concurrent transmission which overlaps the transmission in time and therefore causes a collision. Under the common assumption that frames are generated independently of each other, P e depends on the channel load G = ν × D frame . ν being the intensity of the Poisson process which represents the frequency of generation of new frames by the transmitters and D frame the duration of a frame:

P e Pure-Aloha = 1 -exp (-2G)
The channel use rate, that is to say the time spent transmitting data successfully, is expressed as a normalized useful rate called normalized goodput.

normalized_goodput Pure-Aloha = G × exp (-2G) P e and therefore the performance of the access method can be improved by discretizing the time in slots of constant time, the duration of a frame. The transmissions are required to start at a slot beginning. We then speak of Slotted-Aloha [1]. The performance of this access method is then:

P e Slotted-Aloha = 1 -exp (-G) normalized_goodput Slotted-Aloha = G × exp (-G)
However, the slotted Aloha algorithm requires keeping the transmitters' clocks synchronized, which is sometimes too expensive. Indeed, the transmitters' clocks cannot be perfect and drift. Thus periodical re-synchronize, through beacons for instance, is required. The frequency of re-synchronization might be prohibitive when using low-cost transmitters with imprecise oscillators, like in LPWAN networks. It is fundamental to denote that under "ideal" channel load conditions, i.e. G = 0.5 for Pure-Aloha and G = 1 for Slotted-Aloha, the normalized goodput will only be respectively of 18% and 37%. That is, for Pure-Aloha, the channel will be used for correct transmission barely 18% of the time. It is also fundamental to notice the quick P e fall, almost its collapse, as the channel load increases. Thus, under the optimum load conditions for the useful throughput, only 36% of the frames are transmitted without collisions.

When the receiver is already synchronized on the reception of a frame, the collision by another frame, which is therefore not synchronized with the receiver, may appear as simple noise. This allows good reception despite collisions under the condition of a sufficient power difference [START_REF] Lee | An experimental study on the capture effect in 802.11 a networks[END_REF]. This phenomenon is known as the capture effect. This makes it possible to reduce the impact of collisions and therefore to improve the performance of the Aloha access methods [START_REF] Birk | Increasing Dealine-Constrained Throughput in Multi-Channel ALOHA Networks via Non-Stationary Muliple-Power-Level Transmission[END_REF]. Figure 1.5 plots the performance of the Pure-Aloha access method with capture effect. The capture effect is here under the assumption that in the event of a collision with a single concurrent frame, the transmission still has half the chances to be received:

P e Pure-Aloha-with-capture = 1 -exp (-2G) × 1 + 2G 2 normalized_goodput Pure-Aloha-with-capture = G × exp (-2G) × 1 + 2G 2
The channel can be divided into independent subchannels if they allow simultaneous transmissions without collisions. The subchannels are then said to be orthogonal and the Aloha access method in such a context is called multi-channel Aloha (MC-ALOHA) [4]. Orthogonal subchannels can be separated in frequency [8] or by spreading code [6]. This sub-channel division enables the benefits of narrower band communication or spread spectrum to be enjoyed while maintaining efficient BW utilization. But it does not change the fundamental performance of the Aloha algorithm which remains defined by the offered load G. Indeed, separating the BW into two subchannels will have the effect of dividing by two µ on each sub-channel but also it multiplies by two the transmission time, to finally have no effect on G.

LoRaWAN uses a multi-channel Pure-Aloha access method with on the one hand a division of the channel by frequency (at least 3 distinct channels of 125kHz in Europe), and on the other hand a division of the channel by spreading code (6 channels by orthogonal codes).

Whatever the version and the improvements adopted, the ALOHA MAC remains subject to losses due to collisions, and the collision rate increases drastically with the channel load. In order to provide a reliable link, the MAC layer must then be supplemented by error recovery mechanisms.

Error Recovery at the Link Layer

The radio link of wireless networks is by definition subject to frames losses, because of attenuation, unstable environment as developed in section 1.1.1, or because of collisions in contention channel access methods.

In order to obtain reliability over the radio link, the link layer must be implement an error recovery mechanism:

• The error recovery mechanism can be a retransmission algorithm, typically Automatic Repeat reQuest (ARQ). The lost frames are retransmitted until the reception of an acknowledgment, possibly after a randomized waiting time in order to avoid collisions in series [5].

• The error recovery mechanism can also be an ECC to try to repair lost frames without acknowledgments and retransmissions [START_REF] Anthony | Reliable broadband communication using a burst erasure correcting code[END_REF][START_REF] Birk | Judicious Use of Redundant Transmissions in Multichannel ALOHA Networks with Deadlines[END_REF].

These two error recovery mechanisms can be used in a hybrid [START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF] way.

This thesis focuses on the application to the LoRaWAN technology of ECC, described in section 1.2.2, as an error recovery mechanism for the link layer.

Channel Coding

Coding Techniques in Networks

In information theory, a data can be transformed according to a reversible function called code in order to obtain an encoded data with better characteristics. These techniques are widely exploited in networks:

• Source Coding is the application to networks of information compression techniques. It reduces the BW usage and therefore improves the network capacity [START_REF] Marco | Reliability vs. Efficiency in Distributed Source Coding for Field-gathering Sensor Networks[END_REF]. The source coding can either be a lossless or sacrifice some of the original information by simplifying it to improve compression performance. Several strategies [START_REF] Luna | Joint source coding and data rate adaptation for energy efficient wireless video streaming[END_REF][START_REF] Zhai | Joint source-channel coding for video communications[END_REF] were proposed that mix source coding of the data with channel coding, data rate adaption and transmit power adaption in order to optimize the data quality while saving the network resources like BW, energy, etc. It is typically used for media live streaming, VOIP,...

• Channel Coding is the application to networks of techniques to computing redundancy of information, called ECC. Channel coding allows to recover data corrupted during communication. We develop the techniques and challenges of channel coding in the following section 1.2.2.

• Network Coding is an inter-flow coding scheme. The coding is done at relay nodes and combines data flows from multiple sources and to multiple destinations. This way, one can exploit the broadcast nature of wireless communication in multi-hop environment [START_REF] Fragouli | Network Coding: An Instant Primer[END_REF][START_REF] Fragouli | Wireless Network Coding: Opportunities & Challenges[END_REF].

A simple example is the case when nodes A and B exchange packets through the intermediate node I: by sending the xor of both packet at the intermediate node, the packet exchange can be done in three transmission rounds instead of four. Network coding can improve distributed storage system with a trade-off between storage and repair BW [START_REF] Dimakis | Network Coding for Distributed Storage Systems[END_REF]. This trade-off reveals two extreme points: minimum-storage regenerating codes and minimum-BW regenerating codes.

Notice that multiples coding techniques can be used successively and jointly. Figure 1.6 summarize those 3 categories of coding applied to networks with their position and role. This thesis focuses on channel coding to improve reliability of LoRaWAN communication while reducing as much as possible the BW usage.

Error Correction Code (ECC)

Fundamentals of ECC

ECC are reversible function that compute redundancy from the original data, called dataword, such that corruption of the encoded data, called codeword, can be detected and even recovered. ECC has been developed to improve reliability of digital data storage [START_REF] Gong | Zigzag Decodable codes: Linear-time erasure codes with applications to data storage[END_REF], it is used to insure reliability in storage like compact disks (CD) or redundant array of inexpensive disk (RAID) [START_REF] David A Patterson | A Case for Redundant Arrays of Inexpensive Disks (RAID)[END_REF]. It is out of the (N+M) symbols are received and the full data can be correctly recovered, or less than M symbols are received and not a single correction can be made. So, RS-codes are weak against burst errors longer than N. Although this problem can be handled by interleaving the data. This way the channel is smoothed: the erasures are spread and independently and identically distributed.

Low Density Parity Check (LDPC) codes

LDPC codes [START_REF] Sridharan | Optimizing burst erasure correction of LDPC codes by interleaving[END_REF][START_REF] Paolini | Construction of near-optimum burst erasure correcting low-density parity-check codes[END_REF] are systematic block codes with fixed data-rate that append an arbitrary long sequence of parity symbols. The principle is to combine, i.e xoring, a subset of the data symbols in each redundant symbols. We note LDPC (M,N) a LDPC-code that encode an M symbols long word into a (M+N) long codeword. The encoding and decoding of LDPC-codes can be implemented with complexity of respectively O(N + M ) and O((N + M ) ln( 1 ǫ )) with 0 < ǫ < 1 [START_REF] Michael G Luby | Efficient erasure correcting codes[END_REF][START_REF] Lu | Linear time encoding of LDPC codes[END_REF] . Although they are not MDS, they provides near-optimum erasure correction performances. The codeword can be recovered from any 4 ). If less correct symbols are received, some erased symbols might be recovered anyway.

N × (1 + ǫ) with probability 1 -O((N + M ) - 3

Cliff Effect

Figure 1.10 shows the performances of RS and LDPC codes over the BEC. Both RS and LDPC maintain high Data Delivery Rate (DDR) until the Symbol Erasure Rate (SER) degrades and reaches a tipping point where the DDR drops. Because the ECC is systematic, the DDR drops until it reaches the native SER of the channel. We call this the cliff effect. Notice that the more the ECC operates over large word, the more the cliff effect is pronounced, i.e. steep. This is because large codewords induce more diversity and thus average the local and temporal variation of the PDR (around its mean value). (8,8), RS [START_REF] Jansen C Liando | Known and unknown facts of LoRa : Experiences from a large-scale measurement study[END_REF][START_REF] Jansen C Liando | Known and unknown facts of LoRa : Experiences from a large-scale measurement study[END_REF], LDPC (324,324) and LDPC (972,972), over the binary erasure channel with independently and identically distributed erasures. Each point is a 2 × 10 6 symbols simulation.

Internet Of Things (IoT)

The development of networks, and especially wireless and cellular networks, is based on humancentered use. Web browsing, voice exchange, video streaming generate large amounts of data and have pushed the development of technologies towards increasing throughput and reducing latency [START_REF] Navarro-Ortiz | A survey on 5G usage scenarios and traffic models[END_REF]. These improvements have been made on increasingly powerful and expensive devices (smart-phones, laptops, drones).

In recent years, the integration of computing and radio capacity, as auxiliary functions on various devices, has opened up a new field in the development of wireless networks. The data is generated -or even processed -autonomously by these objects without human intervention. The communication pattern, as the type of terminals, is different and has opened up a new field of development of wireless networks. We speak of IoT and Machine-Type Communication (MTC). The IoT paradigm is one of the strong tendencies in the network evolution of the past decade [START_REF] Gubbi | Internet of Things (IoT): A vision, architectural elements, and future directions[END_REF][START_REF] Margelis | Low Throught Networks for the IoT : Lessons Learned From Industrial Implementations[END_REF].

Two sub-categories are to be distinguish:

• Critical MTC (cMTC) also referred to as Ultra-Reliable and Low Latency Communications (URLLC) requires ultra reliability, ultra low latency and availability for applications such as self-driving cars and factory autonomous automaton [START_REF] Najib | Missioncritical machine-type communication: An overview and perspectives towards 5G[END_REF]. cMTC and URLLC are out of scope of this thesis.

• Massive MTC (mMTC), on which this thesis focuses, aims at providing massive and very low cost connectivity to any objects.

Massive MTC (mMTC)

Indeed, the possibilities and industrial applications are numerous: sensors networks, actuators networks, smart city applications, smart-grid, smart-metering, industrial assets monitoring, logistic, infrastructure monitoring, agriculture, home automation, wildlife monitoring, etc. These IoT applications have specific requirements :

• low energy consumption for long battery-based autonomy;

• wide and deep coverage to connect devices throughout the country, including remote areas and adverse environments;

• device mobility handling;

• and capacity to connect up to thousands or even millions of devices per cell of typical surface of a few square kilometers.

These requirements must be met under a strong economic constraint for the deployment of the systems to be economically viable. The capital expenditure (CAPEX) must be low, the infrastructure cost must be reasonable and terminal devices must be very cheap. The operational expenditure (OPEX) must be low, i.e the network operation and maintenance must be low cost.

Legacy Wireless Technologies

Legacy wireless technologies such as Wireless Wide Area Network (WWAN) or WLAN do not meet these requirements for the vast majority of IoT applications.

Conventional WLAN, like 802.11, provides short range which is not suitable for many IoT usages as range is too short and power consumption too high [START_REF] Lee | A comparative study of wireless protocols: Bluetooth, UWB, ZigBee, and Wi-Fi[END_REF]. Range can be extended by increased transmit power and directional antenna which is impractical for mobile and battery powered IoT devices, not to mention radio spectrum regulation problems.

Conventional cellular WWAN cellular networks (EDGE, GPRS, GSM, LTE, NR, UMTS) provide long range connectivity and a quite good global coverage due to the already deployed infrastructure of

Low Power Area Networks (LPWAN)

LPWAN is a class of wireless networks that provide massive and very low cost connectivity for the IoT. The LPWAN paradigm has strongly gained momentum in the past few years. Many academic studies present the constraints, challenges and future tracks for the LPWAN, while describing and comparing existing technologies [START_REF] Sanchez | State of the art in LP-WAN solutions for industrial IoT services[END_REF][START_REF] Raza | Low power wide area networks: An overview[END_REF][START_REF] Ayoub | Internet of mobile things: Overview of lorawan, dash7, and nb-iot in lpwans standards and supported mobility[END_REF][START_REF] Bembe | A survey on low-power wide area networks for IoT applications[END_REF][START_REF] Mekki | A comparative study of LP-WAN technologies for large-scale IoT deployment[END_REF][START_REF] Foubert | Long-range wireless radio technologies: A survey[END_REF][START_REF] Gu | Survey of the low power wide area network technologies[END_REF]. We give here an overview of these issues based on these studies.

LPWAN Requirements

Following the mMTC requirements, LPWAN must be:

• Low power with battery-based autonomy in the order of a decade.

• Long range connectivity, at least in the order of a kilometer.

• Low cost with radio chips less than 5€ and connectivity less than 1€ by device and by year.

• Able to connect thousands of devices over area from "small" area of only few square kilometers to "large" area up to a hundred of kilometers square, with a single gateway.

To achieve such performance, LPWANs unleash other aspects:

• Low-throughput from few hundred kilobytes per seconds (kbps) and down to to few bytes per seconds.

• Delay tolerant with acceptable latency of a few seconds up to several hours.

• Strongly asymmetric with uplink oriented1 connectivity or even uplink only connectivity.

Such LPWAN fulfill the requirements for IoT applications with massive number objects that produce non-critical, sparse and sporadic data. This matches many IoT applications including smartmetering, smart-city, public or industrial asset monitoring, smart-farming, livestock or wild life monitoring, etc.

Levers For Long Range Low Power Communications

For a given digital modulation the Bit Error Rate (BER) at reception depends on the received energy per bit (E b ) to noise power spectral density (N 0 ) ratio:

E b N 0 = SNR × BW R b .
Therefore, the BER of a digital modulation follows a characteristic function P b :

P b E b N 0 = BER
We give in table1.1 P b functions of widely used modulations.

P b Q( E b N 0 ) Q( 2 E b N 0 ) ≈ 2 log 2 M Q( 2 E b N 0 log 2 M sin( π M )) ≈ Q( 2 E b N 0 )
We define the range of a wireless transmission as the maximal distance d max at which the link P b is good enough for correct demodulation, i.e. the BER is below BER max :

P b E b N 0 d max = BER max (1.11) With E b N 0 d max being the E b N 0 ratio at distance d max . E b
N 0 is the measure of SNR normalized to the amount of bits transported:

E b N 0 = SNR × BW DR net
Therefore:

E b N 0 = P Rx N 0 × DR net
It is fundamental to notice here that N 0 is a given of the system resulting from the electromagnetic environment, thus we cannot control it. This leaves the received power P Rx and the data rate DR net has the only controllable factors to change E b N 0 .

This brings up the 2 fundamental possibilities to increase the communication range: increase the P Rx or reduce DR net .

Increase P Rx

As detailed in section 1.1.1, P Rx is the transmitted output power P Tx amputated by the PL, expressed in dB:

P Rx = P Tx -P L
Thus, P Rx can be increased, either by increasing P Tx or by reducing PL.

Increasing P Tx

Increasing P Tx implies 2 problems: First it requires expensive high quality Power Amplifier (PA) to transmit with higher P Tx without distortion of the output signal. Thereby constant envelope modulation are favored to repel the distortion phenomenon as well as to reduce power consumption. Secondly, in practice the P Tx is restricted, if not by the PA quality, then either by the battery or by regulation.

Reducing Path Loss (PL)

The other way to increase P Rx is to reduce the PL. As detailed in section 1.1.1.2 the PL is dependent on the environment and its geometry on which we do not have control. The use for the terminal devices of high gain directional antennas as well as antenna offset for improved radio waves dissemination is impractical as it implies prohibitive deployment cost and excludes mobility. These techniques are however often used for gateways. The only parameter under control that affects the PL left is the wavelength of the carrier: using lower frequency improve the signal propagation. So, LPWANs using license free bands favor sub-GHz bands for this reason. However, the space in the low frequency bands is reduced and these bands with favorable properties are all the more popular and overused. Finally, the regulations restrict the use of these bands.

Reduce the Data Rate

The main other way to increase the communication range is therefore to reduce the data rate. This trade-off stems from the Shannon Equation (sec.1.1.1.1 eq.1.2).

DR net = BW × log 2 (1 + SNR)
However, the concern of LPWANs being to optimize not the DR net but the range, we must take the Shannon equation from another angle. First the minimal required E b N 0 can be expressed as a function of BW and DR net :

E b N 0 = (2 DR net BW -1) × BW DR net
Thus, another trade off appears clearly, the lower-bound for minimal required E b N 0 depends on the ratio DR net BW , i.e. the spectral efficiency. Therefore, as illustrated in figure 1.12, this lower bound for achievable minimal E b N 0 can be reduced at the expense of a reduced spectral efficiency.

-1.59 dB =    E b N 0   
Finally, relying on the E b N 0 definition, the Shannon equation can be re-written to express the lower bound on minimal required received power as a function of BW and DR net :

(P Rx ) req = (2 DR net BW -1) × BW × N 0 Figure 1.
13 plots the minimal required P Rx as a function of DR net for various BW between 10Hz and 10kHz. This emphasizes the core trade off for long range, yet low power, transmissions: data rate must be sacrificed in favor of sensitivity.

Every LPWAN technologies rely on this trade off, and employ various techniques that trade data rate for sensitivity [START_REF] Goursaud | Dedicated networks for IoT: PHY/MAC state of the art and challenges[END_REF][START_REF] Naik | LPWAN technologies for IoT systems: choice between ultra narrow band and spread spectrum[END_REF][START_REF] Roth | The Physical Layer of Low Power Wide Area Networks: Strategies, Information Theory's Limit and Existing Solutions[END_REF]. These techniques are mainly the use of a combination of: • Spread Spectrum: The DR net and spectral efficiency are reduced by spreading the narrow band signal over a larger BW which improves the received E b N 0 and thus reduces the required P Rx . The low spectral efficiency can be compensated by the use of codes that are orthogonal to each other, thus creating virtual subchannels, or with low auto-correlation coefficients to increase the capture effect.

• Transmission Redundancy: By introducing redundancy in the communication the acceptable BER max from equation 1.11 is lowered. Indeed, the error rate will be lowered by the redundancy. For instance, with the most straightforward simple blind systematic repetition, from a Packet Error Rate (PER) being PER = 1 -(1 -BER) packet_length , the effective Data Error Rate (DER) falls to DER = PER number_of_repetitions . Since the multiple transmissions are spread out over time, and can in addition be on different carriers. This benefits from diversity gain which improve the robustness against temporal and selective fading. Of course, for a fixed time on air the amount of application data is reduced, thus reducing the Applicative Data Rate (DR app ), the data rate available and usable at the application layer:

DR app = DR net
number_of_repetitions . Repetition can be seen as a way of increasing the overall energy to transmit each effective bit of data.

Majors LPWAN Technologies

The success of LPWANs is far from being confined to the academic world and industrial developments are also numerous. So much that the market is now fragmented between various technologies with technical and commercial choices, performances and compromises that sometimes vary and sometimes are quite similar. We provide in table 1.2 a technical overview of the main LPWAN technologies. However the overwhelming majority of the market, around 90% [START_REF]LPWAN Market Report[END_REF], is shared between 4 main players: NBIoT, LTE-M in the mobile operator licensed bands and SigFox and LoRaWAN in the sub-GHz industrial scientific and medical (ISM) bands. Keyword(s) "NBIoT" OR "NB-IoT" "LTE-M" "Sigfox" "LoRa " OR "LoRaWAN " Occurrences 406 26 33 12393

CHAPTER 1. CONTEXT

Chapter Conclusion

In this chapter we described the scientific foundation which will be the framework and the tools with which we will develop this thesis. In particular, this thesis focuses on the reliability of Lo-RaWAN networks, a LPWAN wireless network technology for IoT. The foundations laid down in this chapter give us both the levers and theoretical limits to achieve our goal of a reliable and scalable LoRaWAN link. In particular, the trade-off between throughput and robustness is the keystone of LPWAN technologies and we will use channel coding to further enhance LoRaWAN's robustness. And thus the DR mod is:

DR mod = SF × BW 2 SF
In the current LoRa implementations, SF 5 to 12 are available [167]. Over the same BW, SFs are quasi-orthogonal to each others. So, a GW can simultaneously receive multiple LoRa frames with different SF, which greatly improve the network capacity.

Synchronization

However, chirp symbol demodulation is sensible to frequency offset between the transceivers [START_REF] Bernier | Low complexity LoRa frame synchronization for ultra-low power software-defined radios[END_REF]. LoRa modulation tackles this by starting the frames with both a preamble an a synchronization word (SyncWord).

The preamble is a series of unmodulated up-chirps (typically 8). It triggers the receiver demodulation.

The SyncWord is composed of two modulated identical up-chirps and two and a quarter downchirps. The SyncWord is used to identify the network, to mark the frame start and more importantly to synchronize the clocks of the transceivers. This allows to correct the frequency offset the transceiver. However, the frequency references of the transceivers may drift, causing synchronization loose. LoRa compensate with the low data rate optimization, an undocumented feature, which slightly reduce the data rate and is mandatory for SF ≥ 10. LoRa initial synchronization compensates the use of low precision cheap hardware by making the modulation robust against Doppler effect and frequency drift.

LoRa intra-frame Error Correction Code (ECC)

The inherently robust CSS modulation scheme is complemented by an intra-frame ECC with CR ∈ { 4 5 , 4 6 , 4 7 , 4 8 } based on Hamming coding. The extra redundancy improves the robustness of the transmission at the expense of the DR ph y . The data rate delivered by the physical layer depends on the SF, the BW and the CR2 :

DR ph y ≈ CR × SF × BW 2 SF
Based on this modulation, LoRa provides very high link budget of up to 153.5 dB3 .

Frame Structure

A LoRa frame is composed as follow: First the preamble and the Syncword detailed previously, then an optional physical LoRa header with its own CRC, followed by the physical LoRa payload and its CRC.

The LoRa header and its CRC are encoded respectively over 15 and 5 bits and are protected by ECC with CR = 4 8 . The content of the LoRa header is not precisely described publicly and contains information such as the payload size, the frame CR or the presence or not of a payload CRC. This explicit header can be removed if theses parameters are fixed. The physical payload size is restricted to 256 bytes, and its data integrity might be protected by a 2

LoRaWAN Data Link Layer

LoRaWAN is a strongly uplink oriented protocol. The traffic pattern is expected to be typically sparse and sporadic data from the EDs to the ASs. It is the mass of connected objects that will make the data flow massive at the GWs. However, LoRaWAN also provides downlink capabilities which is a fundamental feature, not only to allow the sending of application data to the EDs, but also allows firmware update over-the-air, uplink traffic acknowledgement (ACK) and sending service commands in order to administer the network and tune its parameters.

Channel Access Algorithm

As LoRaWAN is strongly uplink oriented, different channel access algorithms are defined for the uplink and downlink channels.

Channel Access for the Uplink Channel

LoRaWAN channel access algorithm to transmit uplink frames is Pure-Aloha: every ED transmits at any time whenever data is available without any kind of coordination in a totally asynchronous manner [3]. Limitations of LoRaWAN in terms of capacity and effective throughput are inherent to ALOHA access [START_REF] Adelantado | Understanding the limits of LoRaWAN[END_REF][START_REF] Georgiou | Low power wide area network analysis: Can LoRa scale?[END_REF].

A typical LoRaWAN network operates with multiple CFs: a new CF is randomly chosen for every uplink frame, which mitigates the effect of selective fading. An uplink frame can be sent with various DR mod which is defined jointly by the BW and the SF. Even though more BW and SF might be available depending on the hardware, three BW are available BW ∈ {125, 250, 500}kHz and the SF is restricted to SF 7 to SF 12.

Channel Access for the Downlink Channel

LoRaWAN defines three classes of device with different downlink capabilities: class A (All endevices), class B (Beacon) and class C (Continuously listening).

Class A: EDs listen for a potential incoming downlink frame solely after sending an uplink frame. Each uplink is followed by two short receive window (Rx1 and Rx2) slightly shifted in time as illustrated in figure 2.7. Rx1 is on the same channel (CF and BW) as the uplink frame and with a SF that between an ED and the AS and thus benefits from any additional error recovery mechanisms that are non-native to LoRaWAN.

Error Recovery Mechanisms

LoRaWAN implements two basics mechanisms at the data link layer to provide reliability for the uplink:

• Blind Systematic Repetition (BSR) Uplink frames are systematically repeated a given number of times, which mechanically increases the probability that at least one of the transmissions is received. The number of transmissions parameter being Nb Trans ∈ [1 : 15], from a given FER, the PER drops to PER = (FER) Nb Trans . However it is obvious that as BSR multiplies the Time-On-Air (TOA) and thus the uplink channel load. It must be used sparingly and with care to avoid network congestion. Overuse of BSR could cause collision rate to increases drastically, undermining the reliability goal.

• Confirmed Uplink: Uplink frames are marked as requesting an ACK from the NS and are retransmitted until either an ACK is received or the maximal number of attempt is reached. Each retransmission is done over a new CF, and can be done with another DR mod . Indeed, in case of successive failures, it is recommended that the EDs reduce the DR mod to increase the communication robustness and range. The default strategy recommended by the Lo-RaWAN specification consists in reducing the DR mod by one notch (i.e. generally increment the SF of 1) every 2 consecutive failures. However, because of the limited downlink traffic capacity detailed further in 2.3.1.2 and 2.2.3, ensuring reliable uplink traffic handling by means of Automatic Repeat reQuest (ARQ) or any kind of feedback is challenging due to the very restricted downlink capabilities [START_REF] Adelantado | Understanding the limits of LoRaWAN[END_REF][START_REF] Pop | Does bidirectional traffic do more harm than good in LoRaWAN based LPWA networks?[END_REF], even though improvements are possible [START_REF] Di | Improving Downlink Scalability in LoRaWAN[END_REF].

In the following of the thesis, as we are going to manipulate a lot the notions of data loss at different levels of the communication, we define here the units will use:

• The Frame Erasure Rate (FER) is the physical loss ratio between an ED and a given GW (i.e. without duplicate transmission from LoRaWAN BSR).

• The Packet Error Rate (PER) is the loss ratio between an ED and the NS. PER benefits from multiple GWs reception and frame duplicated transmissions from BSR.

• The Data Error Rate (DER) is the loss ratio between an ED and the AS, thus benefiting from the presence of any additional erasure recovery mechanism.

Notice depending on the layout, they might be equivalent. For instance in the case of a mono-GW cell and with Nb Trans =1, FER is equal to PER. Also, if no additional erasure recovery mechanism is used, PER is equal to DER.

LoRaWAN Fundamental Trade-off: Range for Time-On-Air (TOA)

The LoRaWAN parameters BW, SF, CR and Nb Trans can be tuned to increase the link robustness at the expense of the DR app . Or in others words the range can be improved at the expense of increased TOA. For instance, each SF increments roughly divide the DR ph y by half but reduce the required SNR by 2.5dB. DR ph y ranges from 183bps to 62.5kbps for SF, BW, CR respectively 12, 125kHz and 4 8 , and respectively 5, 500kHz and 4 5 . Similarly, the minimal required SNR range from approximately -2.5dB to -20dB for respectively SF = 5 and SF = 12. Also, Nb Trans reduces the DER at the expense of a TOA multiplied by Nb Trans .

This trade-off is fundamental in LoRaWAN as it offers a wide panel of performances in terms of TOA and range. And, as detailed in sec.3.2.1, both the network reliability and capacity depends on the channel load, thus on the TOA of each ED. Notice that as it is also the main energy consumption of the LoRaWAN algorithm, and thus reducing the TOA is also a gain for ED battery lifetime.

We define the

MAC Commands

MAC commands are standardized commands that are piggybacked in the LoRaWAN headers and transparent for the application. MAC commands exist in both uplink and downlink frames and are used for fundamental network administration operations such as adapt the uplink transmission parameters (P Tx , SF, Nb Trans ), check connectivity, add or delete additional channels, modify Rx receive delay or configuration, ping period for class B devices, etc.

The MAC commands allow LoRaWAN to implement one of its key features: the adaptive data rate (ADR). The ADR is an automatic and dynamic tuning of the uplink transmission parameters to adapt to the network and link conditions. The ADR is detailed below in section 2.3.6.

Adaptive Data Rate (ADR)

The ADR is a mechanism part of LoRaWAN to adapt the EDs transmission parameters over-theair. As described in sec.3.2, the ADR is key in LoRaWAN due to the wide TOA for range tradeoff described in 2.3.4.

With the ADR, the NS estimates the link quality by monitoring the uplink frames metadata and it adapts periodically the ED transmission parameters via MAC commands sent in its rare downlink communication opportunities with the ED. If no downlink frame is received for too long, the ED decreases its DR ph y (increases its P Tx and its SF) to try to regain connectivity. No ADR algorithm is strictly defined in the standard, however some indications and recommended behavior are described. The ADR-ED and ADR-NS algorithms appear respectively in algorithm 1 with Semtech's implementation 5 for the ED side and Algorithm 2 from The Things Network6 (TTN) for the NS side.

Algorithm 1 ADR-ED algorithm. ACK_CNT ++;

25:

end if 26: end while This protocol addresses the following three questions by adjusting its internal parameters:

• How frequently does the ED require a downlink from the NS? ACK_LIMIT and ACK_DELAY bound the acceptable number of consecutive uplinks without an ACK reception. The default recommended values are ACK_LIMIT=64 and ACK_DELAY=32 transmissions.

• How does the NS estimate link quality? ADR TTN takes the SNR maximal value from the last twenty received packets. Even if this maximal value tends to over-evaluate the channel SNR, it is less dependent on the PER than the average, because one expects that the transmissions facing more attenuation are more likely to be missed. Note that this estimation does not take into account the reception by multiple GWs, and neither BSR 7 , both of which tend to increase the estimated SNR.

• How conservative should the transmissions parameters selection by the NS be? The MAR-GIN parameter biases the algorithm towards more robust transmission, at the expense of channel occupancy. The default value is 15dB.

Algorithm 2 ADR-NS algorithm.

Chapter Conclusion

In this chapter we have seen how the LoRaWAN technology works.

LoRaWAN shared channel access method based on non-slotted Aloha is the lightest for the EDs. But with such an access method the frame collision rate increases quickly with the channel load. This can jeopardize the scalability of the network if poorly taken into account.

LoRaWAN provides two reliability mechanisms to handle packet losses, confirmed traffic and BSR. Both are very basic and particularly expensive for the network. None of them can actually provide reliability in LoRaWAN without heavily impacting the network's scalability.

LoRaWAN provides a very wide range of throughput through its SF, CR and Nb Trans parameters. The highest data rate setting is about two orders of magnitude higher than the lowest data rate setting (even before touching the BW parameter). This wide range of available data rates gives amplitude to set the best data rate versus robustness trade-off.

LoRaWAN's ADR algorithm is a keystone of this technology. Its role is to automate the adjustment of the data rate versus robustness trade off in order to use the full potential of LoRaWAN. The optimization of the ADR is therefore fundamental to improve LoRaWAN, especially its reliability and scalability.

Chapter 3

State of the Art

Chapter Introduction

In this chapter we lay down the state of the art on LoRaWAN. Although the technology is only a decade old, LoRaWAN has draw the attention of the scientific community and publications about it number in the thousands. It is not possible for us to make a complete and exhaustive review of all of this work and this is not the point of the chapter of this thesis. We strive to do a commented review of the main works as well as the works that have influenced us and on which we have taken support.

In section 3.1 we review the state of the art of the LoRaWAN link characterization with on the one hand the analytical studies on LoRa modulation and on the other hand the studies based on experimental measurements. In section 3.2 we review studies on the scalability and reliability of LoRaWAN networks. In section 3.3 we present and discuss the few works proposing and testing CP-ECC in LoRaWAN.

LoRaWAN Link Characterization

Driven by academic and industrial success, many studies have been carried out to understand the performance of LoRaWAN networks. To characterize LoRaWAN performances, especially in terms of range, it is first necessary to precisely characterize its physical layer LoRa. Then, to finish characterizing the performance of the network, with reliability and scaling up, it is necessary to understand the link layer, in particular with its channel access algorithm (upstream and downstream) and its link layer reliability mechanisms. In this section we proceed in this order to present the state of the art of the LoRaWAN link characterization.

Two approaches are possible to characterize the performance of a network physical layer. The first option is to study analytically the modulation performance then potentially simulate the result over a given channel model to estimate the performance of the real link. The other option is to directly test and measure the link into a real deployment.

LoRa Modulation Analytical and Simulation Studies

Based on result of MATLAB simulation with an implementation of a CSS-decoder and on the MAT-LAB curve fitting tool, an analytical closed form of the CSS modulation Bit Error Rate (BER) under AWGN has been proposed [START_REF] Reynders | Range and coexistence analysis of long range unlicensed communication[END_REF]:

BER Reynders&Al. = Q log 12 (SF) 2 × E b N 0 (3.1)
Through the simulations, the robustness of LoRa symbols against other types of interference such as continuous wave or a concurrent LoRa symbol is also studied.

From the mathematical description of the LoRa modulation and simulation another projection of the BER CSS modulation as a function of the SNR has been computed [START_REF] Vangelista | Frequency shift chirp modulation: The LoRa modulation[END_REF]. Through simulation the LoRa modulation is compared with FSK modulation with equivalent cardinal under AWGN or frequency selective channel.

From this mathematical description of the LoRa modulation [START_REF] Vangelista | Frequency shift chirp modulation: The LoRa modulation[END_REF], another analytical study derived closed-forms approximation of LoRa BER performance in AWGN [START_REF] Elshabrawy | Evaluation of the BER Performance of LoRa Communication using BICM Decoding[END_REF]. In particular this ex-pression is given:

BER Elshabrawy&Al. = 0.5 ×Q      SNR × 2 SF -(H 2 SF -1 ) 2 -π 2 12 1 4 H 2 SF -1 -(H 2 SF -1 ) 2 -π 2 12 1 2 + 0.5      (3.2)
In figure 3.1 we compare the result from these three studies. We plot both the results for the BER and for the FER with 10 bytes long frames. The earliest study (Reynders & Al. [START_REF] Reynders | Range and coexistence analysis of long range unlicensed communication[END_REF]) is more pessimist than the following two (Vangelist [START_REF] Vangelista | Frequency shift chirp modulation: The LoRa modulation[END_REF] and Elshabrawy & Al. [START_REF] Elshabrawy | Evaluation of the BER Performance of LoRa Communication using BICM Decoding[END_REF]). However these studies do not take into account neither frame imperfect synchronization at demodulation nor LoRa ECC at physical layer. A study based on the approximation of equation 3.2 proposes a formulation of the coded LoRa BER thus taking into account LoRaCR [START_REF] Afisiadis | Coded LoRa Frame Error Rate Analysis[END_REF]. However, the full correction capacity of LoRa physical layer ECC is not taken into account as it is considered that only CR ∈ { 4 7 , 4 8 correct an error. It is true for hard-decoding but not with soft-decoding. Not to profit from the inherent information available at demodulation to improve error correction with soft decoding would be a kind of waste. Our experimental results exposed in section 4.3 show that there is a gain between each CR, advocating that soft-decoding is used in LoRa demodulation. Therefore, the BER of coded LoRa might be over estimated in this study.

• • • • 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 -2 8 -2 6 -2 4 -2 2 -2 0 -1 8 -1 6 -1 4 -1 2 -1 0 -8 -6 -4 -2 BER • • • • 10 -5
Another study based on the approximation of equation 3.1 proposes a formulation of the coded LoRa BER [START_REF] Park | EARN: Enhanced ADR with coding rate adaptation in LoRaWAN[END_REF]. However, two fundamental errors are made, although they might partially compensate each other. First, the correction capability of the LoRa physical ECC is once again con-sidered for hard-decoding only with no correction capability for CR ∈ { 4 5 , 4 6 } and a single bit in error correction capability for CR ∈ { 4 7 , 4 8 }. This underestimates the correction capability of LoRa ECC. Secondly, the ECC gain from LoRa physical layer ECC is already taken into account in the E b N 0 computation, and thus in the computation of the BER. Thus LoRa physical layer ECC gains are accounted twice, which over estimate the correction capability of LoRa ECC. One should either approximate the redundant bits as extra energy injected into the transmission, or count them as bits of the payload, which in a second time are used for error correction by the next sub-layer.

The impact of imperfect synchronization has been demonstrated and as a consequence the role of the frame synchronization algorithm [START_REF] Bernier | Low complexity LoRa frame synchronization for ultra-low power software-defined radios[END_REF]. The LoRa synchronization algorithm being based on the reception of SyncWord, the number of preamble symbols which prepares its detection is therefore also important. It has been shown by simulation and measurements that the number of preamble symbols should be ≥ 6 and beyond this point the gain is marginal.

LoRa Experimental Measurements

However, frame receptions on the field is widely impacted by many environmental factors which can hardly be modeled and taken into account without studying and measuring the LoRa link deployed in real conditions. Thanks to the academic success and ease of deployment of a LoRaWAN network, many experimental measurements are reported in the literature and provides a wide panel of insight on the LoRa channel characterization.

Interference and usage of the 868 ISM band:

The monitoring of the 868MHz ISM radio band in a medium sized city in Denmark at street level [START_REF] Lauridsen | Interference measurements in the European 868 MHz ISM band with focus on LoRa and SigFox[END_REF] gives insight into the interference LoRa may face. It shows that a LoRa channel may experience highly heterogeneous interference patterns, both in periodicity and strength of the colliding signals, even within close distances. Also, we know from an early extensive study of the meta-data of the public TTN network [START_REF] Blenn | LoRaWAN in the wild: Measurements from the things network[END_REF] that the network usage might be highly unbalanced: an overwhelming majority of devices uses SF7 whereas SF12 is the second most used, the 868.1 MHz sub-channel is over-used compared to the others two standards sub-channels (868.3 and 868.5 MHz) and the non-standard sub-channels are almost unused.

The highly heterogeneous interference patterns and the unbalanced network usage emphasize the need for an automatic, dynamic and efficient parameter selection mechanism in LoRaWAN.

LoRa frames collisions:

The results of an analytical study [START_REF] Croce | Impact of LoRa imperfect orthogonality: Analysis of link-level performance[END_REF] corroborated both by simulation and by experimentation showed on the one hand that the capture effect in case of co-SF collision is underestimated -indeed a Signal-to-Interferer (SIR) of 1dB is sufficient for correct reception if the reference signal is correctly synchronized -and in the other hand that the capture effect in case of inter-SF collision is overestimated compared to previous study [START_REF] Goursaud | Dedicated networks for IoT: PHY/MAC state of the art and challenges[END_REF]. These worse SIR thresholds for correct reception in case of inter-SF collision question the approximation of orthogonality between differents SF in LoRa. However, it should be noted that the collisions conditions are rather unfavorable compared to the probable real cases: it is considered equal emission times whatever the SF. It is improbable that different SF frames will have the same broadcast time. For instance, there is a 24 factor between the emission times of an equivalent payload with SF 7 and 12. Finally, this study underlines the strength of LoRa's ECC associated with interleaving and Gray coding which is efficient to correct errors due to mis-synchronization or narrow-band interference.

Another experimental study of LoRa collisions [START_REF] Rahmadhani | When lorawan frames collide[END_REF] shows the impact of arrival time offset between co-SF colliding frames received by a single channel and single demodulation path receiver (LoRa SX1276 module). The receiver is locked on the incoming frame after 4 preamble symbols. Once the receiver is locked, the colliding signal appear as noise. Also the receiver might release the lock if the header CRC is invalid, thus allowing for immediate reception of another frame without waiting for the end of the failed transmission. As the reception is more vulnerable at these times, a stronger colliding frame is likely to benefit from the capture effect if its preamble arrive a these moments.

LoRa range and PL characterization:

It is to be noticed that thanks to its long range and to its adaptability (i.e. the data rate versus range trade-off), LoRa can fit a wide panel of applications and might be deployed in a large variety of environment. It is reflected in the literature, LoRa has been experimented in different outdoor contexts : over sea [START_REF] Petajajarvi | On the coverage of LPWANs: range evaluation and channel attenuation model for LoRa technology[END_REF], in rural areas [START_REF] Aref | Free-Space Range Measurements with Semtech LoRa Technologie[END_REF], in forests [START_REF] Rathod | Performance analysis of wireless devices for a campus-wide IoT network[END_REF][START_REF] Callebaut | Characterization of LoRa Point-to-Point Path-Loss: Measurement Campaigns and Modeling Considering Censored Data[END_REF], in farms [START_REF] Yim | An experimental LoRa performance evaluation in tree farm[END_REF], in various cities [START_REF] Petrić | Measurements, performance and analysis of LoRa FABIAN, a real-world implementation of LPWAN[END_REF][START_REF] Madoune R Seye | An evaluation of LoRa coverage in Dakar Peninsula[END_REF][START_REF] Vatcharatiansakul | Experimental performance evaluation of LoRaWAN: A case study in Bangkok[END_REF][START_REF] Ameloot | A Compact Low-Power LoRa IoT Sensor Node with Extended Dynamic Range for Channel Measurements[END_REF][START_REF] Attia | Experimental Characterization of LoRaWAN Link Quality[END_REF][START_REF] Chall | LoRaWAN network: Radio propagation models and performance evaluation in various environments in Lebanon[END_REF][START_REF] Jansen C Liando | Known and unknown facts of LoRa : Experiences from a large-scale measurement study[END_REF][START_REF] Dieng | Comparing and Adapting Propagation Models for LoRa Networks[END_REF] and even in Antarctica [START_REF] Gaelens | LoRa mobile-tobase-station channel characterization in the Antarctic[END_REF]. Experimental measurements of LoRa can also be found for indoor deployment, for instance in universities [START_REF] Petäjäjärvi | Evaluation of LoRa LPWAN technology for remote health and wellbeing monitoring[END_REF][START_REF] Cattani | An experimental evaluation of the reliability of lora long-range low-power wireless communication[END_REF], office [START_REF] Ameloot | Indoor Body-to-Body LoRa Link Characterization[END_REF], residential [START_REF] Xu | Measurement, Characterization and Modeling of LoRa Technology in Multi-floor Buildings[END_REF] or industrial [START_REF] Haxhibeqiri | LoRa indoor coverage and performance in an industrial environment: Case study[END_REF] buildings and even historic underground monuments [START_REF] Abrardo | A Multi-Hop LoRa Linear Sensor Network for the Monitoring of Underground Environments: The Case of the Medieval Aqueducts in Siena, Italy[END_REF].

As expected with such heterogeneous deployments, the LoRa channel characterizations are also heterogeneous. For instance, empirical path loss exponent reported in the literature range from 0.79 in a empty hallway which gives a wave-guiding effect [START_REF] Ameloot | Indoor Body-to-Body LoRa Link Characterization[END_REF], up to 8.4 in a car park with no line of sight [START_REF] Xu | Measurement, Characterization and Modeling of LoRa Technology in Multi-floor Buildings[END_REF]. The heterogeneity of LoRa channel characterization emphasizes the need for an automatic, dynamic and efficient parameter selection mechanism in LoRaWAN. Also, as pointed in Sec.3.1.3, the LoRa channel characterization is still an ongoing work. Outdoor (with mobility, urban and over sea) + indoor (with mobility) Same as [START_REF] Petajajarvi | On the coverage of LPWANs: range evaluation and channel attenuation model for LoRa technology[END_REF]. See above.

Doppler effect starts to degrade LoRa reception around :

• 38km/h for SF12 • 76km/h for SF11 • 155km/h for SF10 [96] Characterization [START_REF] Blenn | LoRaWAN in the wild: Measurements from the things network[END_REF] NA (Public TTN network) NA

• ∆ (SNR max -SNR min ) ≈ 14dB
Analysis of network meta-data:

• Many EDs send less than 50 packets in their lifetime.

• Very few EDs send more than 1000 packets in their lifetime.

• A majority of devices are close to GWs.

• Most payloads are small (93.7% are <50bytes, 50% <19bytes). • CF=868.1MHz sub-channel is highly overused.

• Most devices use SF7 BW=125kHz.

Notice that it is an early study (data-set from 2015-2016), the network usage was not necessarily mature yet.

[103] Outdoor + indoor <NA;NA;NA;NA;NA> (433MHz ISM band)

• 2km (outdoor) • 120m (indoor) • ∆ (SNR max -SNR min ) outdoor ≈ 5dB • ∆ (SNR max -SNR min ) indoor ≈ 10dB [93]
Outdoor (LOS and NLOS with dense vegetation) <6; Log-distance path loss model with log-normal shadowing:

• Off-LOS γ = 2.2, σ = 5. • Off-OBS γ = 2.4, σ = 5.2.
• Off-NLOS γ = 6.0, σ = 5.9.

• Res-LOS γ = 2.3, σ = 4.9.

• Res-OBS γ = 2.0, σ = 4.6.

• Res-NLOS γ = 5.6, σ = 5.0.

• Car-LOS γ = 1.5, σ = 4.7.

• Car-OBS γ = 1.9, σ = 4.6.

• Car-NLOS γ = 8.4, σ = 5.3.

• War-LOS γ = 1.7, σ = 5.2.

• War-OBS γ = 1.7, σ = 5.1.

• War-NLOS γ = 3.8, σ = 5.5.

Attenuation factor (dB): 1 floor=21.7, 2 floors=25.9, 3 floors=27.2, 4 floors=50.8, Concrete wall=2.2, glass=2.0, wooden door=2.1, soft partition board=2.5. Temporal Fading (TF):

• TF dynamic range is typically about 8dB and occasionally up to 17dB in LOS scenario, and typically 20dB in OBS scenario. • Presence of people in the building highly increases TF.

• TF follows Rician distribution with K-factor (Kf): The coastal experimental data set is likely to be corrupted by handheld device-based experimental campaign.

-Kf Off-LOS = 18.9 -Kf Off-OBS = 12.1 -Kf Res-LOS = 18
Model fitting of the experimental data take into account censored data. The distribution is assumed to be a censored normal distribution.

[121] Outdoor GWs with indoor ED (urban) <11; 4 5 ;125;NA;14> • 18.3km

• Slow Rayleigh channel.

• Only slight impact of payload length on reception rate. RSSI (moving average) variation at fixed distance ≈ 25dBm.

[144] Outdoor (rainforest) <12; 4 5 ;500;NA;14> • 250m

• Dense forest is a very challenging environment for LoRa communication. • Signal is subject to strong variations even in a static experiment, which produce link disruptions. • Small variations of speed at low speed (≤ 12km/h) do not impact

Discussion

The wide availability of LoRa hardware (EDs and GWs) have allowed many researchers and network operators to assess the benefits brought by the technology. One of the focus point of LPWAN is coverage, so a large fraction of the reports look into the PER and P Rx at various distances.

In many cases, though, the authors neglect the fact that the collected data is inherently distorted.

In other cases, authors either simply disregard the specifics of their data collection process or expect the wrong distribution for their data.

Problems of biased experimental data-sets

Losses when P Rx is low

Many studies propose to model large-scale LoRa propagation by fitting well-known models on newly gathered experimental data (the models are typically the log-distance path loss with lognormal shadowing). Unfortunately, in many papers, the authors do not take into account the bias which stems from the fact that only successfully received frames provide a channel gain measure [START_REF] Aref | Free-Space Range Measurements with Semtech LoRa Technologie[END_REF][START_REF] Petajajarvi | On the coverage of LPWANs: range evaluation and channel attenuation model for LoRa technology[END_REF][START_REF] Rathod | Performance analysis of wireless devices for a campus-wide IoT network[END_REF][START_REF] Petrić | Measurements, performance and analysis of LoRa FABIAN, a real-world implementation of LPWAN[END_REF][START_REF] Gaelens | LoRa mobile-tobase-station channel characterization in the Antarctic[END_REF]96,[START_REF] Chall | LoRaWAN network: Radio propagation models and performance evaluation in various environments in Lebanon[END_REF][START_REF] Dieng | Comparing and Adapting Propagation Models for LoRa Networks[END_REF]. Indeed, a frame loss is at least partially dependent on the P Rx for that frame. So, lost frames tend to be the ones arriving at the GW with the lowest P Rx when it is variable, which is often the case in the studies and most probably due to SSF. Consequently, any experimental data-set featuring a significant PER is likely to be truncated, with an underrepresentation of low P Rx values. This effect becomes more salient for the measurements at the coverage edge, where only a fraction of the frames are received. In this case the data-set is not representative of the full P Rx distribution, but only of the upper fraction of the distribution. We illustrate the phenomenon with figures extracted from various studies in Fig. 3.2.

Not taking into account the partial nature of the data potentially biases the model fit for the LSF (i.e. the path loss exponent estimation) by underestimating it. Potentially, it also biases ShF and SSF by making the P Rx distribution look different from what it is (for instance log-normal instead of exponential) and under-estimating the associated variability (i.e. the standard deviation).

Nevertheless, not all real-world studies disregard this bias [START_REF] Attia | Experimental Characterization of LoRaWAN Link Quality[END_REF][START_REF] Callebaut | Characterization of LoRa Point-to-Point Path-Loss: Measurement Campaigns and Modeling Considering Censored Data[END_REF][START_REF] Coutaud | Adaptive Data Rate for Multiple Gateways LoRaWAN Networks[END_REF][START_REF] Coutaud | High Reliability in Lo-RaWAN[END_REF][START_REF] Coutaud | LoRa Channel Characterization for Flexible and High Reliability Adaptive Data Rate in Multiple Gateways Networks[END_REF]. Also some studies do not provides enough information about the PER in their experimental dataset and it is not possible to evaluate whether their conclusions are biased or not [START_REF] Benaissa | Internet of animals: characterisation of LoRa sub-GHz off-body wireless channel in dairy barns[END_REF][START_REF] Hosseinzadeh | Empirical propagation performance evaluation of LoRa for indoor environment[END_REF][START_REF] Ameloot | A Compact Low-Power LoRa IoT Sensor Node with Extended Dynamic Range for Channel Measurements[END_REF][START_REF] Van Torre | Long-range body-to-body LoRa link at 868 MHz[END_REF][START_REF] Xu | Measurement, Characterization and Modeling of LoRa Technology in Multi-floor Buildings[END_REF].

High P Rx corruption:

The opposite phenomenon might happen. As measured and characterized in a experimental work [START_REF] Ameloot | A Compact Low-Power LoRa IoT Sensor Node with Extended Dynamic Range for Channel Measurements[END_REF], the LoRa receiver can saturate, and the reported P Rx has also a ceiling. For instance, the SX1276 chipset SNR measurement saturates slightly above 5dB. Thus measurements from deployment with EDs and GWs close to each other would require measurement equipment with a specific dynamic range [START_REF] Ameloot | A Compact Low-Power LoRa IoT Sensor Node with Extended Dynamic Range for Channel Measurements[END_REF] to be accurate.

Thus many conclusions or reports on LoRa channel characterization must be considered with caution. Also, only a few experimental studies propose a model for LoRa channel characterization and moreover most mainly focus on LoRa LSF for maximal range estimation. Thus ShF and SSF are often poorly described and analyzed. So, the extensive understanding and accurate modeling of the LoRa channel is still an ongoing work.

Other mistakes

Experimental measurements collection with a filtering NS Some NS do not provide the full meta-data of the transmission. Specifically, some NS do not give the full list of GWs that received a specific frame, but only a subset of the GWs. It is a case in an experimental study where the NS only provide the list of the 3 GWs with the best Received Signal Strength Indication (RSSI) for each received frame [96]. This completely skews the data-set, it is impossible to distinguish the real losses due to too low P Rx from the false negatives produced by NS filtering. The filtering introduces a major bias: with just 4 GWs up to 25% of the data can be false negatives, with 6 GWs potentially half of the data set can be censored. No information on the number of GWs in the experiment is given and it is therefore not possible to estimate the bias order of magnitude. We are convinced that attempting to mitigate this bias is ineffective. Indeed, the displayed PL standard deviation is high (σ = 7.1) which implies the subset of the "best 3 GWs " is likely to be highly unstable. This study is, to the extent of our knowledge, the only one in which this specific bias is clearly apparent, but its conclusions on the characterization of the channel are nevertheless widely cited in the literature.

It cannot be ruled out that similar biases exist imperceptibly in the rest of the literature. For instance, we identified a risk during our experiments via the The Things Network (TTN) network: whenever a frame is received by multiple GWs, if one of them has a high latency on the backbone network, the packet might be filtered out by the NS. Indeed it might appear as a BSR duplicate to be filtered out because of its sequence number. This phenomenon can easily go unnoticed but ultimately might represents a significant number of false negatives. To avoid this, it is necessary to deactivate the frame counter check.

Signal envelope is not P Rx

Several studies conclude that their experimental LoRa channel is Rician because the distribution of P Rx seems to correspond to a Rician distribution [START_REF] Benaissa | Internet of animals: characterisation of LoRa sub-GHz off-body wireless channel in dairy barns[END_REF][START_REF] Xu | Measurement, Characterization and Modeling of LoRa Technology in Multi-floor Buildings[END_REF]. But it is not the distribution of the P Rx which is supposed to follow a Rician distribution with such a channel: it is the signal envelope. Likewise, the distribution of the powers received on a Rayleigh channel does not follow a Rayleigh distribution but rather an exponential distribution. Which remotely looks Rayleigh when the power is expressed in dB. The difference is fundamental and is particularly well explained in the literature [START_REF] Goldsmith | Wireless communications[END_REF] (Sec.3.2.2 Envelope and Power Distributions). Consequently, these characterizations should no be considered.

Capacity, Quality of Service and Configuration of LoRaWAN

Network "performance" may cover different meanings. Capacity, that is roughly defined as the maximum number of EDs connected and served by the network, is the most common assessed and optimized performance in the literature on LoRaWAN, then comes reliability and to a lesser extent energy consumption.

Whatever the performance metric of interest, it is trivial to say that it depends on the physical layer, the protocol stack built on top of it, i.e. the channel access algorithm, the use of reliability mechanisms at the Data Link Layer such as confirmed traffic, channel coding... It is also trivial to say that it depends the deployment characteristics, i.e. the channel load (number of nodes, frames TOA, and transmission frequency), the span of the cell, etc. In addition, for LoRaWAN which benefits from a physical layer offering a wide robustness against TOA trade off, the choice of network parameterization is of major importance for the performance. First in sec. 3.2.1 we describe and comment the state of the art on LoRaWAN capacity, i.e. the performance achievable by a network configured optimally apriori and therefore statically. Then in sec.3.2.2 we describe and comment the state of the art of dynamic configuration of the LoRaWAN transmission parameters, i.e. the LoRaWAN ADR algorithm.

Capacity

The LoRaWAN capacity has been a subject of interest and discussion since its early emergence. Many studies, analytical or by simulations, evaluate the number of EDs that can fit in a LoRaWAN network, and the consequent DER. Some works suggest to modify the LoRaWAN channel access algorithm [START_REF] Pham | Towards quality of service for long-range IoT in unlicensed radio spectrum[END_REF][START_REF] To | Simulation of LoRa in ns-3: Improving LoRa performance with csma[END_REF][START_REF] Polonelli | Slotted aloha on lorawan-design, analysis, and deployment[END_REF][START_REF] Kouvelas | p-CARMA: Politely Scaling LoRaWAN[END_REF], or the network topology [START_REF] Ochoa | Evaluating LoRa energy efficiency for adaptive networks: From star to mesh topologies[END_REF], but it does push more complexity to the EDs. In this thesis we focus on the capacity and optimization of the existing LoRaWAN protocol, with its Aloha based channel access algorithm.

The fundamental of the LoRaWAN capacity is the Aloha based channel access algorithm: as the traffic on the network (the channel load) intensifies, each transmission has higher collision probability and faces more interference. Thus the network reliability decreases as the channel load increases and the network tends to saturate. As a consequence, the discussion on the LoRaWAN capacity is about how fast the reliability decreases or at which point the network will saturate and how can this point be pushed further to handle more device with the same infrastructure.

Impact of external factors on LoRaWAN capacity

We call external factors elements not controlled by the network but rather the ones it has to deal with, for instance the span of the cell, the traffic intensity (number of nodes, frames TOA, and transmission frequency), the link properties (PL, ShF, SSF), the duty cycle, GWs hardware, number of GWs, etc... Even though these factors are not controlled by the protocol, they do impact the capacity of the network. Various studies with highly different models result in quite different conclusions about the LoRaWAN capacity. We think this is a reflection of the heterogeneity of the possible deployments of LoRaWAN networks. Also, this variety of studies allows to sketch some elements of understanding about the impact of theses external factors on the LoRaWAN capacity. So, the discussion on capacity with regard to the external factors is mainly how a given external factor impact LoRaWAN capacity and if the model is relevant and corresponds to a credible situation.

An early simulation study [START_REF] Martin C Bor | Do LoRa low-power widearea networks scale?[END_REF] of the FER as a function of the number of EDs found with its "default" configuration -which consists in using only the most robust configuration and therefore the most TOA expensive -that a LoRaWAN cell with a single GW can only handle 120 EDs with FER ≤ 10%, which is far from the expected and required capacity. This study also highlights the major importance of the capture effect as the simulation with capture effect shows a FER reduction up to 40 point of percent. It also assesses the importance of macro-diversity as their results shows a PER reduction of almost 20 points of percent when switching from 1 to 2 GWs. However the channel model of this study considers no ShF, and moreover no SSF. The later being of primer importance for capture effect performance, especially with macro-diversity.

An analytical and simulation study [START_REF] Georgiou | Low power wide area network analysis: Can LoRa scale?[END_REF] proposed an improved model of the LoRaWAN capacity which takes into account the temporal variability of the channel, i.e. the SSF via a Rayleigh channel model. Thus EDs status is no binary with EDs either in or out range with a solid frontier, but rather each transmission can reach the GW with a P Rx above the threshold following the probability of the channel model. However, the traffic model considers that each ED saturates its duty cycle, i.e. each ED transmits 1% of the time on whatever SF it is set. Therefore, each ED does not transmit the same amount of data. For instance, an ED set with SF =7 transmits 18.8 times more data than an ED set with SF =12. This choice is not innocuous when it comes to network capacity measured as an absolute number of ED served rather than an network overall throughput. Indeed, with a fixed application data rate, more EDs could be connected with lower SFs.

Notice that both these studies [START_REF] Martin C Bor | Do LoRa low-power widearea networks scale?[END_REF][START_REF] Georgiou | Low power wide area network analysis: Can LoRa scale?[END_REF] consider single-channel networks, i.e. a single CF, which mechanically increases the channel load and collision rate compared to a standard LoRaWAN network which has at least three distinct channels. Thus the absolute values given as results underestimate the LoRaWAN capacity of LoRaWAN and might be multiplied by 3 for fair capacity estimation.

Another study [START_REF] Adelantado | Understanding the limits of LoRaWAN[END_REF] which also considers a rather pessimistic model as each node saturates its dutycycle whatever is the used SF, and also considers no capture effect, has shown that the number of received packets per hour and per ED decays exponentially with the number of ED in the network.

Interference from overlapping networks can severely damage the reliability of the network, and thus its capacity [START_REF] Voigt | Mitigating inter-network interference in LoRa networks[END_REF]. It has been shown in simulation that 4 interfering networks can increase the FER of the network of interest by about 30 percentage points.

A study which chose a less disadvantageous parameters [START_REF] Magrin | Performance evaluation of LoRa networks in a smart city scenario[END_REF] analyzes the throughput and reliability as a function of the number of EDs but also the coverage of a LoRaWAN network deployed in an urban environment model and obtained through simulation a capacity per GW of about 10000 EDs. Interestingly, the simulation model takes into account the hardware limitations of LoRa GWs with the number of demodulation path limiting the number of frames received simultaneously, independently of the distinct CFs or the orthogonal SF. However, due to the large ShF for indoor nodes, up to 20% of EDs are out of range in their simulation with a single GW cell. Their simulation with multiple GWs shows that this problem of deep indoor coverage is not insoluble, although as underlined by the authors, the GWs densification requires the use of an efficient ADR: indeed, the deployed GWs densification pushes an increasing number of EDs towards the lowest SF which at a certain point will saturate the channel.

A study specifically analyzed the impact of the limited number of demodulation path in GWs equipment, i.e. a standard GW based on the SX1301 chip can detect 48 preambles at once but only demodulate 8 frames simultaneously, and has shown that the probability to drop a frame by lack of available demodulation path can become significant as the load on the network increases [START_REF] Brandborg Sørensen | Analysis of LoRaWAN uplink with multiple demodulating paths and capture effect[END_REF].

The macro-diversity, i.e. the multiplication of the number of GWs increases the capacity of the network [START_REF] Caillouet | Optimal SF allocation in Lo-RaWAN considering physical capture and imperfect orthogonality[END_REF]. Switching from a mono-GW cell to a dual-GW cell increases the capacity by 30% in number of EDs served. However, it is to be noticed that the model of this study has a flaw: although the model considers the SSF with a Rayleigh channel model, the capture effect is calculated with the average of P Rx for each ED. This means that for two given EDs, the collision of their frames will systematically have the same outcome (destruction of both both or capture of the "strongest" ED), and thus it does not take account of the P Rx variability between successive transmissions. However we think it does not invalidate the general dynamic being the capacity improvement with macrodiversity.

It has been shown [START_REF] Heusse | Capacity of a LoRaWAN Cell[END_REF] that the geometry of the cell is of primary importance when assessing the network capacity: a sparse cell 5E D skm 2 can only serve 550 EDs in a 5.9km cell radius while a dense cell (90E D skm 2 can serve more than 3600 EDs in a 3.6km radius cell. In the same vein, an inhomogeneous distribution of EDs within the cell impacts the cell capacity [START_REF] Duda | Spatial issues in modeling lorawan capacity[END_REF]. In particular, a distribution where the density of the EDs closer to the GW is high and decreases with the distance (which is common for the EDs of cellular networks and also for the density of population or the building in urban centers) increases the capacity of the LoRaWAN cell. Indeed with a homogeneous distribution in a large cell, the higher SFs (thus low data rate) start being saturated before the lower SFs (thus high data rate), so the network is saturated, even thought there is still "room" in the low SFs.

Impact of network configuration on LoRaWAN capacity

Even though fundamentally the network tends to saturate as the channel load increases, as LoRa, the physical layer, offers this robustness against throughput trade off (or equivalently range against TOA), the parameterization is key to reach high capacity. Moreover, as this trade-off is done through the use of various orthogonal SF, LoRaWAN benefits from a set of independent virtual channels. Thus a relevant configuration of the network can have huge impact on its capacity. For instance, a basic optimization consists in affecting the lowest SF with regard to the PL and thus minimize the TOA. This multiplies by 13.3 (from 120 to 1600 EDs) the number of EDs served when compared to the dummy affection the highest SF (the most robust and most TOA expensive configuration) to every EDs [START_REF] Martin C Bor | Do LoRa low-power widearea networks scale?[END_REF].

SNR-based optimizations of the network configuration (or equivalently P Rx -based or distancebased) are sub-optimal: each ED is set the lowest SF possible. That is to say the lowest SF such that it is in range of the GW.Indeed, it has been shown that by balancing the SF assignment not only according to the SNR but also according to the contention on each SF, allows to serve more EDs with the required FER on a single-GW cell [START_REF] Heusse | Capacity of a LoRaWAN Cell[END_REF].

The optimization is more complex for multi-GWs networks, but studies proposed solution with Integer Liner Programming for models without capture effet [START_REF] Premsankar | Optimal configuration of lora networks in smart cities[END_REF] and with capture effect [START_REF] Caillouet | Optimal SF allocation in Lo-RaWAN considering physical capture and imperfect orthogonality[END_REF].

It is important to notice that increasing the tolerable FER required improves the capacity of the cell [START_REF] Heusse | Capacity of a LoRaWAN Cell[END_REF]. Thus "relaxing" the maximum tolerable FER constraint from 10% to 40% makes it possible to multiply the number of EDs served by 2.8 for a sparse cell and by 4 for a dense cell. This is of first major importance because the use of an error recovery mechanism at the data link layer level might thus benefits from both the maximized capacity and from a high reliability with a low PER.

Downlink capacity

LoRaWAN is intrinsically uplink oriented and most of the traffic is expected to be from the EDs to the NS. Thus even if LoRaWAN provides downlink connectivity, its downlink capacity is low. The downlink capability is highly limited. The first main reason being that GWs are submitted to the duty-cycle. But also, it has been shown that downlink traffic is severely harmfull for the uplink capacity. First because many GWs are half-duplex, i.e. uplink traffic is drop while transmitting a downlink frame, thus mechanically increasing the FER. But moreover, because EDs will retransmit confirmed frames that GWs where unable to acknowledge, saturation of the downlink might increases drastically the uplink channel load [START_REF] Pop | Does bidirectional traffic do more harm than good in LoRaWAN based LPWA networks?[END_REF]. Moreover, the default retransmission strategy of confirmed traffic is to drift to higher SF every two missed acknowledgements, thus accentuating the channel load increase. As a consequence the network capacity drops in presence of uplink traffic: just 5% of confirmed traffic might reduce the uplink goodput of up to 10%; if 100% of uplink is confirmed traffic, the network capacity drops to 15% of its capacity. So, even though downlink traffic is a key feature of LoRaWAN as it allows over-the-air activation, administration, dynamic configuration over even sporadic applicative downlink traffic, it must be minimized to the strict necessary. For instance the use of systematic confirmed traffic (ARQ) as a reliability mechanism cannot scale [START_REF] Adelantado | Understanding the limits of LoRaWAN[END_REF]. This low downlink capacity can be mitigated by smart scheduling of the downlinks in multi-GWs networks and by combining multiples downlink frames in a single transmission [START_REF] Di | Improving Downlink Scalability in LoRaWAN[END_REF].

Adaptive Data Rate (ADR)

Various studies evaluate and improve the ADR's performances. But because the algorithm is not strictly defined by the LoRaWAN specification, various implementations exist and variations of their interpretation appear in the literature.

A solution based on machine learning improve the ADR by detecting network congestion and thus decides either to wait longer for a downlink or switching to a more robust configuration. Notice that this solution push more complexity to the EDs as it requires them to compute the decision metric, also the NS must periodically broadcast additional data (the learning function weights) to the EDs, thus adding load over the dowlink channel.

Some studies [START_REF] Hauser | Proposal of adaptive data rate algorithm for LoRaWANbased infrastructure[END_REF][START_REF] Slabicki | Adaptive configuration of LoRa networks for dense IoT deployments[END_REF][START_REF] Babaki | Dynamic Spreading Factor and Power Allocation of LoRa Networks for Dense IoT Deployments[END_REF] suggest that the ADR TTN (as described in algorithm 2) tends to overestimate the link quality because of the MAX operator used for the SNR estimation. As a consequence, they suggest to replace it by a MEAN operator or a MIN operator. But because the frames with lowest SNR are likely to be more censored, the current PL estimation might be biased by MIN, MEAN and MAX. Moreover, the SNR variance has a major influence on the ADR's operation [START_REF] Slabicki | Adaptive configuration of LoRa networks for dense IoT deployments[END_REF]. We think that the real matter is to understand how the used metric will be biased to take informed decision on the best configuration. In that sense, the SNR distribution pattern and parameters estimation as described in chapter 4 and chapter 6 are key for optimized ADR decisions.

The ADR can be slow to converge, especially decreasing to more robust and lower data rate, because it relies on EDs to drift toward more robust configuration until a downlink is received [START_REF] Li | How Agile is the Adaptive Data Rate Mechanism of LoRaWAN?[END_REF][START_REF] Finnegan | Analysis and Enhancement of the LoRaWAN Adaptive Data Rate Scheme[END_REF]. For the same reason, the ADR does not converge to the same final configuration depending on its starting configuration. Thus we think the ADR should not be based solely on this drift to switch to a more robust configuration.

In a previous work [START_REF] Coutaud | High Reliability in Lo-RaWAN[END_REF], we improved the ADR protocol by relying on the characterization of the channel as a Rayleigh channel and the use of an application layer ECC algorithm. This solution is only tailored for a single cell LoRaWAN network, which is a major weakness for dense deployments composed of few to many gateways.

The ADR algorithm can be extended as a load-balancing algorithm to maximize the overall throughput on a single cell LoRaWAN network [START_REF] Kim | Contention-aware adaptive data rate for throughput optimization in LoRa WAN[END_REF]. However, this may come at the cost of decreasing the network's reliability. A load-balancing algorithm in the ADR can also aim to minimize the overall energy consumption [START_REF] Park | EARN: Enhanced ADR with coding rate adaptation in LoRaWAN[END_REF]. A load-balancing algorithm can balances the channel load in each SF virtual sub-channel which reduces the overall collisions in a single cell network [START_REF] Khaled | Fair adaptive data rate allocation and power control in LoRaWAN[END_REF], and can be extended to P Tx allocation to reduce near-far problems in the network [START_REF] Reynders | Power and spreading factor control in low power wide area networks[END_REF].

A study proposed a simple way to extend the solution to multiple GWs by virtually associating each ED to the GWs with best P Rx , thus reducing the problem to the single GW case [START_REF] Liao | Adaptive Parameter Adjustment for Uplink Transmission for Multi-gateway LoRa Systems[END_REF]. However this solution do not fully exploit gains from macro-diversity. Also, variations of the P Rx due to SSF might cause excessive re-calculation of both GW-ED pairing and SF affectations. Another multi-GWs solutions consists in mitigating the TOA pressure globally over the network [START_REF] Cuomo | Adaptive mitigation of the Air-Time pressure in LoRa multi-gateway architectures[END_REF]. In a nutshell, the idea is to change the SF of the "stressing" EDs, i.e. EDs that cause congestion to the most GW while they could maintain connectivity using another SF.

Notice that these solutions come at the expense of an increased TOA, and thus energy consumption, for some nodes that are set to use higher SF than required in order to reduce the collision rate. The ADR algorithm can be set to balance this energy consumption overhead and maximize the network lifetime [START_REF] Gao | AdapLoRa: Resource Adaptation for Maximizing Network Lifetime in LoRa networks[END_REF].

An algorithm to select adequate LoRa transmissions parameters to achieve a given reliability between one transmitter and one receiver while reducing energy consumption has been proposed [START_REF] Bor | LoRa transmission parameter selection[END_REF]. It starts from the most robust setting and evolves towards a satisfactory setting after the transmission of a few hundreds probes while temporal dynamics is handled by regular restarts. All of this makes it impractically slow.

Error Correction Code (ECC) in LoRaWAN

Digital communications and especially wireless communications have been using ECC for decades, either at the physical layer (intra-frame) or at the data link layer (cross-packet). In order to match the various requirements of the applications (error/erasure correction capacity, computation/memory constraints), or to match the nature of the channel model (Gaussian noise, burst error, frame loss, byte error,. . . ) various ECC have been developed and deployed, as listed for instance in Table 3.4.

As detailed in sec.2.2.1, LoRa uses intra-frame ECC which improves the demodulation performance. However, in this thesis we focus on CP-ECC to improve the quality of service of LoRaWAN network and intra-frame ECC is out of the scope.

Cross-frame ECC has been used for instance by Y.Birk et al. in satellite communication: a Reed-Solomon code [15] with feedback is used to sharply increase the attainable throughput of a multichannel ALOHA network under delay and reliability constraints [START_REF] Birk | Judicious Use of Redundant Transmissions in Multichannel ALOHA Networks with Deadlines[END_REF].

However, there are seldom works related to CP-ECC for LPWAN.

The Channel Coding Adaptive Redundancy Rate (CCARR) scheme is an example of CP-ECC [START_REF] Coutaud | Channel Coding for Better QoS in LoRa Networks[END_REF]. CCARR uses Reed-Solomon coding to implement CP-ECC at the application layer of LoRaWAN. CCARR sharply boosts the acceptable PER while reducing the channel load by dynamically tuning the effective coding rate. But CCARR relies on periodic downlinks which should be kept as rare as possible in the LoRa context, as discussed in sec.3.2.1. Chen et al. proposed a similar approach but based on fountain code [START_REF] Chen | Exploiting rateless codes and cross-layer optimization for low-power wide-area networks[END_REF]. Notice that as the code used is not a systematic code, and so DER might exceed the PER if no enough packets are delivered (highly congested network for instance).

Marcelis et al. proposed a scheme, called DaRe, to reduce the PER through CP-ECC [96]. DaRe computes redundancy over the application data with an LDPC-like code (linear combination of a pseudo-random subset of previous frames) and it doesn't require any additional downlinks. Even though their result shows a reliability improvement, but the gain is unclear as there are inconsistencies between their analytic and simulation results. However it is expected to achieve low DER with rather low overload if the coding rate matches well the channel state, i.e. the PER. Thus, such channel coding should be included in the ADR in order to run in favorable conditions. Similarly to them, our solution LoRa Fragmentation and FEC (LoRaFFEC) uses LDPC-like encoding, without downlink communication [START_REF] Coutaud | Fragmentation and Forward Error Correction for LoRaWAN small MTU networks[END_REF]. It combines error correcting with a fragmentation mechanism, thus addressing the varying payload length issues of LoRaWAN. This allows to solve two issues while offering a solution which is appropriate given the diversity of transmission parameters of LoRaWAN.

Technology

ECC description

UMTS 3G Turbo code [20] GSM 2G Convolutional code [17] DVB-S2

Low-Density Parity-Check (LDPC) [START_REF] Gallager | Low-density parity-check codes[END_REF] Montejo-Sanchez et al. proposed a scheme with linear combination of previous frames with less timing diversity (frames are XORed two by two) and thus lower delay for data delivery [START_REF] Montejo-Sanchez | Coded redundant message transmission schemes for low-power wide area IoT applications[END_REF]. They compare the performances of piggybacked redundant messages against performances of redundant messages included in independent frames and show that with their coding scheme independent redundancy perform better as long as protocol overhead is not prohibitive. Souza Sant'Ana et al. extended the solution use both coded and uncoded replicas which both increase the network capacity and battery lifetime [START_REF] Michel De Souza Sant'ana | Hybrid coded replication in LoRa networks[END_REF].

Borkotoky et al. use a similar LDPC-like encoding along side piggybacked repetition and propose a protocol which uses periodic feedback to adapt dynamically the data to be included in the redundant symbols [START_REF] Siddhartha S Borkotoky | Application-Layer Coding with Intermittent Feedback Under Delay and Duty-Cycle Constraints[END_REF]. However, the proposed protocol requires many additive downlink which make it impractical with regard to the LoRaWAN downlink capacity.

Chapter Conclusion

Several lessons can be learned from this chapter:

First of all, we must underline the relevance of carrying out studies based on experimental measurement campaigns in the field. Indeed, using the same hardware that will be used by the deployed networks, in the real environment and context is of major importance. The variety of deployment and experimental context, and the variety of obtained results attest of this. For instance, the maximum range obtained varies from a few hundred meters to several tens of kilometers, but also the dispersion of the measured received powers is not at all the same from one study to another, from one environment to another, etc ... Thus carrying out experiential field measurement campaigns over real LoRaWAN deployments makes it possible to be as close as possible to the real mode of operation and therefore to the performances. In addition, this experimental approach with real LoRaWAN hardware which is inexpensive and easy to deploy, allows massive amounts of experimental data to be gathered.

But the consequences of measuring performance in this way must be considered. The equipment used is therefore designed as communication devices and not measurement devices. The difference which may at first seem trivial is in fact determinant here Indeed, the measurements must be taken with a critical viewpoint: the hardware is not necessarily calibrated to provide precise measurements, the hardware does not necessarily have a sufficient measurement dynamic allowing them to correctly record the real values especially the "extreme" values. The analytical processing of the collected data must take into account these potential biases to avoid drawing unfounded conclusions.

The capacity of a LoRaWAN network cannot be dissociated from the transmission configuration of the EDs. Improper use and distribution of EDs' transmission parameters causes network capacity to collapse. Indeed with the most pessimistic assumptions and with the worst parameterization of the EDs, the capacity of the network is reduced to only a few hundred EDs per cell. However, with a more relevant setting -even basic -especially a balanced distribution of SF used, increases

Chapter Introduction

In this chapter we characterize the LoRaWAN link, i.e. the raw LoRa channel and the performance of BSR which is the repetition mechanism of the LoRaWAN MAC layer. To this intent, we carried out campaigns to collect experimental measurements described in sec.4.1. Then we analyze them, in the light on what we have learned and commented in the state of the art chapter, and also with in mind our objective which is to optimize LoRaWAN for high reliability.

Setup and Experiments

We have gathered an experimental dataset by recording LoRaWAN transmissions collected by several GWs in an urban area.

The test-bench consists of one ED1 , placed indoors on the third floor of a residential building, sending traffic to the TTN community network through a set of GWs. The ED transmits series of LoRaWAN frames and randomly varies the transmission parameters from one frame to the next. The transmission parameters are randomized in order to avoid shadow correlations and moderate the effect of possibly congested CFs.

We present in this thesis the results from two measurements sessions. In both cases, we used three CF centered on 868.1, 868.3 and 868.5 MHz, with BW =125kHz.

In the first session, we considered 48 combinations of (P Tx , SF) value pairs. We set the LoRaWAN intra-frame ECCCR to the default CR= 4 5 . The PL was 15 Bytes resulting in LoRa frames with a number of symbols per frame (N s ) from 38 to 53. The experiment ran for a whole week and there were on average 4300 frames transmission attempts per series, i.e. one frame every ≈ 2.4 minutes.

In the second experiment we extended the possible configurations to many more (P Tx , SF, CR) combinations with a payload such that 48 ≤ N s ≤ 50. We also extended the possible configurations for SF =7 with CR ∈ { 4 5 ; 4 6 ; 4 7 ; 4 8 } and with 10 different frame sizes: 48 ≤ N s ≤ 2982 . 336 transmission parameters configurations are thus tested. The experiment ran for twelves days and the dataset includes on average 940 frames transmissions attempts per series, i.e. one frame every ≈ 20 minutes. Table 4.1 summarizes the choice of experimental configurations.

50

Twelve and thirteen TTN GWs showed up within the transmission range of the ED during respectively the first and the second experiment. Among them, 8 were up for both experiments. Fifteen are GWs deployed in the Grenoble urban area within 5 km of the ED. Two GWs are outside the city Finally, we find the ∆Df value for which FER fits the experimental FER, FER XP . We find the adequate ∆Df value using the Ordinary Least Square (OLS) method which consists in minimizing

χ 2 (∆Df) = ( FER -FER XP ) 2 .
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∆ FER (∆ Df = -0.4 dB) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0.
∆ FER (∆ Df = -0.88 dB) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0.

Impact of the Frame Length

Frame length is expected to have a minor impact on successful reception because the latter depends on successful initial synchronization [START_REF] Attia | Experimental Characterization of LoRaWAN Link Quality[END_REF]. Still, our experimental measurements show a noticeable impact of frame length on the FER. To assess the magnitude of this effect, we gather measurements for diverse frame lengths using SF = 7, in Fig. 4 In Fig. 4.6, we compare again the experimental FER difference ∆FER Exp and the expected FER difference ∆ FER(∆Df). using the same methodology as in Sec. 4.3, using the configuration with N s =298 as reference. The OLS fit results are given in Tab.4.2. With our experimental setup, reducing

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 frame length from N s ∈ [296..298] to N s = 128 and N s = 48 produces a sensitivity gain of respectively -1.28 dB and -2.5 dB.

N s • Large Medium ∆ FER XP ∆ FER (∆ Df = -1.28 dB) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0.
However, one must keep in mind that the sensitivity gain from a reduced physical frame length comes at the expense of an increased protocol overhead. Indeed the preamble and protocol header lengths are fixed and only the application payload is reduced. Thus, with a "small" application payload, most of the TOA is spent in the physical preamble and protocol header. For instance, with SF = 7, CR = 4 5 and BW = 125kHz, a frame with N s = 50 encapsulates a 13 bytes applicative payload with TOA/b = 0.59 ms, whereas with N s = 298 it encapsulates a 188 bytes applicative payload with TOA/b = 0.21 ms, i.e. 2.8 times lower. We illustrate this in Fig. 4.7 which plots the ToA/b against the applicative payload from 1 to 250 bytes. Notice that the effective ToA/b for a 30 bytes applicative payload with SF = 7 is equivalent to the one for a 250 bytes applicative payload with SF = 8.

• • • • • • • • • • • • • • • • • • • • • • • • •
0.0 2.5 5.0 7.5 10.0 0 5 10 15 20 25

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0.2 0.4 0.6 50

Channel Burstiness Behavior

Another crucial point from the perspective of providing reliable communication is erasures burstiness. We compare in Fig. 4.8 the proportion of frames lost in erasure bursts in a simulated channel with independent and identically distributed (iid) losses vs. in our experimental data. The experimental data erasure patterns are close enough to be approximated in the following as an iid erasure channel.

However, even though the erasure distribution is iid, it does not prevent the loss of multiple frames in a row, as illustrated by the length of erasure bursts plotted in Fig. 4.9. Moreover, this length increases with the FER. Even over a channel with reasonable FER (< 0.3), a significant proportion of the lost frames comes from erasures bursts (length ≥ 2).

PTX00dBm GW2 PTX06dBm GW6 PTX06dBm GW2 PTX10dBm GW6 PTX14dBm GW2 PTX14dBm GW6 7

Performance of LoRaWAN BSR

The BSR mechanism implemented by the LoRaWAN MAC layer parameter Nb Trans , can be seen as the simplest kind of CP-ECC. The redundancy is a duplicate of the original frame, transmitted successively, thus it is weak against burst losses. However, although the channel erasures are close to iid, the probability to loose multiple frames in a row mechanically increases with the FER. For instance, over a FER =0.25 iid erasures channel around 15% of the lost frames are lost in burst of length≥ 3.

We use our real-world experimental measurement series to emulate BSR in order to better understand its limits and assess its performance. By replaying our experimental data set, we emulated the MAC layer parameter Nb Trans over our experimental data and the results are illustrated in Fig. 4.10 with the PER as a function of the FER for various Nb Trans . LoRaWAN BSR indeed provides important reliability improvement: Nb Trans = 2 reduces PER by more than 20 percentage points over a channel with FER =0.5. Increasing Nb Trans from 2 to 4 reduces PER by around 20 percentage points over a channel with FER =0.65. Nb Trans can be increased to reduce the PER without changing the SF and with no decoding latency. However, even with Nb Trans as high as 32, residual erasures appear over a channel with FER > 0.7. As expected, with the FER increase, BSR quickly fails to provide high reliability as it is weak against burst erasures and residual erasures are left uncovered. Moreover it becomes impractical due to its tremendous channel occupation overhead.

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Additional Remarks

LoRaWAN communication is often confronted to a FER floor In our experimental measurements, the SNR increases as we increase the P Tx and this in turn reduce the FER. Such behavior is expected. However, for many of our experimental series, the FER decreases until it reaches a floor which depends on the GW. For instance this ceiling is FER ≈ 0.15 for GW {2, 5} and is apparent for instance for GW2 in Fig. 4.11. Hence, the reception has typically a

Chapter Conclusion

From extensive experimental measurements and analysis with consideration for bias from censored experimental data, we found that the LoRaWAN channel in an urban environment follows a quasi-static Rayleigh channel model. This corresponds to the multi-path propagation of the signal. Thus, the received power corresponds to the LSF multiplied by the ShF (therefore the average received power), then multiplied for each transmission by a new drawing of the SSF which therefore follows a random variable of unit mean exponential distribution.

We also found that frame losses are mutually independents. However, notice that -obviously -this does not prevent multiple frames to be lost in a row when the FER is high. Thus LoRaWAN BSR is poorly designed to provide high reliability.

Our experimental data shows that -unlike to what can sometimes be suggested in the literature [START_REF] Afisiadis | Coded LoRa Frame Error Rate Analysis[END_REF][START_REF] Park | EARN: Enhanced ADR with coding rate adaptation in LoRaWAN[END_REF] -each LoRaWAN intra-frame ECCCR reduction does improve the modulation robustness.

Chapter Introduction

The finding that the channel can be modeled as a Rayleigh channel as detailed in Sec. 4.2 is key to understand the challenge to efficiently provide high reliability (DER <0.01) in LoRaWAN. The fact that the distribution of the frames SNR follows an exponential distribution, implies that a fraction of the frames faces a significantly higher path loss than the average. For instance, 10% of the transmissions will face a -9.8 dB SNR from the SNR. Likewise, respectively 5% and 2% of the frames will face a -12.9 dB and -16.9 dB SNR from the SNR. As a consequence, either an extremely robust transmission configuration, therefore over-robust most of the time, is used to received those few "very low SNR" frames, either the communication protocol faces this "erasure floor". The solutions based on acknowledgement frames, such as ARQ, are strongly limited by the asymmetry of LoRaWAN networks where downlink transmission opportunities are scarce [START_REF] Pop | Does bidirectional traffic do more harm than good in LoRaWAN based LPWA networks?[END_REF]. As expressed in sec.4.6, the LoRaWAN BSR mechanism is weak to provide high reliability and has a tremendous channel occupation cost. In this chapter we present two CP-ECC protocols for high reliability in LoRaWAN. By introducing more time diversity in the communication, more elaborate CP-ECC can provide high reliability at a lower cost [96,[START_REF] Coutaud | Channel Coding for Better QoS in LoRa Networks[END_REF]. In this chapter we propose two overlay protocols using CP-ECC which ,transparently for both the application and the LoRaWAN protocol, recover the losses and provide high reliability in LoRaWAN.

Channel Coding Adaptive Redundancy Rate (CCARR)

With the aim of providing high reliability (PER < 0.01)) while maintaining the ED TOA as low as possible, we propose in the following CCARR, a protocol that uses Reed-Solomon based CP-ECC and scarse completion acknowledgments.

CCARR Algorithm

With CCARR (n,m), the information to be sent is gathered in a (n + m) frames long segment where each frame has l bytes length. The first n frames contain application data and the following m frames contain redundant data. The redundant frames are build from a RS-code computed vertically over the preceding frames as shown in Fig. 5.1. Notice that n, the maximal amount of redundant frames, is adjustable, for instance to the application requirement, the physical payload needs and also to adjust downlink channel load. The ratio n n+m is the maximal coding rate of the CCARR instance. We call it CR CCARR to make the distinction with CR from the LoRa native intra-frame ECC.

Algorithm.3 defines the ED side of the CCARR protocol: the CCARR (n,m) protocol sends the frames of the segment one by one. It only starts listening for acknowledgement in the downlink at the n t h frame transmission. If no such acknowledgement is received, it then continues sending the following frames of the segment one by one in a sequential manner, until the reception of the segment completion acknowledgement.

Thanks to RS-code properties, the NS will be able to retrieve the whole application data from any n received frames. As described in algorithm 4, CCARR (n,m) only triggers the downlink acknowledgement(s) emission to the ED when it received n frames, i.e. enough to reconstruct the entire segment. Notice that the NS keeps acknowledging when it receives new uplink frames for an already retrieved segment because this means that the previous acknowledgement(s) was(were) lost. In the best case of a loss-free channel, CCARR (n,m) transmits only n uplink data frames and one downlink acknowledgement. And if some frames are lost, CCARR (n,m) keeps transmitting Algorithm 3 CCARR (n, m) segment uplink emission on ED side. lostSegmentError(); 12: end if

CCARR Probabilistic Analysis

Reliability

One can notice that the segment completion acknowledgement is triggered by any n frames receptions over (n + m) sent. Thus, in the analysis with i.i.d. frame losses, this results in a cumulative binomial law for the probability of successfully receiving the full data of the segment [START_REF] Bernoulli | L'art de conjecturer[END_REF].

For CCARR (n,m) over channel with PER = P e , we can write more formally the segment transmission failure probability P fail CCARR(n,m) :

P fail CCARR(n,m) = B c (n -1, n + m, (1 -P e ) = n-1 i =0 n + m i (1 -P e ) i (P e ) n+m-i (5.1)
with B c the cumulative value of the binomial law B(i , 1 -P e ) when i varies from 0 to n + m, and 1 -P e is the probability of success.

We plot in fig. 5.2 the probability to fail the reception of a single segment as a function of the channel FER, for various CCARR configurations having the same CR CCARR = 1 5 , namely CCARR [START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Lee | A comparative study of wireless protocols: Bluetooth, UWB, ZigBee, and Wi-Fi[END_REF], CCARR (5,[START_REF] Berrou | Near Shannon limit errorcorrecting coding and decoding: Turbo-codes. 1[END_REF] and CCARR (1,4), the latter being equivalent to the failure probability of LoRaWAN BSR with Nb Trans = 5. The failure probability remains low until P e approaches a given tipping point which depends the maximal available CR CCARR . After this point, the probability of failure takes off quickly. We call this a waterfall effect. The waterfall effect is all the more pronounced the longer the segment length of CCARR is. This is an advantage and then a disadvantage before and after the tipping point, respectively. With the objective being high reliability and not just a reliability improvement, it is therefore better to use long segments.

In fig. 5.2 the erasure probability is computed for a single segment for each configuration, meaning that the amount of application data is not equivalent. Thus for fair comparison we plot in fig. 5.3 the probability to fail at receiving 1 segment of CCARR [START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Lee | A comparative study of wireless protocols: Bluetooth, UWB, ZigBee, and Wi-Fi[END_REF], 2 segments of CCARR (5,[START_REF] Berrou | Near Shannon limit errorcorrecting coding and decoding: Turbo-codes. 1[END_REF] and 10 segments of CCARR (1,4). It shows that CCARR is way better than LoRaWAN BSR (n=1) to provide an highly reliable connection. It also emphasizes even more the fact that CCARR with a longer segment makes is better to provide highly reliable channel.

Time-On-Air (TOA)

As stated in sec.3.2, the capacity is a key element of LoRaWAN and it must be preserved. Thus, any reliability mechanism must use as few TOA as possible. We define R T O A , a comparison metric, that represents the channel over-usage ratio (including uplink and downlink), i.e. T O A useless , the redundant transmissions duration that occurs while the data have already been recovered, over T O A useful , the transmissions duration that was necessary to complete these data reception:

R T O A = T O A useless T O A useful
Thus, the "perfect" channel usage would result in R T O A = 0, which means that all the transmissions that happened, including the redundant ones, were strictly necessary to recover the data. Consequently, R T O A > 0 reflects the "wasted" network capacity normalized relatively to the useful transmissions necessary in order to successfully transmit the data with the given protocol. For instance R T O A = 1 arises when the data is re-transmitted once while it was already recovered by the

NS.

Considering symmetric behavior of the channel, thus equal i.i.d PER = P e for both uplink and downlink, the cost of sending an uplink frame with CCARR depends on:

• a i which the TOA generated by the i t h frame transmission attempt (with regard to T and T ′ the TOA of respectively an uplink data frame a downlink acknowledgement).

• b i which is the probability to reach this i t h transmission attempt.

• c i the probability that not enough successes occurred (i.e. less than n frames) to retrieve the whole data at this i t h attempt.

Formally:

a i = T + (1 -c i ) × (1 -P e ) × T ′ b i = i -1 k=1 (1 -c k ) × (1 -P e ) 2 )
c i = B c (n -1, i , 1 -P e )
And, as a result: Segment Text (flash) BSS(RAM) Size (Bytes) 6320 5160 of this cloud NS. Especially its internal policy where it implements downlink transmissions using a lower SF and the maximum downlink allowed P Tx 7 . Hence, this acknowledgement channel was lossless during the experiments. Notice that, compared with the simulation context, it is advantageous for the CCARR protocol to get 100% of its completion acknowledgments. With our testbed experimental setup, the acknowledgement's TOA was a tenth of the uplink frame's TOA, as detailed in Table 5.1. We used the maximal SF = 12 to generate contentions easily.

R TOA-CCARR = n+m i =1 (a i × b i ) n+m i =1 (a i × b i × (1 -c i )) (5.2)
The ED LoRaMac firmware from [155] was modified to implement the CCARR protocol and its RScoded CP-ECC. In particular, we modified an open-source 8 RS code library software [39] in order to fit our embedded software needs in terms of memory management, computation complexity, maximum size of dataword and codeword. The resulting CCARRCP-ECC computation does not constrain the communication system because it takes less time to compute than the frame TOA on our end-device MCU 9 . However, even optimized, the RS-code memory footprint is still relatively expensive on our typical MCU 10 . So we limited the segment dimension in order to adjust CP-ECC to typical LoRa frames and metering application demand. This resulted in a CCARR [START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Coutaud | Adaptive Data Rate for Multiple Gateways LoRaWAN Networks[END_REF] protocol implantation with twenty-nine bytes frame for uplinks and 15 Bytes frames for downlinks 11 and a code size fitted to our ED as described in Table 5.2.

In order to variate the channel FER, we created various contention levels, by using 1, 2 or 3 ED within a single uplink CF =868.1MHz, at SF = 12. The uplink P Tx is set to 2dBm, the minimum allowed by the ED. Then the desired channel FER was adjusted by tuning the intensity of the frame generation process of the EDs interfering on the contention-based ALOHA channel while respecting the LoRaWAN protocol and especially its active listening on receive slots. As a result each ED emitted at around 0.25Hz. We monitored the channel FER, the DER and the TOA on both the uplink and downlink. Each experiment was conducted until 150 packets were delivered to the application. Interestingly, CCARR [START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Coutaud | Adaptive Data Rate for Multiple Gateways LoRaWAN Networks[END_REF] protocol provides DER = 0 for all tests up to FER = 0.67 which is the highest stable FER that we were able to reach with our experimental platform. 7 SF9 and an effective radiated power (ERP) of 27dBm over the 125kHz wide channel centered on 869.525MHz. 8 Under GPL license. 9 32 MHz STM32L151C8U6 10 10kBytes RAM and 64kBytes flash 11 Respectively 16 and 2 Bytes of data with 13 control Bytes. 12 Compiled with arm-none-eabi-gcc version 5.4.1.

LoRaFFEC, is thus needed to ensure application compatibility with any legislation and any link quality.

LoRaFFEC Protocol

LoRaFFEC considers uplink communications between an ED and the NS as a stream of packets which need to abide by the regulation of the considered frequency band. The stream implements LDPC-like CP-ECC by computing redundancy packets on the fly using pseudo-random linear combinations of already sent data. On top of that mechanism, application data is fragmented to fulfill the stream packet size.

Thus LoRaFFEC implements the fragmentation of the application payload, called Application Data Unit (ADU) and thanks to the CP-ECC, it allows the recovery of lost data. On the one hand, fragmentation has a strong negative impact on the DER: every single fragment of the ADU needs to be received for reconstructing the full original ADU:

DER = 1 -(Fragment_Reception_Rate) #fragments
So it is natural to supplement a fragmentation scheme with an erasure recovery such as CP-ECC to regain a satisfactory DER. On the other hand, CP-ECC implies more payload overhead to carry the additional redundancy control information. This reinforces the need for fragmentation, in order to be able to transmit any payload size, by splitting if necessary the data over multiple packets while optimizing the use of each packet transmission with the aggregation of many fragments when possible. This interdependence affirms the need for a protocol ensuring both fragmentation and reliability.

LoRaFFEC is realized through three sub-layers performing respectively: integrity check, fragmentation and erasure recovery. A LoRaFFEC ED first sends data fragments, followed by a number of redundancy fragments as shown in fig. 5.14. Thus, the ED has to store a window of previous fragments. On the NS side, when a data fragment is missing, the previously received data and redundancy fragments form a linear system of equations which enables to attempt to rebuild the data. This involves storage and relatively heavy computation. The corresponding ED and NSLoRaFFEC algorithms are presented in sec.5.2.1.7 and 5.2.1.8 with a precise evaluation of the memory and computational complexity costs.

To precisely assess LoRaFFEC, several parameters have to be discussed: the Window Length (WL) on which the CP-ECC is computed, the Redundancy Density (RD) which is the number of data fragments combined in each redundancy one, and the Decoding Depth (DD) that the NS considers when building the system of equations.

Integrity Sub-layer

The integrity sub-layer guarantees that no false positive is delivered to the upper layer, i.e. it guarantees that the output of LoRaFFEC (at NS side) is effectively an ADU produced by the application (at ED side). As shown in fig. 5.11, each ADU is identified in the implementation by a 4-bytes Application Counter (Cnt App ) and a 2-bytes hash computed on the ADU and its Cnt App . The concatenation of the Cnt App , the ADU and the hash forms the Integrity Data Unit (IDU) .

In order to reduce protocol overhead, the three Most Significants Bytes (MSB) of the Cnt App are truncated after computing the hash and before fragmentation, only the Least Significants Bytes (LSB) are sent along the data.

Encoding on the ED

On the ED, following the algorithm described in algo.5, the encoding process computation complexity for each redundancy fragment is WL × RD . The real bottleneck is the memory footprint: the ED needs a buffer of WL × f bytes, where f is the fragment length, to store the past ADUs that are used to compute the current redundancy fragments.

Algorithm 5 Fragmentation and redundancy fragment encoding algorithm using MPC .

Decoding on the NS

The decoding is computed using a best effort linear resolution of the equation system. The work matrix lines are filled with all the received fragments indexes followed by their data. The linear system solving operations are determined and computed from the indexes structure. All the corresponding (XOR) operations are applied to the whole data part of the fragment in order to reconstruct the lost elements. When a new fragment comes in, diagonalization of the index matrix is advanced as much as possible using Gaussian elimination on the new fragment and then with the fragment itself and possible new pivot(s). In the end, each updated index line which only contains a single "1" has its data part delivered to the de-fragmentation procedure. Otherwise, it stays as is, waiting for the next fragment diagonalization to be applied for possible complete decoding later on.

Algorithm 6 Decoding and update algorithm of the index and data matrices. end if 8: end for At the NS side, from the algorithm presented in algo.6, the decoding process computation complexity is O(WL 2 × DD) for each received fragment and it requires a buffer of size (DD × WL) 2 /8 + (DD × WL × f ) bytes in memory to store the decoding matrices. With the discussed practical numbers, this stays very reasonable for a NS.

LoRaFFEC Simulation

We performed extensive simulations to evaluate the performance of LoRaFFEC with parameter variations. The simulation scenario decodes a LoRaFFEC stream with random i.i.d packet erasure.

Simulator Description

To evaluate the LoRaFFEC protocol and check the proposed CP-ECC, a simulator 13 was designed which executes the actual LoRaFFEC protocol on a simulated communication channel. The sim- Latency increases when the FER is between 0.3 and 0.5. In this case, the decoder is often in an intermediary state where so many data fragments are lost that it can barely extract lost data from redundancy fragments. For FER > 0.5, the latency concerns a few exceptional corrections when very short linear combination gear effect is successful. ), but at this point reaches a threshold and cannot recover more lost fragments. In the opposite, the longer window (WL = 128) keeps correcting lost data fragments for longer and up to full recovery (cumulated value = 1).

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LoRaFFEC Experimental Results

LoRaFFEC is not yet deployed in the field but based on the field experiments from Chap.4 we evaluate LoRaFFEC in a real LoRaWAN traffic scenario. We replay the experimental collected stream applying LoRaFFEC on it and thus validate the potential benefit. For the sake of comparison, a simulation of LoRaWAN BSR with Nb Trans = 2 is also computed.

Streams Replay Reconstructed Results

The first reconstructed transmission uses LoRaFFEC (128, 0.6, 2 × w), no fragmentation and no aggregation, i.e. data fragments and redundancy fragments, are sent in different frames. Fig. 5.24 For comparison, the DER of transmission using LoRaWAN BSR with Nb Trans = 2 is also plotted. The plots from experimental erasure patterns corroborate very closely the simulated results with i.i.d. erasure patterns discussed in Section 5.2.1. This allows to distinguish three practical scenarii that can guide LoRaFFEC usage in field deployments: Rare values are slightly out of the global trend: this may be explained by the length of the streams, over seven days one can experiment a short period of harsh environment and FER will be temporally worse than its average value. The average FER of the stream may hide some variations of the channel over time (day and night shifts, professional occupancy, weather variations with cloudy humid days, etc.) [START_REF] Ameloot | A Compact Low-Power LoRa IoT Sensor Node with Extended Dynamic Range for Channel Measurements[END_REF]. For instance, the FER might be above 0.4 temporarily and for a bit too long, resulting in application level losses even if the overall FER if below 0.4. Also, the comparison with the case of LoRaWAN BSR with Nb Trans = 2, is favorable to LoRaFFEC only with FER < 0.45. Thus, from a reliability perspective, a mix of the two strategies(CP-ECC and BSR) would be effective. This emphasizes the need for an appropriately tailored ADR to support LoRaFFEC: the LoRaWAN ADR should be triggered in order to increases Nb Trans (along P Tx , SF, and CR) and thus keep channel FER in a range where the LoRaFFEC protocol will ensure an almost null DER. We discuss this in Section 6.2.1.

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Chapter Conclusion

In this chapter we proposed two novel approaches that improve LoRaWAN reliability by the means of CP-ECC.

The first proposed protocol, CCARR, uses Reed-Solomon codes and an intrinsic dynamic coding rate. The strength of CCARR is its ability to regulate itself according to the real effective channel PER. However, the price to pay is seldom segment-based downlink acknowledgments. Hence, CCARR provides high reliability over lossy channels with low overload on the network compared to the existing LoRaWAN strategy (BSR). As a result, for a given PER over the channel, the TOA is smaller with CCARR. For instance, in our experiments, CCARR [START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Coutaud | Adaptive Data Rate for Multiple Gateways LoRaWAN Networks[END_REF] sustains DER < 0.01 over a PER = 0.33 channel with TOA increased by a factor 2.3 only due to the redundancy overload.

The second proposed protocol, LoRaFFEC, combines fragmentation and application-level error correction based on fragment pseudo-random combination. For instance, LoRaFFEC with coding rate 1 2 reaches satisfactory data delivery (DER < 0.01) over channels with PER up to 0.4. However, LoRaFFEC is unable to exploit the redundancy if the PER is higher than this recovery threshold. Thus LoRaFFEC needs to be integrated within a tailored ADR to maintain the PER below the required threshold.

Both CCARR and LoRaFFEC performances are demonstrated over simulated channels and experimental deployment or reconstructed experimental erasure patterns frame streams.

CCARR and LoRaFFEC shows that using CP-ECC as a reliability layer on top of LoRaWAN stack has the ability to provide high reliability over a lossy channel. Moreover, this approach as the potential to relax the constraint on the EDs transmission parameters and thus use less conservative parameters and reduce the TOA within equivalent or even higher reliability. This opens new perspectives for ADR optimization and might lead to substantial improvement in network capacity while ensuring high reliability.

Chapter Introduction

In this chapter, we re-invest and cross the results from chapters 4 and 5 to improve the ADR algorithm described in the section 2 in order to provide a reliable LoRaWAN connection at a large scale. That is to say that we are going to dynamically configure the network (the EDs transmissions parameters) to keep the DER low, while keeping the EDs TOA as low as possible as well. On the one hand we propose to optimize the "native" parameters of LoRaWAN (Nb Trans , SF, P Tx ). On the other hand we propose to use the opportunity of using a CP-ECC to relax the constraints on the "native" parameters and this way achieve high reliability at lower TOA cost.

In this chapter, it is fundamental to keep in mind the precise definitions of the FER, the PER and the DER:

• The Frame Erasure Rate (FER) is the physical loss ratio between an ED and a given GW (i.e.

without duplicate transmission from LoRaWAN BSR).

• The Packet Error Rate (PER) is the loss ratio between an ED and the NS. PER benefits from multiple GWs reception and frame duplicated transmissions from BSR.

• The Data Error Rate (DER) is the loss ratio between an ED and the AS, thus benefiting from the presence of an additional erasure recovery mechanism such as a CP-ECC.

Needs, constraints and levers for ADR optimization

As already described in Chapter 4, because of the multipath propagation, the LoRaWAN link is likely to follow a Rayleigh channel model. As a consequence, appropriate tuning of the SF and P Tx is thus fundamental to obtain connectivity with a reasonable FER, but it is not sufficient to establish a highly reliable channel, as the link might be subject to an erasure floor of few percents. Hence, it is hopeless to only rely over P Tx and SF increases to provide a high reliability with Lo-RaWAN.

It requires the use of an erasure recovery mechanism, either the LoRaWAN BSR with Nb Trans > 1, or a CP-ECC algorithm. These erasure recovery mechanisms can be complementary and should be carefully used to exploit the full potential of each solutions.

See for instance in Fig. 6.1 which plots the DER, for replayed experimental series with SF and Nb Trans such that their TOA is roughly equivalent, with various P Tx (and thus different P Rx conditions). There is no best Nb Trans and SF combination for all cases but rather locally best combination. However, when the GW is far (emulated by lower P Tx ), a configuration with high SF and low Nb Trans provides better DER because the GW is simply out of range if using lower SF. When the GW is in a reasonable range (emulated by higher P Tx ) for lower SF, the tendency is quickly inverted and low SF with high Nb Trans provides better DER. This shows the potential for complementary of the SF and Nb Trans parameters to reach the best DER for a given TOA budget. Thus, this calls for a smart response against Rayleigh channels to avoid a counter-productive increase of SF or Nb Trans .

ADR for Single Gateway LoRaWAN Network

In this section we start by optimizing the ADR algorithm in the simplified context of a mono-GW LoRaWAN network.

Improving Adaptive Data Rate

Based on the insights gained previously, we design ADR opt-SG , an improved version of ADR. It consists in a precise computation of the ADR algorithm's parameters (described in algorithms 1 and 2): MARGIN, PER High , PER Med , PER Low , for LoRaMAC ® using CP-ECC and LoRaWAN BSR.

We first turn our attention to evaluating the PER degradation due to the channel overload caused by BSR in a pure-Aloha network. Considering (unslotted) ALOHA access without capture effect [3], DER over the channel is defined as P (λT ) = 1 -e -2λT where λ is the Poisson process intensitythe number of packets generated per second-and T is the average frame duration. The formula extends to Nb Trans duplicated transmissions with: We saw in Section 5.2 that LoRaFFEC (128;0.6;2) over a PER = 0.4 channel provides high reliabil-ity, thus ADR opt-SG will be tailored to provide PER < 0.4 to the LoRaFFEC layer. Also, x > 2 only provides DER improvement over a low load channel and otherwise, performances quickly drop, as illustrated in Fig. 6.2 with P (x, λT ) computations. Thus, ADR opt-SG should operate mainly with Nb Trans =2, with fluctuation up to 3 and down to 1 when the channel is either highly degraded or of high quality. Hence, LoRaFFEC will eventually operate with fitted PER and provide the high reliability. Thus, we set PER High , PER Med and PER Low which are the threshold for Nb Trans adaptation to respectively 10%, 30% and 70%. This way PER is maintained under 0.4 and this reduces the overall TOA.

P (Nb Trans , λT ) = (1 -(e -2Nb
Assuming a Rayleigh channel for LoRa, the SNR follows an exponential distribution with cumulative distribution function, F (x) = 1 -e -x (and its inverse

F -1 (x) = -l og (1 -x)).
Notice that the NS estimates the link quality by taking the maximal SNR over the last 20 received packets without taking into account neither duplicates from BSR or losses. Hence, the effective sample's size increases with Nb Trans and FER. Finally, 60 is an acceptable tradeoff to estimate the number of frames effectively used for the link quality estimation, as it matches the targeted functioning point Nb Trans =2 and PER ≈ 0.4.

Thus, we can compute F -1 (0.9 1/60 ) = -l og (1 -0.9 1 60 ) ≈ 6.3 ≈ 10 8 10 , which means that there is 90% chances over the last 60 received frames, the maximal measured SNR is less than 8 dB over the SNR.

Also, F -1 ((1 -0.4) 1/2 ) = 1 = 0dB, i.e, 0 dB is the SNR threshold such that PER = 0.4 with Nb Trans =2. So, MARGIN = 8dB is a good approximation for PER = 0.4 with Nb Trans =2, as it gives minimum TOA. Eventually, this PER is enough for CP-ECC to recover the remaining erasures as shown in Chapter 5.2.

Moreover we modify the initialization of the ADR: if the NS did not received enough packets, instead of introducing extra margin, it just waits for a minimum of 5 received packets before replying to the ED with an ADR command.

Without loss of generality, we disabled the power control as it only keeps P Tx to its max unless SNR is strong enough and SF is already minimal which corresponds to unavailable data rate (SF=7 BW=250kHz or SF=6).

Performance comparison

First we show ADR opt-SG performances over a simulated Rayleigh channel. Then we confirm the results from simulation by emulating ADR opt-SG over our experimental series, i.e by replaying the real-world data-set gathered from the experiments described in chapter 4.

For simplicity, we assume a perfect downlink channel which allows to transmit all the ADR commands. We assume LoRaFFEC is used as CP-ECC and consider that payload's overhead is piggybacked into existing packets and so, the LoRa payload increases from 28 to 50 bytes 1 . Note that the frame size has little impact on the FER with such sizes (see Section 4.4) and so, we do not consider any FER penalty for longer frames.

The simulated Rayleigh channel is a serie of frames with a fixed SNR mean (SNR), which correspond to fixed positions of the ED and the GW. For each frame f , SNR f = SNR × X where X is a unit mean exponential probability density function. Thus, a frame is dropped if SNR f < SN R floor .

We simulate it for SNR in [-30 dB, 10 dB] by steps of 0.5 dB with series of 5000 frames, each experiment is repeated 50 times.

We simulated ADR opt-SG and ADR TTN in a single GW LoRaWAN network with Rayleigh channel and SNR ranging from -30dB to 10dB. We do not simulate congestion on the network. Figure 6.3 plots the simulated DER and TOA of ADR opt-SG , ADR TTN .

ADR opt-SG sharply adapts the transmission parameters and provides DER < 0.01 over a channel with SNR > -21.5 d B . This corresponds to SF =12 with LoRaFFEC (128;0.6;2) and Nb Trans =3, sort of "Maximal Effort" policy result in this context. However, ADR opt-SG 's TOA is higher than ADR TTN 's for channel with SNR ≤ -17 d B . This corresponds to the extra energy invested by ADR opt-SG to achieve a reliable communication. For channel with SNR > -17 d B , the transmissions parameters of ADR opt-SG are more accurate and thus reliability is obtained with lower TOA .

ADR opt-SG performances over real world series of transmissions are shown in figures 6.4 and 6.5. The results real-world traces results confirm the simulations: ADR opt-SG provides adequate tuning for the transmissions and either DER < 0.01 is achieved or a most robust available configuration is used. Except for GW7, DER < 0.01 is reach for every GW with P Tx > 6 d B m. However, in some rare cases (for GW 3 and 6 at P Tx 2 and 4 dBm), ADR opt-SG slightly under-performs because the variations of the channel conditions are faster than the adaptation rate.

From experiments and models, ADR opt-SG proposes large optimizations of the LoRaWAN ADR using both LoRaFFEC and carefully computed parameters. ADR opt-SG software protocol successfully provides high reliability, with DER < 0.01 in LoRaWAN networks even over channel with low SNR. The proposition is validated both by simulation and experimental channel transmissions replays. Moreover, ADR opt-SG employs no more additional downlinks than the legacy LoRaWAN ADR. ADR opt-SG 's TOA is bounded by the maximal effort configuration which advocates for its scalability and makes it realistic for real life deployment.

•••• • • • • • • • • • • • • • • ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 0.0 0.
•••••••••••••••••• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• •• ••• •••••••••••••••••••••••• 0
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • GW7[3.41km] GW8[13.82km] GW5[1.44km] GW6[2.13km] GW3[1.03km] GW4[1.34km]
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • GW7[3.41km] GW8[13.82km] GW5[1.44km] GW6[2.13km] GW3[1.03km] GW4[1.34km]

ADR for Multiple Gateways LoRaWAN Network

In this section, we deepen the ADR opt-SG optimization proposal from section 6.2. In particular we extend the optimization to fully take into account the case of a multi-GW LoRaWAN cells, and thus fully exploit the LoRaWAN's natural macro-diversity.

ADR opt-MG a Configurable and Optimized ADR

First, we propose ADR opt-MG , an NS-side flexible ADR algorithm, optimized for Rayleigh channel model. ADR opt-MG is flexible in the sense that it is configurable to target any given PER (PER target ). The EDs transmissions parameters will be tuned to reach PER target with minimized TOA. ADR opt-MG uses "raw" LoRaWAN, i.e. no additional CP-ECC layer is used.

ADR opt-MG Algorithm

For the sake of simplicity we restrain the available transmission configurations to any combinations of SF ∈ {7..12}, CR = 4 5 and Nb Trans ∈ [1..3] with BW = 125kHz and CF ∈ {868.3, 868.5, 868.8}MHz. Finally, we consider a constant P Tx , as it is reduced from its maximal value only when the signal is very strong and both SF and Nb Trans are set to the lowest values, thus P Tx has little influence on the performance of ADR in terms of PER and TOA.

ADR opt-MG , detailed in 7, extrapolates a presumable PER for each [SF; Nb Trans ] pair from the observation on the channel over the previous transmission period. ADR opt-MG then chooses the transmission parameters to maintain PER just below the target level PER target .

The ADR opt-MG FER estimation function is based on the assumption that the channel is Rayleigh as described in section 4.2. In the following, we refer to SNR as the computed extrapolation, therefore imperfect, of SNR. For a given GW, we can compute SNR over a period of time. Assuming that the channel does not change drastically for the next period, we can compute the expected FER for any transmission parameters. And eventually, with the assumption that each transmission and reception by different GWs are independent, we can extrapolate the PER by combining the FER for each of the GWs in the reception range of the transmitting ED.

Because a loaded network would distort the estimation of SNR from the observed FER, we choose to rely on another characteristic of the exponential distribution that would not suffer such bias: the highest received SNR: SNR max . As the channel history buffer keeps a limited number of received frames 2 We combine this SNR with the typical SNR demodulation floor of LoRa [START_REF]LoRa® Modulation Basics[END_REF]:

SNR floor<SF> = (-20) + ((12 -SF) * 2.5).
Thus FER <GW i ;SF> , the estimated FER between the ED and GW i using the given SF, is:

FER <GW i ;SF> ≈ CDF exp (10 SNR floor<SF> -SNR 10
).

Which leads to PER <Nb Trans ;SF> ,

PER <Nb Trans ;SF> ≈ ∀GW i ( FER <GW i ;SF> ) Nb Trans
These formulae compute an accurate approximation of the FER between the ED and a given GW and consequently the PER between the ED and the NS, for each available transmission parameters combination.

With ADR opt-MG the PER target is an input parameter of the algorithm that can be fixed to an arbitrary value. Thus ADR opt-MG adapts to arbitrary reliability needs.

ADR opt-MG Simulation

We assume a perfect downlink channel which allows to transmit all the ADR opt-MG piggybacked commands and parameters into downlink ACKs. The Rayleigh channel describes a series of frames with a fixed SNR mean (SNR), which corresponds to fixed positions of the ED and the GW. For each frame f , SNR f = SNR× X where X is a random variable following the UMED distribution function. Thus, a frame is dropped if SNR f < SNR floor<SF> . We simulate this for SNR in [-30..10] dB by steps of 0.5 dB with series of 6000 frames repeated 60 times.

ADR opt-MG performance over the simulated Rayleigh channel appears in Fig. 6.7 and Fig. 6.6 in presence of 1, 2, 4 and 8 GWs when the SNR to all GWs are equal. Notice that in a configuration with unequal SNR, GWs with relatively low SNR bring little benefits: the overall performances tend to be the performances of a network with only the best SNR GW, i.e. most of the time the closest ones.

ADR opt-MG sharply adapts the transmission parameters to reach PER target . We distinct three cases:

• SNR is too low and PER target cannot be met. In this case, ADR opt-MG uses the most robust and most TOA expensive transmission configuration available. The ability to meet the required PER target is conditioned by the most robust available configuration. The most robust parameters combination is, in our case, SF =12 with Nb Trans =3. It is also conditioned by the

ADR opt-MG on Replayed Traces

We ran the experiments over several subsets of our real world transmission records described in chapter 4. It appears that the reachable GWs can be classified following their SNR range. Fig. 6.8 and Fig. 6.9 show the results for these subsets: GWs 5 and 6 that have low SNR (respectively SNR ≈ -8.1 dB and SNR ≈ -12.1 dB with P Tx =14dBm), GWs 9 and 17 that have medium SNR (respectively SNR ≈ -5.8 dB and SNR ≈ -6.6 dB with P Tx =14dBm), GWs 2 and 7 that have high SNR (respectively SNR ≈ 4.6 dB and SNR ≈ -0.4 dB with P Tx =14dBm), and finally the aggregation of GWs 2, 5, 6, 7, 9 and 17.

The results derived from our real world transmission traces confirm the simulations of section 6.3.1.2. For any subset and P Tx configuration, ADR opt-MG provides adequate tuning for the transmissions and either PER < PER target is achieved or the most robust available configuration is used. Notice that the performances for the subset with GWs 2, 3, 4, 5, 6 and 8 is strongly dominated by the GWs providing the best signal reception, i.e. GWs 2 and 3. As a consequence, its performances is just slightly better than the subset with GWs 2 and 3.

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • <GW5;GW6> Low SNR.
<GW9;GW17> Medium SNR.

<GW2;GW5;GW6; GW7;GW9;GW17> <GW2;GW7> High SNR.

ADR HR for High Reliability

Cross-frame ECC for LoRaWAN

In the following, we refine ADR opt-MG with the additional use of a CP-ECC layer, to provide highly reliable LoRaWAN communication (DER < 0.01) with minimized TOA.

We choose to use CP-ECC scheme based on a linear combination of packets, LoRaFFEC described

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • <GW5;GW6> Low SNR.
<GW9;GW17> Medium SNR.

<GW2;GW5;GW6; GW7;GW9;GW17> <GW2;GW7> High SNR. in section 5.2, which is efficient to recover the typical residual errors from a Rayleigh channel up to PER ≈ 0.3. We use LoRaFFEC (128;0.6;2), which spreads the redundancy over 128 frames and so, introduces more time diversity. Notably, the redundancy spreading is higher than the default ADR downlink transmission period 3 . Moreover, LoRaFFEC does not require additional downlink signaling. The redundant data overhead of LoRaFFEC, can either be transmitted in separate frames or piggybacked into existing ones. Here, we choose to piggyback, as the LoRa and LoRaWAN headers overhead are then paid only once, which improves the ToA/b. The frame are lengthened4 by a ratio < 2 and so, the sensitivity loss is not prohibitive as it stays less than one dB as detailed in Sec.

4.4.

ADR opt-MG is set to keep the PER above the correction threshold of LoRaFFEC (128;0.6;2), i.e. PER target =0.3 in our case 5 . LoRaFFEC (128;0.6;2) recovers the remaining erasures and provides high reliability with DER <0.01.

We call ADR HR this combination of LoRaFFEC (128;0.6;2) with ADR opt-MG .

ADR HR Simulation

We compare the performances of ADR HR with ADR TTN the default ADR implementation of TTN. We consider 15 bytes application payload. For the sake of simplicity we do not take into account the sensitivity impact of the varying frame length. The simulated channel is the same as in section 6.3.1.2.

ADR HR performance over the simulated Rayleigh channel appears in figures 6.11 and 6.10 in presence of 1, 2, 4 and 8 GWs when the SNR to all GWs are equal. ADR HR sharply adapts the transmission parameters to reaches DER <0.0.1. For instance, in figure 6.11 ADR HR provides DER < 0.01 over a single GW network with SNR ≥ -21.5 dB. This threshold is reduced as the number of GWs increases. ADR HR provides DER < 0.01 over an 8 GWs network with SNR ≥ -25 dB to all GWs.

However, as shown in figure 6.11, ADR HR TOA is higher than ADR TTN for channels with low SNR (-17 dB and -23 dB for respectively 1 or 8 GWs). This corresponds to the extra energy invested by ADR HR to achieve a more reliable communication than ADR TTN . For higher SNR values, the transmission parameters adjustments of ADR HR are more fine-grained and the same reliability is obtained for lower TOA as shown in figure 6.11.

ADR HR on Replayed Traces

The results from real world traces replay, with same subset as in Sec. 6.3.1.3 shown in Fig. 6.12 and Fig. 6.13 confirm the simulation results. Either the most robust transmission parameters are used or DER <0.01 is achieved.

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • <GW5;GW6> Low SNR.
<GW9;GW17> Medium SNR.

<GW2;GW5;GW6; GW7;GW9;GW17> <GW2;GW7> High SNR. .12: DER as a function of P Tx , for selected real world series of frames replays.

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • <GW5;GW6> Low SNR.
<GW9;GW17> Medium SNR.

<GW2;GW5;GW6; GW7;GW9;GW17> <GW2;GW7> High SNR.

Chapter Conclusion

Conclusion

In this chapter we used the channel model draw from the traffic collected on a real-world Lo-RaWAN deployment to tailor optimized ADR.

First, we describe ADR opt-SG , which statically optimizes the LoRaWAN ADR parameters in the presence of a CP-ECC-based reliability layer in the case of a mono-GW cell. This first approach demonstrates the substantial gains that can be obtained, in reliability and in TOA, by the joint use of CP-ECC and an optimized ADR. However, ADR opt-SG is a rough approximation and does not exploit the natural macro-diversity of LoRaWAN multi-GWs cells.

Then, we describe ADR opt-MG which derives the expected PER for any transmission parameter settings in presence of an arbitrary amount of GWs in range. This PER prediction is the basis allowing ADR opt-MG to be configured to match an arbitrary reliability goal in terms of PER. ADR opt-MG inherently takes into account macro-diversity and the observed channel variability due to SSF.

Finally we described ADR HR which is the integration of CP-ECC into ADR opt-MG . ADR HR efficiently provides high reliability (DER < 0.01) in LoRaWAN networks, even for challenging transmission conditions. It is a significant improvement over the LoRaWAN ADR implemented by The Things Network. ADR HR tackles the inevitable frame losses with LoRa communications by the use of CP-ECC. ADR HR does not necessitate any additional downlink transmissions compared to the legacy LoRaWAN ADR.

ADR opt-SG , ADR opt-MG and ADR HR TOA are bounded by the maximal effort configuration, warrant scalability and are realistic options for current and future deployments. The ADR opt-SG , ADR opt-MG and ADR HR propositions are validated both by simulation and by replaying experimental channel transmission traces.

We adopted here the quasi-static Rayleigh channel model which corresponds to an urban Lo-RaWAN deployment. But as we detailed the design steps of our optimized ADR opt-MG , we give the opportunity to adapt the same method to other channel models such as Rice or AWGN channel models.

Chapter 7 Conclusion

This concluding chapter summarizes the main contributions of this thesis and highlights their consequences for the use and future evolutions of the LoRaWAN technology.

The chapter 4 shows that the LoRaWAN link in an urban environment can be characterized as following a quasi-static Rayleigh channel model (also called slow Rayleigh channel). It means that the received signal power varies for each new transmission around its average following an exponential law. As a result, a significant fraction of frame transmission is confronted to an extremely hostile channel. Correctly decoding and receiving this small fraction of frames would require the use of the most robust modulation parameters. Such modulation parameters are therefore overkill for most transmissions which do not undergo such attenuation. Moreover, these more robust modulation parameters have a lower data rate and thus have longer transmission time. It results in higher network load and higher energy consumption for the terminals devices. For instance 5% of frames experience an attenuation 13dB above the average, which is more than the sensitivity delta between least and more robust parameters of a standard LoRaWAN network (-12.5dB from spreading factor 7 to 12). We claim it is counterproductive to seek to receive these frames only by pushing the modulation towards a better sensitivity. It is therefore necessary to either design the applications so that they are tolerant to this data loss floor, or to design an accurate reliability protocol in LoRaWAN.

Due to the strong constraints of LoRaWAN, mostly the non-slotted Aloha access method, the large amount of terminal devices to be connected and the extremely restrained downlink capacity, the design of an efficient and viable reliability protocol is challenging. Indeed, the conventional error control methods such as acknowledgments or blind systematic repetition of each frame a large number of times are inadequate because these methods congest the network. We show in chapter 5 that the use of error correcting codes applied across packets is particularly adapted and can provide high reliability in LoRaWAN. This approach introduces time diversity into the communication and therefore smooths the channel packets losses. Thus the residual packet losses, including the losses in burst, are compensated and repaired by the error correcting code, without having to resort neither to acknowledgments at a high frequency, nor to resorting to an over-calibrated frame repetition rate. The two solutions for LoRaWAN's reliability build on cross-packet error correction code can maintain the data loss rate below 1% despite packet loss rates of up to 40% and 92% respectively.

The availability of a reliability protocol based on cross-packet error correction code changes the paradigm for the use of the LoRaWAN physical layer: the LoRa modulation. Thanks to the ability to compensate for packet losses, the constraints on the LoRa modulation parameters are relaxed.

In particular, in order to receive the full data, it is no longer necessary for all the frames to be received with a power above the demodulation threshold. On the contrary, as we show in chapter 6, it is possible and even relevant to configure the parameters of the physical layer in order to voluntarily obtain a packet loss rate just below the tolerance threshold of the reliability layer. The cross-packet error correction code ensures the stability and reliability of the communication, and the transmission time is optimized.

CMAC

Figure 1 . 2 :

 12 Figure 1.2: Basic digital modulations of valence V = 2: The information is encoded by (a) the amplitude of the baseband signal (b) the amplitude of the signal on a carrier, (b) the frequency on a carrier, (c) the phase on a carrier.

Figure 1 .Figure 1 . 5 :

 115 Figure 1.5 plots the performance of the Pure-Aloha and Slotted-Aloha methods.

  0

Figure 1 .

 1 Figure 1.12: Minimal E b N 0 as a function of the spectral efficiency ( DR net BW ) following the Shannon Equation.

Figure 2 . 4 :Figure 2 . 5 :

 2425 Figure 2.4: LoRa chirps for spr ead i ng f ac t or (SF) ∈ [7..12] and BW ∈ {125, 250, 500}k H z on the CF =868.5MHz channel.

  ToA per application bit, ToA/b, to be the overall time spend for the transmission of one application bit: ToA/b = Time-On-Air Number of bits in the application payload . In Fig. 2.11 we show the ToA/b cost to transmit a 25 bytes application PL with SF ∈ [7..12], CR ∈ { 4 5 ; 4 8 } and Nb Trans ∈ [1..3] with BW =125 kHz. The ToA/b cost smoothly increases as we move toward more robust transmission parameters. The transmission with the most robust configuration is two orders of magnitude more costly in TOA than the least robust one.

Figure 2 . 11 :

 211 Figure 2.11: Time-On-Air by applicative bit (ToA/b) cost for 25 bytes applicative payload over a 125kHz bandwidth for selected transmissions parameters.

Contents 3 . 1

 31 LoRaWAN Link Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.1 LoRa Modulation Analytical and Simulation Studies . . . . . . . . . . . . . . 46 3.1.2 LoRa Experimental Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.3.1 Problems of biased experimental data-sets . . . . . . . . . . . . . . 53 3.1.3.2 Other mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Capacity, Quality of Service and Configuration of LoRaWAN . . . . . . . . . . . . 55 3.2.1 Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.2.2 Adaptive Data Rate (ADR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Error Correction Code (ECC) in LoRaWAN . . . . . . . . . . . . . . . . . . . . . . . 60 3.4 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Figure 3 . 1 :

 31 Figure 3.1: Simulated BER (top figure) and FER for a 10 bytes payload (bottom figure) of uncoded LoRa modulation at SF ∈ {7, 10, 12} following closed-form approximations [81, 102, 127].

  Tables 3.1, 3.2 and 3.3 provide an overview of the experimental characterization of LoRa found in the literature.

3 5 -

 5 models fitted with MMSE: • Log-distance path loss model with log-normal shadowing: γ ground = 2.75 γ 1 st floor = 2.σ ground = 1.3dB σ 1 st floor = 1dB • ITU : N ground = 27.8 N 1 st floor = 25.5 • Multi-wall COST231: α glass = 1.53 α concrete = 4 α brick = 3.2 α glass ;15;14> • ≈ 400m (hybrid) ∆ (RSSI max -RSSI min ) ∈ [10, 40

. 6 - 1 - 4 •

 614 Kf Res-OBS = 23.Kf Car-LOS = 22.6 -Kf Car-OBS = 11.1 -Kf War-LOS = 17.6 -Kf War-OBS = 21.Notice that this P Rx distribution fit is erroneous. See Sec.3.1.3.

[ 123 ]

 123 Outdoor (urban + forest + coastal) <12;NA;NA;NA;20> • 1km (urban) • 4km (coastal) • 800m (forest) Log-distance path loss model with log-normal shadowing: • Urban: γ = 2.7, σ = 11.2 • Coastal: γ = 3.6, σ = 27.5 • Forest: γ = 2.0, σ = 6.9

  path loss model with log-normal shadowing : • Indoor: γ = 2.9, σ = 8 (with walls and floors attenuation factors). • Outdoor: γ = 3.1, σ = 9.7 (with ED height factor H f = -4.7 × log 10 (H ED )). • Urban: γ = 4.2, σ = 7.2 (with H f = -6.3 × log 10 (H ED )) • Rural: γ = 3.0, σ = 6.4 (with H f = -6.65 × log 10 (H ED )) [143] Outdoor (urban + suburban) <NA;NA;NA;NA;14> • 1km (urban) • 4km (suburban) HataLoRa model (derived from Hata model) for Large Scale Fading: • PL(d ) = 122 + 16 log 10 ( d d 0 ) (It is equivalent to log-distance path loss model with γ = 1.6 and PL 0 = 122).

Figure 4 . 3 : 10 ( 10 )

 431010 Figure 4.3: Distribution of the measured SNR and FER as a function of the CR for selected series of frames.

Fig. 4 .

 4 Fig. 4.4 shows FER ref and FER XP for each CR. The black curves show the fitted reliability gain ∆ FER = FER ref -FER XP for the fitted ∆Df. The experimental FER gain ∆FER XP distributions matches the shape of the theoretical FER gain distributions induced by sensitivity gains -0.40 dB, -0.88 dB, -1.21 dB for respectively CR 4 6 , 4 7 and 4 8 .

Figure 4 . 4 :

 44 Figure 4.4: Comparison of the FER with CR = 4 5 against CR = 4 6 , CR = 4 7 and CR = 4 8 . The black curve is the computed FER gain expected for sensitivity gain over a Rayleigh channel.

. 5 .

 5 It shows the SNR distribution for frames of various lengths N s ∈ {48, 128, 298} and the FER for various 5 values of N s ∈ [48..298].Reliability clearly decreases as N s increases. Up to 20 percentage points of FER can be lost between the shortest and longest frames.

Figure 4 . 5 :

 45 Figure 4.5: Distribution of the measured SNR and FER as a function of the number of symbols per frame (N s ) for selected series of frames.

Figure 4 . 7 :

 47 Figure 4.7: ToA/b as a function of the application data payload length for SF 7 and 8 with BW =125kHz and CR= 4 5

Figure 4 . 9 :

 49 Figure 4.9: FER against SF showing the distribution of erasure burst lengths for several LoRaWAN series of frames with two GWs and several P Tx .

Figure 4 . 10 :

 410 Figure 4.10: Experimental PER as a function of FER using BSR with various Nb Trans values.

Figure 5 . 2 :

 52 Figure 5.2: Probability to get less than n successes over a Bernouilli process with n × z trials and a (1 -P e ) success probability. This is the probability to fail at receiving a segment (n, n×z -k) (z = 5 which correspond to CR CCARR = 1 5 ) over a channel with PER = P e . Notice that n=1 is equivalent to LoRaWAN BSR.

Figure 5 . 3 :

 53 Figure 5.3: Probability to get less than n successes in a least one of dn a Bernouilli process with n × z trials and a (1 -P e ) success probability. This is the probability to fail at fully receiving 10 application data frames with CR CCARR = 1 5 with CCARR[START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Lee | A comparative study of wireless protocols: Bluetooth, UWB, ZigBee, and Wi-Fi[END_REF],(5,[START_REF] Berrou | Near Shannon limit errorcorrecting coding and decoding: Turbo-codes. 1[END_REF] or(1,4).

Fig. 5 . 1 CR

 51 Fig. 5.4 shows the computed R TOA-CCARR , the overload ratio to send uplink frames with CCARR, as a function of the channel's PER and z = 1 CR CCARR ∈ {1..15} 1 , with T and T ′ being typical LoRaWAN 1 z = 15 matches the redundancy of the LoRaWAN BSR maximal Nb Trans .

Fig. 5 .

 5 Fig.5.9 displays the DER reached by LoRaWAN BSR with Nb Trans = 5 and our CCARR[START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Coutaud | Adaptive Data Rate for Multiple Gateways LoRaWAN Networks[END_REF] implementation as a function of the FER. LoRaWAN BSR with Nb Trans = 5 measurements have DER = 0 up to FER ≈ 0.25, DER = 0.02 with FER = 0.43, and DER = 0.13 for FER = 0.6. This corresponds to the probabilistic behavior described in sec.5.1.2, as (0.43) 5 < 0.02 and (0.60) 5 < 0.09. Interestingly, CCARR[START_REF] Choi | IEEE 802.11 MAC-Level FEC scheme with retransmission combining[END_REF][START_REF] Coutaud | Adaptive Data Rate for Multiple Gateways LoRaWAN Networks[END_REF] protocol provides DER = 0 for all tests up to FER = 0.67 which is the highest stable FER that we were able to reach with our experimental platform.

Fig. 5 .

 5 Fig.5.10 displays the measured TOA consumed by LoRaWAN BSR with Nb Trans = 5 and our CCARR

1 :

 1 sequence ← Random(fragment#) 2: for all j ∈ sequence do 3: redundantFragment ← LinearCombinaison(WL,RD,fragment[j]); 4: end for 5: Transmit(redundantFragment)

1: for all newFragment do 2

 2

Figure 5 . 20 :

 520 Figure 5.20: Simulated DER as a function of FER with LoRaFFEC (128; 0.6; DD) for various DD. The red dashed line marks the DER = 0.01 threshold.

Figure 5 . 22 :

 522 Figure 5.22: Simulated latency mean of LoRaFFEC (WL; 0.6; 2) as a function of FER.

Fig. 5 .

 5 Fig.5.23 compares the latency's cumulated frequencies of LoRaFFEC with WL = 8 and WL = 128 and over an erasure channel with FER = 0.4: the short window length (WL = 8) recovers more fragments with low latency (latency < 35), but at this point reaches a threshold and cannot recover more lost fragments. In the opposite, the longer window (WL = 128) keeps correcting lost data fragments for longer and up to full recovery (cumulated value = 1).

Figure 5 . 23 :

 523 Figure 5.23: Simulated cumulative frequency of LoRaFFEC (WL; 0.6; 5) as a function of latency over an erasure channel with FER = 0.4.

Figure 5 . 24 :

 524 Figure 5.24: DER of LoRaFFEC (128;0.6;2) as a function of FER on experimental data streams, each dot is an independent experimental stream, with different GW, SF, P Tx combination. The red dashed line marks the DER = 0.01 threshold.

Figure 6 . 3 :

 63 Figure 6.3: Simulation results for DER and TOA as a function of SNR for ADR opt-SG and ADR TTN in a single GW LoRaWAN networks.

Figure 6 . 4 :

 64 Figure 6.4: DER of ADR opt-SG over replayed real world series of packets for several GW.

Figure 6 . 5 :

 65 Figure 6.5: TOA of ADR opt-SG over replayed real world series of packets for various GW. TOA normalized against no FEC, SF7 and Nb Trans =1, for several GW.

Figure 6 . 8 :

 68 Figure 6.8: DER as a function of P Tx , for selected real world series of frames replays.

Figure 6 . 9 :

 69 Figure 6.9: ToA/b as a function of P Tx , for selected real world series of frames replays.

Figure 6

 6 Figure 6.12: DER as a function of P Tx , for selected real world series of frames replays.

Figure 6 . 13 :

 613 Figure 6.13: ToA/b as a function of P Tx , for selected real world series of frames replays.

Table 1

 1

	.1: BER for Binary Frequency Shift Keying (BFSK), BPSK, Multiple Phase Shift Keying (MPSK),
	Quadrature Amplitude Modulation (QAM) [13]. The approximations are consistent for modulation using
	grey mapping and with relatively high SNR.
	Modulation	BFSK	BPSK	MPSK	QAM

•

  Narrow Band: The data rate is reduced with the BW, therefore reducing the noise and improving communication range. A subcategory is the Ultra Narrow Band (UNB) category. UNB defined either by a BW < 1kHz or by a BW narrower than the uncertainty of the transmitter oscillator. It allows for long range communication with efficient spectral efficiency at very low data rate.

			BW	10000Hz		1000Hz		100Hz		10Hz
		-130
	Signal min (dBm)	-150
		-170
		0	100	200	300	400	500	600	700	800	900	1000
						Débit D (bits/s)
					Figure 1.13: Shannon AWGN capacity.

Table 1 .

 1 2: Technical overview of the main LPWANs technologies.Among them, LoRaWAN also knows the stronger academic success. LoRaWAN open-source model, hardware availability, large open networks existence and private network ease of deployment were further catalysts for its success in the research world. We compare in Table1.3, the number of matching articles found via the IEEE Xplore search engine 2 .

	Technology		Frequency Band Modulation		Long Methods	Range	Multiplexing	BW	Uplink Data Rate	Experimental Range
	LoRaWAN [45, 46, 73, 48, 49, 52, 53, 55, 56, 59, 65]	Sub-1GHz ISM		LoRa (CSS) | FSK		SS (CSS) + ECC to x15) (Hamming) + Repetitions (up	Pure-Aloha + CDMA	∈ {125, 250}kHz	183bps-50kbps	30km LOS [74] 14km Urban [153]
	Sigfox [45, 46, 48, 49, 53, 55, 56, 59, 65]	Sub-1GHz ISM		DBPSK		UNB + Repeti-tions (x3)	Pure-Aloha	100Hz	100bps	15km Urban [68]
	Dash7 [49, 52, 53, 56, 65]	Sub-1GHz ISM		GFSK		NB + ECC (Con-volutional)	CSMA/CA	∈ {25, 200}kHz	9.6kbps-166.67kbps 1500m LOS [51]
	802.11ah [56]		Sub-1GHz ISM		(B|Q)PSK (16|64|256)QAM	|	ECC (Convolu-tional + LDPC)	CSMA/CA	∈ [1, 16]MHz	150kbps-86Mbps	500m LOS [64]
	NB-Fi (WAVIoT) [53, 56, 71]	Sub-1GHz ISM		D-BPSK		UNB		TDMA+FDMA	∈ [50Hz, 25.6kHz]	50bps-25.6kbps	NA
	802.15.4k [49, 55, 65]	Sub-1GHz 2.4GHz ISM	|	DSSS (B|Q)PSK | (G-)FSK	SS (DSSS) + NB + ECC (Convolu-tional)	CSMA/CA | Pure-Aloha	∈ [12.5kHz, 1MHz]	3bps-128kbps	3800m LOS 2100 NLOS [50]
	802.15.4g [49, 65]	Sub-1GHz 2.4GHz ISM	|	FSK | PSK | OFDM	SS (DSSS) + NB + ECC (Convolu-tional)	CSMA/CA	∈ [12.5kHz, 1.2MHz]	2.4kbps-800kbps	800m Rural 250m Semi-Rural 150m Urban [60]
	Weightless-N 49, 56, 65]	[46,	Sub-1GHz 2.4GHz ISM	|	DBPSK		UNB + ECC + to x8) Repetitions (up	Slotted-Aloha	200Hz	30kbps-100kbps	NA
	Weightless-P [46, 49, 53, 56, 65]	Sub-1GHz 2.4GHz ISM	|	GMSK | O-QPSK		NB + ECC		TDMA+FDMA	12.5kHz	150kbps-86Mbps	NA
	Telensa [49, 53, 65]	Sub-1GHz ISM |TVWS	BFSK		UNB		NA	NA	62.5bps	NA
	Ingenu OnRamp)[45, 46, 49, (RPMA-53, 56, 65]	2.4GHz ISM		D-BPSK+DSSS +RPMA		SS (DSSS) + ECC	TDMA+CDMA	1MHz	30bps-78kbps	NA
	BLE5-Coded [57]	2.4GHz ISM		GFSK		SS (FHSS) + ECC	TDMA | RTS/CTS	1MHz	112kbps-382kbps	1km LOS 150m NLOS [57]
	Weightless-W [49, 56, 65]	470-790MHz TVWS		16-QAM, OBPSK, QPSK, DBPSK	SS (DSSS) + ECC (convolutional)	TDMA+FDMA	5MHz	1kbps-10Mbps	NA
	Nb-IoT CatNB1) [48, 52, (LTE 53, 55, 56, 59, 65, 67]	700-900MHz Li-censed (LTE or GSM bands)	BPSK|QPSK		SS (FHSS) + ECC + Repetitions (up to 2048 DL and 128 UL)	OFDMA|SC-FDMA	180 kHz	20kbps-50kbps	700m Urban [58] 1km Idoor [69] Open Field 16km [61]
	LTE-M		700-900MHz Li-
	(LTE CatM1 | eMTC)	censed (LTE or	16QAM		SS + ECC		OFDMA|SC-FDMA	1.08MHz	up to 1Mbps	NA
	[56, 65]		GSM bands)
	EC-GSM-IoT [53, 56, 65]	800-900MHz bands) Licensed (GSM	GMSK|8PSK		SS + ECC		CDMA	200kHz	70kbps-240kbps	NA

Table 1.3: Number of keywords occurence in article titles in IEEE Xplore search engine.

Table 2 .

 2 2: Maximal LoRa payload according to protocol documentation and regulation for various regional ISM bands.

	Band	Maximal LoRa payload size (bytes)
		DR ph y min	DR ph y max
	EU863-870	64	255
	US902-928	24	255
	CN779-787	64	255
	EU433	64	242
	AU915-928	24	255
	CN470-510	64	255
	AS923	32	263
	KR920-923	64	255
	IN865-867	64	255
	RU864-870	641	255

Table 2 .

 2 3: Maximal application payload size for packet without any optional fields in the header (i.e. MAC commands) for the minimal and maximal DR ph y in various regions.

	Band	Maximal application payload size (bytes)
		DR ph y min	DR ph y max
	EU863-870	51	242
	US902-928	11	242
	CN779-787	51	242
	EU433	51	242
	AU915-928	11	242
	CN470-510	51	242
	AS923	19	250
	KR920-923	51	242
	IN865-867	51	242
	RU864-870	51	242

  0.41 0.60 0.72 0.82 1.03 1.19 1.23 1.34 1.44 1.79 1.89 2.05 2.16 2.47 2.67 3.08 3.45 3.78 4.01 4.94 5.35 5.67 6.90 7.40 7.56

	ToA/b (ms)	10 20 30 40	SF 7 8 9	10 11 12																							9.87 10.35 10.69	13.80 15.11 16.04	19.74	22.67	27.61	29.61	41.41
		0	< 7;4/5;1>	< 7;4/8;1>	< 8;4/5;1>	< 7;4/5;2>	< 8;4/8;1>	< 7;4/8;2>	< 7;4/5;3>	< 9;4/5;1>	< 8;4/5;2>	< 7;4/8;3>	< 9;4/8;1>	< 8;4/8;2>	< 8;4/5;3>	<10;4/5;1>	< 9;4/5;2>	< 8;4/8;3>	<10;4/8;1>	< 9;4/8;2>	< 9;4/5;3>	<10;4/5;2>	<11;4/5;1>	< 9;4/8;3>	<10;4/8;2>	<10;4/5;3>	<11;4/8;1>	<12;4/5;1>	<10;4/8;3>	<11;4/5;2>	<12;4/8;1>	<11;4/8;2>	<11;4/5;3>	<12;4/5;2>	<11;4/8;3>	<12;4/8;2>	<12;4/5;3>	<12;4/8;3>
																	Configuration <SF;CR;NbTrans>

Table 3 . 1 :

 31 Survey of the experimental LoRa performance measurements.[1/3]

			Maximal	Experi-
		Environment	mented Range (Config. <SF;CR;BW	Characterization
	[72] Outdoor (rural)	(kHz);PL(B);P Tx (dBm)>) <10; 4 6 ;250;10;NA> • 8.15km	RSSI std. dev. ∈ [0.3, 5.6] dB
			<12;NA;125;NA;14>	Log-distance path loss model with log-normal shadowing:
	[74] Outdoor and over sea) (urban [75] Outdoor (open, straight road and wooden areas) [79] Outdoor (urban and rural)	• 15km (ground) • 30km (over sea) <7; 4 5 ;125;NA;P Tx > • 1.21km <12; 4 5 ;125;25(including MAC);14> • 6km	• γ ground = 2.32 • γ sea = 1.762 Log-distance path loss model: • γ open area = 2.8 • γ straight road = 3.2 RSSI std. dev. ∈ [1.12, 5.89] dB	• σ ground = 7.8dB • σ sea = 8dB • γ moderately wooded = 5.9 • γ heavily wooded = 3.5
			<7; 4 5 ;125;NA;14>
	[76] Outdoor (urban)	• 2.3km 5 ;125;NA;14> <12; 4	-
			• 3.5km
	[78]	Indoor (multi-floor university/office building)	<12;NA;125;NA;14> • 390m	RSSI std. dev. ∈ [4.95, 10.51] dB
	[92] Indoor	<12; 4 5 ;125;NA;14> • ≈ 30m

Table 3 .

 3 2: Survey of the experimental LoRa performance measurements.[2/3]

	Outdoor (flat rural and urban)	<12;NA;125;NA;14> • 7.5km	• Log-distance path loss model with log-normal shadowing: γ = 2.71, σ = 7.11dB . • Biased experimental data set: Logger reports only the three
			best receiving GWs for each transmission.
			• Log-distance path loss model with log-normal shadowing:
	[84] Indoor (barn with cows)	<NA;NA;NA;NA;14> • 40m

γ ≈ 2, σ ∈ [2.2, 3.7]dB • Temporal fading: Rician distribution with K-factor ∈ [6.4, 10.2]dB (thus fade margin ∈ [6.0, 10.8]dB) (Erroneous, see 3.1.3.)

Table 3 .

 3 Tx and/or SF might not decrease PER.• Good level of SNR might result in average PDR. • Variation in PDR are important over a day. Std. dev. of the average P Rx 1.29dB and 2.09dB (Outdoor).• Rainfall has negative impact: up to 10dBm are lost (might be due to humidity on outdoor antenna). • Presence of people in the building increases P Rx std. dev.(from 0.8 to 3.5 dBm). 3: Survey of the experimental LoRa performance measurements.[3/3]

			4 5 ;500;9;7>
			• 450m (LOS)
			<6; 4 5 ;500;9; 20>	• High temperature has severe impact on the communica-tion range.
			• 90m (NLOS with dense vegetation) <8; 4 8 ;125;9;7>	• Vegetation has severe impact on the communication range. • P Tx is not key to range.
			• 900m (LOS)
	[101] Outdoor (urban)	• 8km <12; 4 5 ;125;NA;14>	-
	[88]	Outdoor (antartic LOS and NLOS)	<12; 4 5 ;125;3;14> (868 and 433 MHz bands) • ≈ 30km	• Log-distance path loss model: γ ∈ [1.5, 2.3] • ∆ (SNR max-SNR min ) indoor ≈ 3.5dB
	[116] Outdoor (tree farm LOS)	<7; 4 5 ;250;9;13> • 200m	• Fresnel zone clearance, and thus antenna height, has se-vere impact on reliability: PDR increases from 25% to 100% for antenna height increasing from 0m to 2m.
	[111] • Increasing P [105] Outdoor (urban over public net-work) <11; 4 5 ;125;NA;14> • 13.2km Outdoor (sub-urban) + indoor (office) (434MHz and 868MHz ISM bands) <12;NA;NA;2;NA;> • 2.4km (NLOS) • 4km (LOS) • [133] Outdoor (subur-<12; 4 5 ;125;NA;14> • Log-distance path loss model: γ toward = 3.9 γ away = 5.2 • Signal fluctuations become more apparent for larger dis-ban LOS body-to-• 1.44km tances because of increasing influence of ground and sur-body) rounding buildings reflections.
	[120] Outdoor (urban + suburban)	<12;NA;NA;16;10> • 2.1km (LOS 434MHz • 10.6km (NLOS only 868MHz) and	• Received power fluctuates periodically: it drops by more than 20dBm for approximately an hour twice a day.
			434MHz)
	[118]	Outdoor/Indoor (high density ur-ban area NLOS + suburban/rural)	<12; 4 5 ;125;NA;14> • 200m (urban) • 2km (subur-ban/rural)	• LoRa ED to ED has lower range than ED to GW. • Signal in rural environment is more stable than in urban environment.

• Cause of these received power drops is not fully determined. It might be due to daily changes in the troposphere's index of refractivity.

Table 3 .

 3 4: ECC usage in various networking technologies.

Table 4 .

 4 1: Transmissions configurations used in the experiments

	P Tx (dBm)	SF	CR	N s
	XP1 {0; 2; 4; 6; 8; 10; 12; 14} [7..12] XP2 {0; 2; 4; 6; 8; 10; 12; 14}    7 7 [8..12]	4 5 6 ; 4 5 ; 4 { 4 7 ; 4 8 } { 4 5 ; 4 8 } 4 5	{38; 43; 48; 53} (15 Bytes PL) 50 {80;98;128;178;200;224;248;280;298}

Table 4 .

 4 Comparison of the FER with N s = 48 (Small) and N s = 128 (Medium) against N s ∈ [296..298] (Large). The black curve is the computed FER gain expected for sensitivity gain over a Rayleigh channel. 2: Ordinary Least Square (OLS) values of the ∆Df gains for various frame lengths compared to N s ∈ [296..298].

	Frame Error Rate					0.00 N s • Large 0.25 ∆ FER XP 00 0.25 0.50 0.75 1.00 ∆ FER (∆ Df = -2.5 dB) 0.50 Small	0.75	1.00
				Frame Error Rate with Large frames.
	Figure 4.6: N s	48 [78..80] [96..98] 128 [17..178] 200 [223..224] 248 [278..280] [296..298]
	∆Df (dB)	-2.50 -1.93	-1.74 -1.28	-0.85	-0.70	-0.48	-0.39	-0.11	0
	χ 2 (×10 -4 )	8.844 4.903	3.673 2.366	2.018	1.693	1.393	2.056	0.949	0
	Frame	0.16	0.27	0.33	0.43	0.6	0.96	0.75	0.83	0.94	1
	Length
	Ratio

Table 5 .

 5 1: Frames TOA during experiments.

	Link	SF TOA (ms) Payload (Bytes)
	Up	12	1646.6	16
	Down	9	164.9	2

Table 5 .

 5 2: CCARR implementation extra code sizes12

  • Link FER ∈ [0; 0.4[: with this link quality, LoRaFFEC is very efficient and provides DER < 0.01. With the same overhead, BSR with Nb Trans = 2 is less reliable, with a DER difference comprised between a few percentage points up to more than 15 percentage points . • Link FER ∈ [0.4; 0.6[: in this case, LoRaFFEC DER increases toward the FER, crossing BSR with Nb Trans = 2 DER for FER ≈ 0.47 at DER = 0.75. With such "bad quality channel", it is difficult to ensure a high DER with a reasonable overhead. Other actions to reduce the FER, such as SF or P Tx increase, need to be taken. • Link FER ∈ [0.6; 1]: LoRaFFEC does not provide any erasure recovery and LoRaWAN BSR is better but this very high DER range is already unpractical . Overall, LoRaFFEC is very efficient in the FER ∈ [0; 0.4[ range.

  Experimental DER as a function of P Tx using several combinations of SF and Nb Trans with roughly equivalent TOA .

						GW3[1.03km]
		1.0	•
				•
		0.9
					•
		0.8
		0.7
	Data Error Rate	0.4 0.5 0.6				•
		0.3				•
		0.1 0.2	•	SF07x32 SF08x16 SF09x8	SFxNB TRANS SF10x4 SF11x2 SF12x1		•
		0.0						•	•
			0	2	4	6 P Tx (dBm) 8	10	12	14
	Figure 6.1:

  , we have to compute what would be the size of the sample (Size sample ) with its censored part, i.e. the erased frames: SNR ≈Max (S UMED ) = 10 × log 10 CDF -1 exp 0.95 (1/Size sample ) 2 SNR = ChHistory GW (SNR max ) -SNR ≈Max (S UMED ).

			+	10 × log 10 CDF -1 exp 0.05 (1/Size sample ) 2
	From this we estimate SNR in dB:
	Size sample =	20 (1 -FER current )	× Nb Trans
	We then estimate what would be the maximal value of such a sample following Unit Mean Expo-

nential Distribution (UMED). We approximate the theoretical SNR Max (S UMED ) by SNR ≈Max (S UMED ) that we define as the middle of the interval in which there is 90% chances that this maximum SNR lies, with Size sample trials:

  cypher-based message authentification code. 38 Cnt App LoRaFFEC Applicative Data Unit Counter. 91 CP-ECC Cross-Packet ECC. 16, 18, 46, 60, 73, 78, 88, 90-92, 94, 95, 103, 106, 108, 109, 114, 116, 119, 126 CR coding rate. 16, 19, 34, 35, 40, 43, 47, 48, 50-52, 64, 66-69, 75, 78, 83, 103, 114, 121, 141, 142 CRC cycling redundancy check. 18, 34, 35 CSMA Carrier Sense Multiple Access -Also refered to as Listen-Before-Talk (LBT). 11, 12 CSMA/CD Carrier Sense Multiple Access with Collision Detection. 11 CSS chirp Spread Spectrum. 32, 34 D Distance between the transmitter and the receiver. 9, 10, 149, 151 d 0 Reference distance for the log-distance model. 10, 150 D frame Frame duration. 12, 13, 67, 141 DAB Digital Audio Broadcasting. 4 DD LoRaFFEC Decoding Depth parameter. 77, 91, 94-98, 143 DER Data Error Rate. 25, 38, 40, 56, 60, 78, 85-91, 96-99, 102, 103, 106-112, 117, 119, 121, 122, 124, 126, 143, 144 Applicative Data Rate -The data rate available and usable by the application layer. 25, 40 DR mod Modulation Data Rate -The data rate of the physical modulation (sometimes refered to as "gross bit rate" or "raw bit rate"), i.e. the symbol rate of the modulation mutiplied by the signal valence. 6, 7, 34, 36, 39, 148 DR net Physical net Data Rate -The data rate provided by the physical layer i.e. the number of bits -transmitted to the upper layer thus excluding protocols overhead and potential erasure correction code overhead-transmitted per seconds. 7, 23-25, 141 DR ph y Physical Data Rate -The data rate of the physical layer i.e. the modulation data rate (DR mod ) multiplied by the coding rate of the potential erasure correction code redundancy. 7, 34-36, 38-41, 145 Rx divided by the number of bits in the packet. 22-25, 46, 48, 141, 151 ECC Error Correction Code -Also known as Forward Error Correction (FEC). v, 3, 4, 11, 15-19, 26, 34, 35, 45, 47, 48, 59, 60, 63, 64, 66, 75, 78, 79, 105, 119, 141, 148 LSB Least Significants Bytes. 91 LSF Large Scale Fading. 9, 10, 53, 75, 149 LTE Long-Term Evolution. 4 MAC Medium Access Control. 5, 11, 14, 30, 64 MIC message integrity code. 38 MPC Multiple Parity Check. 92, 95 MPSK Multiple Phase Shift Keying. 22, 145 MSB Most Significants Bytes. 91 µ Means of the natural logarithm of random variable following the log-normal distribution. 11, 12, 149 N 0 Noise Spectral Density, i.e. the noise power per unit of bandwidth. 7, 8, 22-25, 46, 48, 141, 151 N s number of symbols per frame. 64, 67-69, 142, 145 Nb Trans LoRaWAN number of frame transmission: NB Trans = 2 each frame is emitted twice. 39-43, 73, 80, 82-89, 96, 100, 102, 103, 106-110, 113-117, 142-144 NS Network Server. 30-32, 38, 39, 41, 42, 55, 58, 59, 77-80, 82, 85, 87, 88, 91, 93-95, 106, 109, 114, 115, 142 OLS Ordinary Least Square. 67-69, 145 OSI Open Systems Interconnection. 5, 30, 141 P e Probability of error. 12-14, 18, 81, 82, 141, 143 P g Processing gain of a spread spectrum modulation: P g = BW narrow BW wide . 8 P N Noise floor power, i.e. the strengh of the sum of all noise sources. 7 P Rx Received signal power, i.e. the strengh of the received signal. 3, 7-10, 23-25, 51-53, 55-59, 74, 106, 141, 148, 151 P Tx Transmitted signal power, i.e. the strengh of the transmitted signal. 9, 10, 23, 34, 35, 40-42, 50-52, 59, 64-67, 72-74, 88, 97, 102, 103, 106, 107, 109, 110, 114, 119, 120, 124, 125, 142, 144, 151 PA Power Amplifier. 23 PER Packet Error Rate. 25, 38-40, 42, 53, 56, 58, 60, 73, 78-85, 103, 106, 108, 109, 114-117, 119, 121, 126, 142, 143 π 3.1415. 9, 10, 22 PL Path Loss -The attenuation of the signal between the transmitter and the receiver: PL = P Tx P Rx . 9-11, 23, 40, 55, 56, 58, 59, 64, 85, 149, 150 PL 0 PL at the reference distance d 0 for the log-distance model. 10 PMR446 Private Mobile Radio 446. 4 QAM Quadrature Amplitude Modulation. 22, 145 RD LoRaFFEC Redundancy Density parameter. 77, 91, 94-97, 143 RS Reed-Solomon. 18, 19, 141 RSSI Received Signal Strength Indication. 55 S Surface power density emitted by an isotropic antenna -S = P Tx 4×π×D 2 . 9, 10 sensitivity Minimal required received power for correct demodulation, it can either be in absolute value P Rx or relative to the noise power with a minimal SNR or a minimal E b N 0 . 7, 24 SF spreading factor. 32-34, 36, 37, 39-43, 46-48, 50-52, 56-61, 64, 66-69, 73, 74, 83, 88, 97, 102, 103, 106, 107, 109, 110, 114, 115, 117, 121, 142, 144 ShF Shadow Fading. 9-11, 53, 56, 57, 75, 149 σ 2 Variance of the natural logarithm of random variable following the log-normal distribution. 11 SNR Signal-to-Noise Ratio. 7, 8, 22-24, 40-42, 46, 47, 53, 58, 59, 65-68, 73, 74, 78, 109-111, 114, 115, 117-119, 121-123, 142-145, 151 spectral efficiency Spectral efficiency -Number of bits transmitted per second and per hertz (noted η). 7, 24, 25, 141 SSF Small Scale Fading. 9, 11, 53, 56, 57, 59, 75, 126 T symbol Symbol duration. 32 TDMA Time Division Multiple Access. 12 TOA Time-On-Air. 29, 39-41, 55, 56, 58-60, 69, 74, 77-79, 81-84, 86-89, 103, 106, 107, 109-111, 113-115, 117, 119, 121, 126, 143-145 TTN The Things Network. 55, 64 UMED Unit Mean Exponential Distribution. 114, 115 UMTS Universal Mobile Telecommunications System. 4 V Valence of a signal -Number of possible differents states of a transmitted signal. 6, 7, 141 W Watt -Power unit: 1W = 1kg × m 2 × s -3 . 9, 10 WL LoRaFFEC Windows Length parameter. 77, 91-97, 99-101, 143 WLAN Wireless Local Area Network. 4, 20 WPAN Wireless Personal Area Network. 4, 21 WWAN Wireless Wide Area Network. 20, 21

	Df demodulation floor. 65-69, 142, 145
	dPMR446 Digital Private Mobile Radio 446. 4
	DR Data Rate. 90
	DR ap p DSSS Direct Sequence Spread Spectrum. 26
	DTT Digital Terrestrial Television. 4

DVB-S

Digital Video Broadcasting -Satellite. 4 E b Energy per bit, i.e. the P

from the devices to the gateways

Search for keyword occurrence in title from https://ieeexplore.ieee.org on the 24/06/21.

Few off-topic results prior to 2010 where filtered out.

The equation is an approximation because the CR is fixed to4 8 over the preamble and lower CR are applied only over the payload and its CRC.

With Semtech SX1301[171] chip and 14dBm transmission power (P Tx ).

Version 1.0.3 github.com/Lora-net/LoRaMac-node [172].

github.com/TheThingsNetwork/lorawan-stack

For a given received LoRaWAN packet only the best SNR value is kept.

B-L072Z-LRWAN1 LoRa®/Sigfox™ Discovery kit.

Notice that because each SF does not encode the same amount of bits and because the intra-frame ECC add redundant Bytes to the payload in a non continuous manner, some value of N s might not be feasible with some transmissions parameters combination. Frame with up to 2 less symbols are then used.

In particular 48 and 298 that are key values to compare precisely between different SF and CR.

Code is available at https://gricad-gitlab.univ-grenoble-alpes.fr/coutaudu/LoRa_QoS

[START_REF] Goldsmith | Wireless communications[END_REF] (LoRaWAN headers) + 15 bytes to 13+1+(15+3)×2 = 37 bytes of payload respectively without and with LoRaFFEC.

The TTN NS keeps only the last 20 frames.

Limited to ACK_LIMIT+ACK_DELAY=96 frames.

A 15 bytes application payload needs

symbols at SF =7. This becomes with LoRaFFEC 1 + (15 + 3) × 2 = 37 bytes, and 83 symbols at SF 7 (with CR =4 5 ).5 Notice that a slightly higher PER target could be used at the expense of stability and latency.

the capacity to thousands of EDs per cell. This observation underlines the need for an efficient automatic parameterization mechanism in LoRaWAN, i.e? an optimized and efficient ADR.

Chapter 4

LoRaWAN Link Characterization // Compute a prediction of the PER for each configuration. //Choose the best configuration that fits the PER requirement and minimal ToA.