Francesca Cuomo

Julio César

Carrasquel Gámez

Antonio Maurizio

Laura Scipione

Manuel Campo

Alberto Caponi

Giuseppe Bianchi

Giampaolo Rossini

Patrizio Pisani

Towards Traffic-oriented Spreading Factor allocations in LoRaWAN systems

Keywords: Low power wide area networks, Internet of Things, LoRaWAN, Spreading Factors, Resource Allocation

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Within the captivating wave of The Internet of Things (IoT), the LoRaWAN (Long-Range Wide Area Network) has raised up as a prominent network infrastructure for long-range communication of ultra low-powered devices. Nonetheless, still some challenges regarding the network scalability need to be addressed. For serving an enormous amount of devices, and thereby for exploiting the LoRaWAN potential, it is essential to come up with a suitable allocation of the wireless resources. Different standards have arisen in this field, like it is surveyed in [START_REF] Raza | Low power wide area networks: An overview[END_REF]. As for the wide-range technologies three main standards have been designed: i) Sigfox, which uses the industrial, scientific and medical (ISM) radio band to transmit data over a very narrow spectrum to and from connected objects; ii) LoRaWAN, emerging as a power efficient wireless communication over very long distances; iii) Narrowband IoT, a new 3GPP cellular technology providing wide area coverage for the IoT. The first uses the ISM band efficiently (by occupying narrow chunks of spectrum), and it experiences low noise levels; the price is a maximum throughput of about only hundreds of bit/s. The LoRaWAN, designed by the LoRa Alliance [START_REF] Sornin | LoRaWAN Specification[END_REF], is operated in the ISM band using a proprietary spread spectrum technique developed and commercialized by Semtech Corporation [START_REF] Semtech | LoRa[END_REF] [START_REF] Bor | LoRa for the Internet of Things[END_REF]. It provides a bidirectional communication at data rates up to 50 kbit/s and is able to cover radio ranges of the order of kilometers [START_REF] Petäjäjärvi | Performance of a low-power wide-area network based on LoRa technology: Doppler robustness, scalability, and coverage[END_REF]. Finally, the NB-IoT [START_REF] Gozalvez | New 3GPP Standard for IoT [Mobile Radio[END_REF] [START_REF] Wang | A Primer on 3GPP Narrowband Internet of Things[END_REF] is a new cellular system operating in a narrowband spectrum portion of the LTE (licensed). It is suitably designed for applications requiring low latency and having the need to communicate more frequently than the ones used in LoRaWAN. LoRaWAN indeed can be ideal for applications that have sporadic communication requirements (e.g. a couple of times per day) and need low energy consumption in order to increase battery lifetime. In this framework, several works have analyzed the potentialities of LoRaWAN systems in terms of scalability and performance [START_REF] Bor | Do LoRa Low-Power Wide-Area Networks Scale?[END_REF] [START_REF] Voigt | Mitigating inter-network interference in lora networks[END_REF].

In our preliminary work [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF] we defined the EXPLoRa-Air Time (AT) solution playing with the LoRa modulation technique based on the Spreading Factors (SF) to improve the throughput and Data Extraction Rate (DER) performance compared with the Adaptive Data Rate (ADR) proposed in [START_REF] Semtech | LoRa[END_REF]. The main result of EXPLoRa-AT is that there is the possibility, in the radio range of a LoRa Gateway (GW), to allocate different SFs to the transmitting End-Devices (ED), with the goal of ensuring a similar Time on Air period to all of them and inducing less collisions and ultimately an higher throughput. However, the EXPLoRa-AT was designed under the assumption of having all end-devices transmitting with the same message rate and payload. In this work, we extend that approach to provide an EXPLoRa solution tailored to the different applications and traffic loads that will be supported in LoRaWAN systems. The remainder of this paper is structured as follows. Sec. II presents the current literature related to our research topic. Sec. III briefly describes the considered LoRaWAN system. Sec. IV describes our proposed algorithms; Sec. V reports the simulation scenario and results. Finally conclusions are highlighted in Sec. VI. (i) Works analyzing the current capabilities and limitations of LoRaWAN [START_REF] Adelantado | Understanding the limits of lorawan[END_REF][5] [START_REF] Georgiou | Low Power Wide Area Network Analysis: Can LoRa Scale?[END_REF][8], and studing its performance under specific settings [START_REF] Magrin | Performance Evaluation of LoRa Networks in a Smart City Scenario[END_REF][14] [START_REF] Varsier | Capacity limits of LoRaWAN technology for smart metering applications[END_REF]. (ii) Papers proposing novel approaches and heuristics to optimize the network performance [START_REF] Bor | LoRa for the Internet of Things[END_REF][16] [START_REF] Abdelfadeel | Fair Adaptive Data Rate Allocation and Power Control in LoRaWAN[END_REF][18] [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF]. As for the first group, Adelantato et al. surveyed in [START_REF] Adelantado | Understanding the limits of lorawan[END_REF] the limits of LoRaWAN. An issue concerns the maximum duty cycle (DC) allowed within the ISM band. For instance, the 1% for the U E 868 M Hz band turns out into a maximum transmission time of 36 secs in an hour, for each device. This also limits the LoRa gateways in the down-link channel, which have to comply with the DC regulation. Another important analysis in [START_REF] Adelantado | Understanding the limits of lorawan[END_REF] regards the use of ALOHA in a LoRaWAN deployment, which simplifies the network implementation, but at the expense of the throughput that is significantly limited by collisions. Petäjäjärvi et al. in [START_REF] Petäjäjärvi | Performance of a low-power wide-area network based on LoRa technology: Doppler robustness, scalability, and coverage[END_REF] analyzed the capacity of a LoRaWAN cell. For applications requiring transmission of only a single packet per day, the cell may serve up to millions of devices. However, in case of applications reporting messages every minute, only few hundreds of devices may be hosted. Petäjäjärvi et al. in [START_REF] Petäjäjärvi | Performance of a low-power wide-area network based on LoRa technology: Doppler robustness, scalability, and coverage[END_REF] also evaluated the performance of the LoRa communication under the presence of the doppler shift. The results concluded that with SF = 12 (which enables the longest range) the communication deteriorates when relative speed exceeds 40 km/h whereas with a lower mobility it can be assured a reliable communication; finally, it was also evaluated the coverage attained by a LoRa device transmitting with SF = 12 and a transmission power of 14 dBm; as a result, it was determined the feasibility of communicating within a distance of 2 -5 km, and in a range of 15 -30 km on the water.

Georgiou et al. in [START_REF] Georgiou | Low Power Wide Area Network Analysis: Can LoRa Scale?[END_REF] showed how the coverage probability drops exponentially as the number of network devices grows due to the interfering signals using the same spreading factor, which is concluded to be perhaps the most significant limits towards scalability on LoRa. Scalability issues also have been addressed in by Bor et al. in [START_REF] Bor | Do LoRa Low-Power Wide-Area Networks Scale?[END_REF] where it was identified a LoRa link model for the communication range and the collision behavior. They also provided the LoRa simulator (LoRaSim) implementing the link behavior model.

In addition, it has been of interest the evaluation the LoRaWAN performance in smart city scenarios. Magrin et al. in [START_REF] Magrin | Performance Evaluation of LoRa Networks in a Smart City Scenario[END_REF] implemented a model using the ns-3 simulator to study the performance in a typical urban environment. It was developed a path loss model where devices inside the buildings may be affected by building penetration losses. There were executed simulations with thousands of devices following a Pareto distribution. It was concluded that LoRaWAN with the ADR scheme may scale well only if there are numerous gateways suitably deployed across the system. i.e., a packet success rate of 95% for 15000 devices is attained only if there are 75 gateways. Other works dealt with application-tailored deployments such as in [START_REF] Petäjäjärvi | Evaluation of LoRa LPWAN technology for remote health and wellbeing monitoring[END_REF] where it was studied the support of LoRa for health care monitoring, or in [START_REF] Varsier | Capacity limits of LoRaWAN technology for smart metering applications[END_REF] for hosting smart metering devices.

For optimizing the performance of LoRa, many works have addressed the scalability issue. To this aim, several heuristics have been focused on how to efficiently allocate the wireless resources. Reynders et al. in [START_REF] Reynders | Power and spreading factor control in low power wide area networks[END_REF] developed a scheme to efficiently assign the SF and the transmission power across the devices. On the other hand, Abdelfadeel et al. presented in [START_REF] Abdelfadeel | Fair Adaptive Data Rate Allocation and Power Control in LoRaWAN[END_REF] a fair adaptive data rate algorithm (FADR) which computes a data-rate and transmission power allocation in order to achieve fairness in data-rate and reduce collision among nodes.

Conversely, the EXPLoRa heuristic [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF] aims to efficiently distribute the SFs among end-devices: the EXPLoRa-SF tries to equally distribute the SFs among the total number of nodes only constrained by the Receiver Signal Strength Indicator (RSSI) values. A more sophisticated approach, EXPLoRa-AT tries to equalize the Time-on-Air of the transmitted packets among the SF channels. The solutions presented in this paper are an upgrade of the latter approach by taking into account different traffic areas as well as variable payloads and message periods, thereby being able to precisely determine and equalize the traffic load for each SF channel, expressed in terms of symbol time.

Other efforts for optimizing the network have been done tackling other solutions such as the usage of new LoRa transceivers [START_REF] Bor | LoRa for the Internet of Things[END_REF] or the development of multi-hop communication for choosing the minimal Time-on-Air path [START_REF] Sartori | Enabling RPL multihop communications based on LoRa[END_REF].

III. LORAWAN

The LoRaWAN architecture has a star topology, where enddevices are connected to one or more gateways which, in turn, are connected to a common Network Server (NetServer). The communication between end-devices and gateways is spread out on different frequency channels and data rates. LoRaWAN uses up to 6 different programmable Spreading Factors (SF): 7, 8, 9, 10, 11, 12. Furthermore, also the adopted bandwidth can be configured: 125 kHz, 250 kHz and 500 kHz (typically 125kHz for the 868 ISM band.) For a given SF, the narrower the bandwidth is, the higher the receiver sensitivity.

The selection of the data rate is a trade-off between communication range and message duration, given that communications at different SFs do not interfere with each other. LoRaWAN data rates range from 0.3 kbps to 50 kbps. To maximize both battery lifetime of the end-devices and overall network capacity, the LoRaWAN network infrastructure can manage the data rate and Radio Frequency output for each end-device individually by means of the ADR scheme. The relation between nominal bit rate and SF is given as: R = SF * CR 2 SF /BW , where BW is used bandwidth and CR the adopted Code Rate.

In the following we propose two schemes that can be easily applied at the NetServer in order to allocate to the EDs the SFs to transmit their data to a GW.

IV. TRAFFIC-ORIENTED EXPLORA HEURISTICS

EXPLoRa aimed at allocating in a suitable way the SFs to network devices in order to improve the Data Extraction Rate (DER) and the network throughput. Similarly to [START_REF] Bor | Do LoRa Low-Power Wide-Area Networks Scale?[END_REF] we define the DER as the ratio of messages correctly received by the GWs to the transmitted messages either from all network devices (overall DER) or from just a single ED, computed in a given time period.

The selection of a specific SF value firstly depends on the average RSSI with which messages arrive to the gateways. The RSSI value depends on the distance between the ED and the gateway according to the L pl (d) path loss model [START_REF] Bor | Do LoRa Low-Power Wide-Area Networks Scale?[END_REF]:

L pl (d) = L pl (d 0 ) + 10γ log( d d 0 ) + χ σ [dB] (1)
where L pl (d 0 ) is the mean path loss at the reference distance d 0 , γ is the path loss exponent and χ σ ∼ N (0, σ 2 ) is the normal distribution with zero mean and σ 2 variance to account for shadowing. For each SF, Table I presents the sensitivity and distance thresholds for EDs operating at 125 kHz, based on the LoRaWAN specification and the described path loss model. For instance, a device within a maximum distance of 74 meters from the gateway needs to have a RSSI value greater than -126.50 dBm to be successfully decoded at the GW; to this aim a SF = 7 must be assigned.

In the LoRaWAN, the allocation of SF to an ED is important for different reasons: a high spreading factor value corresponds to a high coverage distance within which the ED messages can be correctly received, but it implies a low bit rate and a consequent high Time-on-Air (ToA). The Time-on-Air for an ED message is defined as T s • P L sym where T s is the symbol time of the message defined as T s = 2 SF BW whereas P L sym is referred as the payload size expressed in symbols. Clearly, the higher the spreading factor the higher the symbol time T s is. Thus, in case of high SFs [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF][START_REF] Adelantado | Understanding the limits of lorawan[END_REF][START_REF] Georgiou | Low Power Wide Area Network Analysis: Can LoRa Scale?[END_REF], the communication channel will be occupied for a long time, increasing the possibility of collisions between packets concurrently transmitted. However, since different SFs are mutually orthogonal (or pseudoorthogonal) this enables to have more communications in the same channel without collisions. The idea of EXPLoRa [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF] was to play with this tradeoff, so we planned to use all available SF values (7, 8, ..., 12) for all EDs covered by a GW with the objective of improving the DER (by reducing the collision rate) and the throughput.

A. EXPLoRa -K-means

A first evolution of EXPLoRa is the K-means based one (named EXPLoRa-KM) which aims to improve the behavior of EXPLoRa-AT when in the considered scenario there exist some critical areas, i.e. crowded regions with a significant concentration of nodes with a high probability of collisions. In particular, it employs the K-means technique described in [START_REF] Bishop | Pattern Recognition and Machine Learning (Information Science and Statistics)[END_REF] to identify in the considered scenario these critical areas. The K-means is simply used to derive centroids of the EDs covered by a GW in order to identify critical areas. Notice that a GW collects and transmits to the NetServer all the RSSI values and positions of the EDs in its area. It is assumed that the majority of nodes belonging to a critical area will have the same SF since those nodes are particularly close to each other and, according to the allocation of SFs based on ADR (like EXPLoRa-AT), nodes with the same geographical position have the same RSSI and are likely to have allocated the same SF. EXPLoRa-KM works as follows: first, it determines the Voronoi diagram for a given scenario, in which the EDs and the GW are represented in Cartesian coordinates, whereby it is applied the K-means algorithm. As stated before, the centroid of each cluster represents the center of a critical area. Then, the collisions that happen in such regions are monitored (e.g. by measuring for a period of time the resulting DER), and depending on the number of collisions for a certain node in that area, its SF is increased. In particular, the SF is increased if the number of collisions is greater than the number of messages that the ED transmits in the monitored period. Another important aspect to consider is the choice of the number of clusters for a given scenario. In particular, if this number is too big, then there might be the risk of performing clustering on regions that are not indeed critical areas. On the other hand, if a really small amount of clusters is chosen, the opposite issue is encountered: the application of K-means will not be able to identify all the critical areas. Therefore, in order to maintain a suitable balance regarding the number of clusters, the following rule is imposed:

K = C • N/A ( 2
)
where N is the number of EDs, A is the area covered by the GW, and C is a proportional parameter which contains the prior knowledge of the density of a scenario. The term N/A represents the density of EDs in the scenario; the higher the density, the bigger the number of clusters will be. If the density is particularly low, no clustering is performed: the allocation of SFs performed by EXPLoRa-AT is sufficient and our algorithm is not applied. Finally, we remark that in the considered scheme, the region of influence of a critical area cannot include a number of EDs greater than the 5% of the total.

B. EXPLoRa -Time Symbol

While EXPLoRa-KM works only on the basis of the topological setting of the LoRaWAN, EXPLoRa-TS takes into account also the traffic load. It operates in conjunction with the EXPLoRa "ordered water-filling" approach proposed in [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF], hereinafter referred by EXP water filling in order to balance the traffic load (measured in symbol times) among the SF channels as Figure 1 presents. Channels are modeled as a set of buckets (see Figure 2) where symbols that are associated to the different EDs transmissions are suitably inserted.

According to the ED message payload (P L) size (in bytes) and the SF value, EXPLoRa-TS uses the following equations, given by the LoRa specifications, in order to compute the payload size in symbols, that is N sym mess:

8 + max{ 8P L -4SF + 28 + 16CR -20H 4(SF -2DE) • (CR + 4), 0} (3)
In the considered model, the coding rate 4 4+CR has been set to CR = 1, implicit header is disabled, H = 0, and data-rate optimization option is not enabled, DE = 0. Hence, Eq. ( 3) is simplified into Eq. ( 4) only as a function of PL (in bytes), and SF:

8 + max{ 2P L -SF + 11 SF • 5, 0} (4)
EXPLoRa-TS aims to allocate in a suitable way the SFs to EDs in order to balance the occupation time, measured in time symbols, in the different SF channels. Each SF channel Algorithm 1 EXPLoRa-TS

N messi ← T /M Pi ∀i ∈ [1 • • • N ] 4:
N sym messi ← P Lsym(P Li, SFi) Eq. 4

5:

N sym usri ← N sym messi • N messi return S 12: end function is modeled as a bucket. Thus, we define six buckets (one for each SF) such that the capacity of bucket k is equal to B k symbols. The buckets are filled with the EDs messages and figuratively transport these messages to the sink (modeling the GW). The task is to efficiently allocate all EDs messages (with their symbols) within these buckets.

As illustrated in Alg. 1 the procedure takes as input three vectors SF vec , M P vec , P L vec collecting respectively the SFs, message periods, and payload sizes for all the N EDs. It is also considered a vector w collecting the symbol time weights for each SF (in accordance with the values in LoRa [START_REF] Sornin | LoRaWAN Specification[END_REF]). Finally, a time window T is used to estimate the channels usage within a given time period. Algorithm 1 starts by evaluating N mess i i.e., the number of messages to be sent by each ED considering their message periods within T . Then, it computes N sym mess i i.e. how many symbols characterize each single message in accordance with Eq. ( 4). Hence, it is possible to estimate N sym usr i , i.e. how many symbols are sent by each ED within the time T . Later, it is computed the vector N sym SF which aggregates the total amount of symbols transmitted for each SF channel. Hence, it is calculated the vector P ADR = N sym SF • w which for each channel expresses the traffic load measured in symbol time.

We proceed to balance the weighted vector P ADR in order to have an equalized traffic load among the SF channels; for the latter, it is used the EXP water filling [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF]. This procedure will result into a new vector P T S with a more balanced distribution of the symbol times between the channels. Figure 1 presents an insight of the procedure. The P T S is the maximum permitted symbol time consumption that each SF channel k is allowed to use in the network in order to assure channel occupancy fairness. Finally, it is computed the vector B = P • w -1 containing the buckets sizes, i.e. how many symbols have be to allocated within each SF channel.

The second part of the solution addresses the allocation of messages in the buckets. This challenge resembles classical optimization problems such as bin-packing or knapsack. However, in our case, there are two specific constraints: (i) The message size, expressed in symbols, changes according to the chosen bucket (since it depends on the used SF). (ii) An ED who has allocated by the ADR a SF = k is not able to put its messages in a bucket k-1 since, given the RSSI, the ED signal cannot be decoded by the GW at SF = k -1. To solve this problem we defined an heuristic where EDs having longer payloads are served first. Allocating messages of EDs whose payload size is longer will significantly increase probabilities of having space left in the buckets for allocating shorter messages, thereby respecting the buckets capacities that were previously derived from the EXP water filling. The heuristic, invoked as f ill buckets(B) in Algorithm 1, performs the following steps:

1) It selects the first bucket, representing the channel with SF = 7 as the current bucket pbucket.

2) It serves EDs having SF k = 7 which are sorted in a list L according to their PL size: EDs whose PL size is bigger are served first. 3) For each ED i in L, the procedure allocates into the current bucket pbucket the ED messages N mess i which have a size of N sym mess i symbols. Each time a message is allocated, the bucket capacity B pbucket is decremented by N sym mess i symbols. This to represent that such message are transmitted with SF = pbucket. 4) If through Step 3, the current bucket end the space for allocating further messages, then the subsequent messages are be allocated in the next bucket pbucket + 1. Since the SF is changed to pbucket + 1, the size of the ED messages in symbols is calculated again using Eq. ( 4) in order to place its messages in the new bucket. 5) After all messages of all EDs in L are allocated in the buckets, then the next devices with SF k = 8, 9, ...12 are served using the same procedure starting from Step 2. 6) When all EDs belonging to the different SFs were served, the f ill buckets(B) returns an output vector indicating with which SF value the EDs are going to transmit their messages (according to the operations done in Step 3).

If the described approach is not be able to allocate all messages with the given buckets capacities, for the subsequent messages, it is chosen a bucket r that has the largest available space. In particular, for an ED transmitting with SF = k, it is chosen a bucket in the range SF k ≤ r ≤ 12 in such a way to satisfy the initial problem constraints.

Figure 2 provides an insightful representation of the explained procedure. As seen, the implementation allows an ED to transmit its messages with more than one SF value. However, as the number of EDs grows on the network, the number of devices using multiple SFs is negligible. This because the size of the buckets will be enlarged notably.

V. SIMULATION MODELS AND PERFORMANCE RESULTS

The performance assessments for both strategies, EXPLoRa-KM and EXPLoRa-TS, have been done by extending the SimP y simulator LoRaSim [START_REF] Bor | Do LoRa Low-Power Wide-Area Networks Scale?[END_REF]. In both cases, there were considered single-gateway scenarios with N = 500 fixed EDs generated around the gateway. The settings for the radio parameters for the EDs, and the values for the adopted path loss model are listed in Table II.

A. Managing an overcrowded area with EXPLoRa-KM

In this case, it is considered a scenario with 90% of EDs placed around the GW within a radius of 50 meters. Each ED tries to transmit 15 messages in a simulation time period of 30 minutes, and a rate of a message every 50 seconds. First, EXPLoRa-AT is applied in order to allocate the SFs on the nodes; the resulting allocation is illustrated in Figure 3(a). The number of clusters K that was used, having C = 5×10 2 , N = 500 and A = 240 × 240, is K = 4. The resulted clustering procedure, and the relative centroids are shown in Figure 3(b).

By applying EXPLoRa-KM, the SFs are modified, as illustrated in Figure 3(c). It is clearly visible that, around the centroids of the pink, red, and blue clusters, a significant number of EDs have increased their SFs, while around the centroid of the light blue cluster, there is almost no reaction. Indeed, this is mainly due to the fact that this critical area is not as dense as the others.

In the considered scenario, the use of EXPLoRa-KM is compared to ADR and to EXPLoRa-AT. In addition, their performance with and without retransmissions were evaluated simulating the presence of the retransmissions mechanism as described in [START_REF] Bankov | On the Limits of LoRaWAN Channel Access[END_REF]. In the LoRaWAN, the retransmission mechanism aims to retransmit a message when an ED does not receive an acknowledgment (ACK). The retransmission is computed in a randomly chosen channel if ACK-TIMEOUT seconds have passed from the first transmission, and if no acknowledgment has been received. The recommended behavior is to set up ACK-TIMEOUT between 1 -3 seconds [START_REF] Bankov | On the Limits of LoRaWAN Channel Access[END_REF].

In Figure 4, it can be observed how ADR, by using the retransmission mechanism, results in a poor DER performance with respect to the case without retransmissions. This is, however, plausible; as a matter of fact, in this scenario most of nodes have SF = 7 with ADR. Thus, by retransmitting messages, the collisions keep happening. On the other hand, EXPLoRa-AT distributes the SFs more fairly, so it leads to an increment of the DER of 10% with respect to the case without retransmissions. Finally, EXPLoRa-KM shows a significant improvement of the DER of 21% with respect to the case without retransmission and most importantly, of 11% with respect to EXPLoRa-AT.

As far as the fairness is concerned, an algorithm is fair if all the nodes are treated equally, in our case if it achieves a fair DER among all nodes. Since EXPLoRa-KM performs a discrimination, namely it selects only a subset of nodes for the re-allocation of the SFs, then it is necessary to check if fairness is kept. This is obtained by measuring the DER values in each cluster. They are similar: 90% for the blue and red clusters, 91% for the pink cluster and 89% for the light blue cluster, thereby evidencing fairness among the EDs when applying EXPLoRa-KM.

Performance results using EXPLoRa-AT [START_REF] Cuomo | EXPLoRa: Extending the performance of LoRa by suitable spreading factor allocations[END_REF] came up with a DER equal to 80% with retransmissions (70% without retransmissions). In the considered scenario, EXPLoRa-KM provides a DER equal to 90%, which demonstrates the usefulness of applying this technique on top of EXPLoRa-AT.

B. Addressing distinct traffic zones with EXPLoRa-TS

In this case we defined two traffic zones as in Figure 5: there is an inner area covering a radius of 50 meters around the GW. EDs placed on this area are considered aggressive and transmit messages with payload size (P L) between 120 -160 bytes and with a message period (M P ) ranging from 30 -60 seconds. Then, there is an outer area settled within an interval range of 50 -130 meters with respect to the GW. EDs placed in this outer zone load less traffic on the network, transmitting a message whose P L goes between 20 -40 bytes, and with a M P in the range of 10 -30 minutes. These two categories can represent two main applications planned within an IoT city deployment. We carried out different simulations where both zones enlarge or shrink based on the number of EDs placed in each of the two areas. To determine the number of EDs placed in each area we used a parameter p = 0.1, 0.2, ..., 1, such that p * 100% of N EDs are placed within the inner area, and they are generated as aggressive EDs whereas the other (1 -p) * 100% generated in the outer zone are non-aggressive. For instance, with p = 0.4, 40% of EDs belong to the highly congested inner area whereas 60% are placed at the lighttraffic outer area. For each value of p, there were executed 100 simulation runs. The performance results represent the mean values within a confidence interval of 95%.

Figure 6 presents the measured network DER and throughput values when the traffic load increases by incrementing the p parameter. For all possible p values, EXPLoRa-TS outperforms the ADR and EXPLoRa-AT since it is able to calculate the traffic load, measured in symbol times, of each SF channel into the network. For example, Figure 7 presents how the SF values have been distributed when 30% of EDs belongs to the congested internal area: ADR allocates SF values to EDs taking into account just the RSSI, so it naively assigns SF = 7 to the majority of the EDs. EXPLoRa-AT goes one step further by balancing the Time-on-Air, but assuming that the same traffic load is put in network. EXPLoRa-TS, through the symbol time balancing procedure among the SF channels, correctly considers how should be the distribution of the SFs across the SF channels/traffic zones. The high-level channel usage of the EDs in the heavy-traffic inner area, representing a 30% of the total of EDs, is proportional to the low channel usage of the other 70% of EDs that belong to the outer area. This reasoning, as Figure 7 (c) presents, is translated into a convenient SF allocation: the SF = 7, 8, 9 values are mostly assigned within the inner zone whereas a lot of devices in the Fig. 6. DER performance with respect to an increasing traffic in the area near the gateway.

outer zone result with SF = 10, 11, 12. Hence, for the case p = 0.3, the overall DER from a value of 0.21 in case of ADR increases to 0.44 with EXPLoRa-TS. Similarly, the network throughput improves from 0.35 kbps to 1.06 kbps. In addition, Figure 8 provides a heatmap for the p = 0.3% case which let us to understand how the EXPLoRa-TS improves the single DER for each ED. As seen in Figure 6 this performance improvement on the overall network is equivalent for other possible distributions of the EDs within the traffic zones (i.e. for other values of p)

In addition, it was simulated an opposite case where in the inner zone were placed the non-agressive EDs, whereas in the outer area were placed the aggressive ones, using the same ranges of M P and P L for each class of ED; as a result, Figure 9 illustrates how, as p increases, the traffic load decreases since all EDs transmit at a reduced rate in the inner area. The latter is a non-stressed case ideally for the ADR, but that EXPLoRa-AT was not able to cope with. Thus, it is shown how EXPLoRa-TS outstrips EXPLoRa-AT, and it is able to maintain the same performance level of the ADR. It is important to remark that in both situations, either aggressives EDs near to the gateway or far from it, when p = 1 it means that 100% of the EDs belong to just one class, so it means a traffic-balanced case (i.e. all SF channels/traffic zones using the channel at the same rate). From Figures 6 and9 it can be observed EXPLoRa-TS maintains the same DER performance levels previously obtained from ADR and EXPLoRa-AT.

As a second benefit from EXPLoRa-TS, either in trafficbalanced scenarios or not, is that the fact of allocating first ED messages whose payload size is longer yields a convenient channel usage fairness among EDs regardless of their P L. Inevitably, EDs whose P L is longer may have a longer Timeon-Air, increasing their collision probability. However, the EXPLoRa-TS heuristic applies an allocation policy based on the P L, so EDs whose P L size is longer will be benefited being sent in a minor symbol time. For the previous simulations, there was performed an alternative case where the devices P L were in the range of 20 -250 bytes, regardless of their class; as a result, Figure 10 shows how EXPLoRa-TS achieves better DER of the single ED than EXPLoRa-AT and ADR.

VI. CONCLUSIONS

In the framework of the IoT, the Low Power, Long Range technologies are emerging. These have many potentials that can be exploited once there is the possibility to support different applications and traffic types in network scenarios composed by hundreds of devices. In an incremental order of complexity we presented two approaches. First, it was introduced EXPLoRa-KM, for the reallocation of the SFs of LoRaWAN devices, which are located in overcrowded areas, thereby reducing gradually the amount of collisions, and increasing the Data Extraction Rate. EXPLoRa-KM also provides a good fairness among the EDs. Afterwards, we presented EXPLoRA-TS, an enhanced version of EXPLoRA-AT that takes into account different traffic configurations, payload sizes and message periods. We defined an allocation scheme for transmissions at different SFs by nodes placed around a gateway, and we showed via simulations that, by suitably balancing the SF channels occupation time (e.g. measured in terms of symbol time), the EXPLoRA-TS presents very good performance in terms of DER. Both approaches may be combined in order to provide an overall framework for realistic scenarios. i.e. applying EXPLoRa-TS taking into account different message rates and payload sizes of each ED, and then executing EXPLoRa-KM in order to assist critical regions with a high probability of collisions. Future research will address such work including as well multigateway experiments, and energy-consumption evaluations.

  ISBN 978-3-903176-05-8 c 2018 IFIPII. RELATED WORKThe LoRaWAN has attracted the IoT community as a promising platform for supporting smart city deployments. Thus, throughout the last years, different works have analyzed the technology limits and addressed open issues such as scalability. In this context, we can classify the related literature as follows:

Fig. 1 .

 1 Fig. 1. Example of performing the EXP water filling [10] in order to balance the traffic load measured in symbol times among the SF channels.

Fig. 2 .

 2 Fig.2. Heuristic for allocating EDs messages within the buckets (representing the different SF channels). The EDs messages are allocated according to their payload size (longer payloads are served first). Such allocation is illustrated by the solid arrows; if for an specific message there is no space left in a bucket, then it is placed in the next bucket (as shown by the dashed arrows).

6 : 7 : 8 :

 678 N sym SF k ← number of sym per SF k ∀k ∈ [7 • • • 12] PADR ← N sym SF • w PT S ← EXP water f illing(PADR, w)

Fig. 3 .Fig. 4 .

 34 Fig. 3. SF allocation with EXPLoRa-AT (a) Calculation of clusters and centroids (b) and SF allocation with EXPLoRa-KM (c)

Fig. 5 .

 5 Fig. 5. Distinct traffic zones: An overloaded inner area where EDs make incessant use of the network and a light-traffic outer zone where EDs may sporadic use of the channel.

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. SF allocation when 30% of nodes belong to the congested inner zone: (a) ADR, (b) EXPLoRa-AT and (c) EXPLoRa-TS

1 :

 1 function EXPLORA-TS(P Lvec, M Pvec, SFvec, T )

	2:	w ← {1, 2, 4, 8, 16, 32}	Symbol times [in ms] per SF
	3:

TABLE II SIMULATION

 II PARAMETERS.

	Parameter	Value
	Carrier Frequency (MHz)	860
	Bandwidth (kHz)	125
	Code Rate (CR)	4/5
	Transmission Power (TP)	14 dBm
	Path loss values (Eq. (1))	d 0 = 40 m, γ = 2.08, σ 2 = 0
		L pl (d 0 ) = 127.41 dB

ACKNOWLEDGEMENTS

This research was supported by the EU Commission within the Horizon 2020 symbIoTe project (Grant no. 688156).


Marco Giordani

Michele Polese

Arnab Roy

Douglas Castor
email: douglas.castor@interdigital.com

Michele Zorzi
email: zorzi@dei.unipd.it

Initial Access Frameworks for 3GPP NR at mmWave Frequencies

Keywords: 5G, mmWave, initial access, 3GPP, NR

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

The 5th generation (5G) of mobile cellular networks is currently being standardized by the 3GPP as NR [START_REF] Gpp | NR and NG-RAN Overall Description -Rel[END_REF], and is designed to enable a fully mobile and connected society, in order to address the tremendous growth in connectivity and density/volume of traffic that will be required in the near future [START_REF] Boccardi | Five disruptive technology directions for 5G[END_REF]. In particular, 5G cellular networks are designed to provide very high throughput (1 Gbps or more), ultra-low latency (even less than 1 ms in some cases), ultra-high reliability, low energy consumption, and ultra-high connectivity resilience [START_REF] Boccardi | Five disruptive technology directions for 5G[END_REF].

The mmWave spectrum -roughly comprised between 10 and 300 GHz -has been considered as an enabler of the 5G performance requirements in micro and picocellular networks [START_REF] Rangan | Millimeter-Wave Cellular Wireless Networks: Potentials and Challenges[END_REF]. These frequencies offer much more bandwidth than current cellular systems, which are allocated in the congested bands below 6 GHz, and initial capacity estimates have suggested that mmWave networks offer orders of magnitude higher bit-rates than 4G systems [START_REF] Akoum | Coverage and capacity in mmwave cellular systems[END_REF]. However, the increased carrier frequency makes the propagation conditions more demanding than at the lower frequencies traditionally used for wireless services, making the communication less reliable [START_REF] Pi | An introduction to millimeter-wave mobile broadband systems[END_REF]. MmWave signals suffer from a higher pathloss and severe channel intermittency, and are blocked by many common materials [START_REF] Lu | Modeling human blockers in millimeter wave radio links[END_REF]. As a result, the quality of the wireless link between the User Equipment (UE) and the network can be highly variable.

To overcome these limitations, next-generation cellular systems will be equipped with high-dimensional phased arrays both at the UE and at the Next Generation Node Base Station (gNB), in order to establish highly directional transmission links and to benefit from the resulting beamforming gain. Directional links, however, require fine alignment of the transmitter and the receiver beams, a procedure which might greatly increase the time it takes to access the network. In this regard, defining efficient Initial Access (IA) procedures, which allow a mobile UE to establish a physical link connection with a gNB (a necessary step to access the network), is particularly challenging at mmWave frequencies [START_REF] Giordani | Initial access in 5G mmWave cellular networks[END_REF]. In current Long Term Evolution (LTE) systems, IA is performed on omnidirectional channels, whereas beamforming or other directional transmissions can only be performed after a physical link is established [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-UTRAN); Overall description[END_REF]. On the other hand, in the mmWave bands, it may be essential to exploit the antenna gains already during the IA phase, otherwise there would be a mismatch between the range at which a cell can be detected (control-plane range), and the much longer range at which a user could directionally send and receive data using beamforming (user-plane range).

A. Related Work

Papers on IA (e.g., [START_REF] Giordani | Initial access in 5G mmWave cellular networks[END_REF], [START_REF] Liu | User association in 5G networks: A survey and an outlook[END_REF]) in 5G mmWave cellular systems are very recent. 1 Most literature refers to lower frequencies in ad hoc wireless network scenarios or, more recently, to the 60 GHz IEEE 802.11ad WLAN and WPAN scenarios (e.g., [START_REF] Nitsche | IEEE 802.11ad: directional 60 GHz communication for multi-Gigabit-per-second Wi-Fi[END_REF]). However, most of the proposed solutions present many limitations (e.g., they are appropriate for short-range, static and indoor scenarios) which prevent them from matching the requirements of cellular systems.

Recently, new solutions specifically designed for mobile wireless networks have been proposed. In [START_REF] Jeong | Random access in millimeter-wave beamforming cellular networks: issues and approaches[END_REF], [START_REF] Barati | Directional cell discovery in millimeter wave cellular networks[END_REF], the authors proposed an exhaustive method that performs IA over mmWave frequencies by periodically transmitting directional synchronization signals to scan the angular space. With this approach, a large number of antennas at the transceiver makes it possible to reach more users with respect to the case with a single omnidirectional antenna, at the cost of a longer delay for the IA. Additionally, more sophisticated discovery techniques (e.g., [START_REF] Desai | Initial beamforming for mmWave communications[END_REF]) decrease the exhaustive search delay through a multi-phase hierarchical procedure, in which access signals are first sent over a few directions, with wide beams, and then iteratively refined until the beamforming gain is sufficiently high. In [START_REF] Choi | Beam selection in mm-Wave multiuser MIMO systems using compressive sensing[END_REF] a low-complexity beam selection method is derived by exploiting the sparsity of mmWave channels, and thanks to compressive sensing it is possible to avoid explicit channel estimation for beam management.

The performance of the association techniques also depends on the beamforming architecture implemented in the transceivers. Preliminary works aiming at finding the optimal beamforming strategy refer to WLAN scenarios. For example, the algorithm proposed in [START_REF] Chandra | Adaptive beamwidth selection for contention based access periods in millimeter wave WLANs[END_REF] takes into account the spatial distribution of nodes, to allocate the beamwidth of each antenna pattern in an adaptive fashion and satisfy the required link budget criterion. Since the proposed algorithm minimizes the collisions, it also minimizes the average time required to transmit a data packet from the source to the destination through a specific direction. In 5G scenarios, papers [START_REF] Jeong | Random access in millimeter-wave beamforming cellular networks: issues and approaches[END_REF], [START_REF] Barati | Directional cell discovery in millimeter wave cellular networks[END_REF], [START_REF] Desai | Initial beamforming for mmWave communications[END_REF] give some insights on tradeoffs among different beamforming architectures in terms of user association's quality.

B. Contributions of This Paper

In this paper we provide the first global comprehensive evaluation of mmWave measurement frameworks for IA, using 3GPP NR scenario configurations (e.g., the NR frame structure and other relevant physical-layer parameters), and assess how to optimally design fast, accurate and robust control-plane management schemes through measurement reports. We focus on Downlink (DL) and Uplink (UL) frameworks, and on Standalone (SA) and Multi-Connectivity (MC) architectures. We simulate their performance in terms of (i) detection accuracy, i.e., how representative the measurement is; (ii) reactiveness, i.e., how quickly a mobile user gets access to the network; and (iii) overhead, i.e., how many resources are needed for the measurement operations. Finally, we illustrate some of the complex tradeoffs to be considered when designing IA solutions for 3GPP NR. The results prove that the optimal design for implementing efficient and fast IA must account for several specific features such as the gNBs density, the antenna geometry, the beamforming configuration and the level of integration and harmonization of different technologies.

The rest of the paper is organized as follows. In Sec. II we provide an introduction on 3GPP NR procedures for IA at mmWave frequencies, and present the IA frameworks we will evaluate. In Sec. III we describe the system model, the metrics that will be considered and the 3GPP parameters that will be configured. In Sec. IV we present our main findings and results, while Sec. V concludes the paper.

II. INITIAL ACCESS FRAMEWORKS

3GPP NR will support a wide range of frequencies and use cases, and is designed to support beamforming operations for both data and control planes [START_REF] Gpp | NR and NG-RAN Overall Description -Rel[END_REF] in the Physical (PHY) and Medium Access Control (MAC) layers. In particular, for IA, the concept of Synchronization Signal (SS) block and burst recently emerged for the periodic transmission of synchronization signals from the gNBs [START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF]. These signals can be used at the receiver side to estimate the channel and select the best gNB to attach to. An SS block is a group of 4 Orthogonal Frequency Division Multiplexing (OFDM) symbols in time and 240 subcarriers in frequency [START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF], and carries the Primary Synchronization Signal (PSS), the Secondary Synchronization Signal (SSS) and the Physical Broadcast Channel (PBCH). The DeModulation Reference Signal (DMRS) associated with the PBCH can be used to estimate the Reference Signal Received Power (RSRP) of each SS block. For each slot of 14 symbols there can be up to two SS blocks [START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF]. The SS blocks are grouped in an SS burst, which lasts up to 5 ms, and can be repeated after T SS ∈ {5, 10, 20, 40, 80, 160} ms [START_REF]NR -Radio Resource Control (RRC) protocol specification -Release 15[END_REF]. The maximum number L of SS blocks in a burst is frequencydependent [START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF], and above 6 GHz there could be up to 64 blocks per burst. When considering frequencies for which beam operations are required, each SS block is mapped to a certain angular direction.

Moreover, 3GPP NR specifications include a set of basic procedures for beam management [START_REF] Gpp | NR and NG-RAN Overall Description -Rel[END_REF]. We analyze two different deployment architectures. With the standalone option, the UE connects only to an NR gNB at mmWave frequencies. With multi-connectivity, instead, each UE maintains multiple possible signal paths to different cells at different frequencies (e.g., NR at mmWave and LTE at conventional frequencies), thus providing both high capacity and robust connections [START_REF] Polese | Improved Handover Through Dual Connectivity in 5G mmWave Mobile Networks[END_REF]. We also distinguish between a downlink and an uplink framework. In the downlink case, the gNBs transmit synchronization signals (i.e., SS blocks) which are collected by the surrounding UEs, while in the uplink case the measurements are based on Sounding Reference Signals (SRSs) transmitted by the mobile terminals. Notice that the 3GPP considers only the downlink framework for IA. Nonetheless, it is worth comparing the downlink and uplink solutions, given that the rising heterogeneity in cellular networks is dramatically changing the traditional notion of a communication cell [START_REF] Boccardi | Five disruptive technology directions for 5G[END_REF], increasing the importance of the uplink traffic and advocating the design of UL-driven solutions for both the data and the control planes.

The first procedure for IA is beam sweeping, i.e., covering a spatial area with a set of beams transmitted and received according to pre-specified intervals and directions. The second procedure, denominated beam measurement, requires the UEs in a downlink framework (or the gNBs in an uplink one) to evaluate the quality of the received signal. Different metrics could be used [START_REF] Gpp | NR -Physical layer measurements -Rel[END_REF]. In this paper, we consider the Signal to Noise Ratio (SNR), which is the linear average of the received power on different resources with synchronization signals divided by the noise power. The third procedure is beam determination, i.e., the selection of the best beams at the gNB and at the UE, according to the measurements obtained with the beam measurement procedure. This procedure differs in the DL and UL frameworks. In downlink, the UE performs autonomously a decision on the best direction in which IA should be performed. In uplink, instead, the gNBs forward the channel measurements to a central controller, which then decides which is the best direction. 2 The fourth and final procedure is beam reporting, i.e., information on the quality of the received beamformed signals and on the decisions in the beam determination phase is exchanged. In a standalone downlink (SA-DL) framework, as proposed by the 3GPP, the mobile terminal has to wait for the gNB to schedule the Random Access Channel (RACH) opportunity towards the best direction that the UE has just determined, for performing random access and implicitly informing the selected serving infrastructure about the optimal direction through which it has to steer its beam. As reported in [START_REF]Discussion on NR 4-Step Random Access Procedure[END_REF], it has been agreed that for each SS block the gNB will specify one or more RACH opportunities with a certain time and frequency offset and direction, so that the UE knows when to transmit the RACH preamble. When a multi-connectivity downlink (MC-DL) scheme is considered, instead, the UE can use the LTE connection to report the optimal set of directions to the gNBs, so that it does not need to wait for an additional beam sweep from the gNB to perform the beam reporting or the IA procedure. Similarly, in a multi-connectivity uplink (MC-UL) framework, the network reports to the UE the optimal direction and the resources for random access. Notice that we do not consider the SA-UL configuration for IA, since we believe that uplink-based architectures will likely necessitate the support of an LTE overlay for the management of the control plane and the implementation of efficient measurement operations.

III. SYSTEM MODEL

A. Performance Metrics

The performance of the different architectures and beam management procedures for IA will be assessed using three different metrics. The detection accuracy is measured in terms of probability of misdetection P MD , defined as the probability that the UE is not detected by the base station (i.e., the maximum SNR is below a threshold Γ) in an uplink scenario, or, vice versa, the base station is not detected by the UE in a downlink scenario after a complete beam sweeping in all the available directions. The reactiveness is the average time to find and report the best beam pair for IA, i.e., the time needed to perform the beam management procedures for IA described in the previous section. Finally, the overhead is the amount of time and frequency resources allocated to the framework with respect to the total amount of available resources.

The simulations for the detection accuracy performance evaluation are based on realistic system design configurations where multiple gNBs are deployed according to a Poisson Point Process. The channel model is based on recent realworld measurements at 28 GHz in New York City, to provide a realistic assessment of mmWave micro and picocellular networks in a dense urban deployment [START_REF] Akdeniz | Millimeter wave channel modeling and cellular capacity evaluation[END_REF].

B. 3GPP Framework Parameters

In this section, we list the parameters that affect the performance of the measurement architectures, and provide insights on the impact of each parameter on the different metrics.

As depicted in Fig. 1, we consider the frame structure of 3GPP NR, with different subcarrier spacings ∆ f . For frequencies above 6 GHz, the subcarrier spacing ∆ f is 15×2 n kHz, with 2 ≤ n ≤ 4 (i.e., ∆ f = 60, 120 or 240 kHz) and 14 OFDM symbols per slot. The slot duration in µs is given by T slot = 1000/2 n , while the duration of a symbol in µs is T symb = 71.42/2 n [START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF]. Since the only subcarrier spacings considered for frequencies above 6 GHz are ∆ f = 120 and 240 kHz, we will only consider these cases. Therefore, the slot duration is 125 µs or 62.5 µs, respectively. Moreover, since the maximum number of subcarriers allocated to the SS blocks is 240, then the bandwidth allocated for the SS blocks would be respectively 28.8 and 57.6 MHz. We consider a maximum channel bandwidth B = 400 MHz per carrier.

Moreover, it is possible to configure the system to exploit frequency diversity, D. Given that 240 subcarriers are allocated in frequency to an SS, the remaining bandwidth in the symbols which contain an SS block is B -240∆ f . Therefore, it is possible to adopt two different strategies: (i) data (as represented in Figs. 1(b) and (d)), i.e., it is used for data transmission towards users which are in the same direction in which the SS block is transmitted, or (ii) repetition (as displayed in Figs. 1(a) and (c)), i.e., the information in the first 240 subcarriers is repeated in the remaining subcarriers to increase the robustness against noise and enhance the detection capabilities. The number of repetitions is therefore N rep = 1 if frequency diversity is not used (i.e., D = 0, and a single chunk of the available bandwidth is used for the SS block), and N rep = 11 or N rep = 5 when repetition is used (i.e., D = 1) with ∆ f = 120 kHz or ∆ f = 240 kHz, respectively. There is a guard interval in frequency among the different repetitions of the SS blocks, to provide a good tradeoff between frequency diversity and coherent combining [START_REF] Barati | Directional cell discovery in millimeter wave cellular networks[END_REF].

We also consider different configurations of the SS blocks and bursts. The maximum number N SS of SS blocks in a burst for our frame structure and carrier frequencies is L = 64. We assume that, if N SS < L, the SS blocks will be transmitted in the first N SS opportunities. The actual maximum duration of an SS burst is D max,SS = 2.5 ms for ∆ f = 240 kHz and D max,SS = 5 ms for ∆ f = 120 kHz. We will also investigate all the possible values for the SS burst periodicity T SS .

Another fundamental parameter is the array geometry, i.e., the number of antenna elements M at the gNB and UE and the number of directions that need to be covered, both in azimuth N θ and in elevation N φ . At the gNB we consider a single sector in a three-sector site, i.e., the azimuth θ varies from -60 to 60 degrees, for a total of ∆ θ = 120 degrees, while the UE has a single array panel which covers the whole ∆ θ,UE = 360 • angular space. The elevation φ varies between -30 and 30 degrees, for a total of ∆ φ = 60 degrees, and also includes a fixed mechanical tilt of the array pointing towards the ground. There exists a strong correlation among beamwidth, number of antenna elements and beamforming gain. The more antenna elements in the system, the narrower the beams, the higher the gain that can be achieved by beamforming, and the more precise and directional the transmission. Thus, given the array geometry, we compute the beamwidth ∆ beam at 3 dB of the main lobe of the beamforming vector, and then N θ = ∆ θ /∆ beam and N φ = ∆ φ /∆ beam . The results are shown in Table I. Additionally, different beamforming architectures, i.e., analog, hybrid or digital, can be used both at the UE and at the gNB. Analog beamforming shapes the beam through a single Radio Frequency (RF) chain for all the antenna elements and therefore it is possible to transmit/receive in only one direction at any given time. This model saves power by using only a single pair of Analog to Digital Converters (ADCs), but has small flexibility since the transceiver can only beamform in one direction. Hybrid beamforming uses K BF RF chains (with 1 < K BF ≤ M ), and thus is equivalent to K BF parallel analog beams, as it enables the transceiver to transmit/receive in K BF directions simultaneously. Nevertheless, when hybrid beamforming is used for transmission, the power available at each transmitting beam is the total node power constraint divided by K BF , thus potentially reducing the received power. Digital beamforming requires a separate RF chain for each antenna element and therefore allows the processing of the received signals in the digital domain, potentially enabling the transceiver to direct beams at infinitely many directions at the same time [START_REF] Dutta | 5G Millimeter Wave Cellular System Capacity with Fully Digital Beamforming[END_REF]. Although the digital transceiver is able to process an infinite number of received streams, only M simultaneous and orthogonal beams can be handled without significant inter-beam interference (i.e., through a zero-forcing beamforming structure [START_REF] Yoo | On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming[END_REF]). For this reason, we limit the number of parallel beams that can be generated to M . Furthermore, for energy-saving purposes, we implement a digital beamforming scheme only at the receiver side. For the sake of completeness, we also consider an omnidirectional strategy at the UE, i.e., without any beamforming gain but allowing the reception through the whole angular space at any given time.

Finally, the last parameter is the density of base stations λ b , expressed in gNB/km 2 .

IV. RESULTS AND DISCUSSION

In this section, we present some simulation results aiming at (i) evaluating the performance of the presented IA schemes in terms of detection accuracy (i.e., probability of misdetection), as reported in Sec. IV-A; (ii) describing the analysis and the results related to the performance of the measurement frameworks for the reactiveness and the overhead, respectively in Sec. IV-B and Sec. IV-C. Final considerations and remarks, aimed at providing guidelines to characterize the optimal IA configuration settings as a function of the system parameters, are contained in Sec. IV-D.

A. Detection Accuracy Results

In Fig. 2 we plot the Cumulative Distribution Function (CDF) of the SNR between the mobile terminal and the gNB it is associated to, for different antenna configurations and considering two density values. Notice that the curves are not smooth because of the progressive transitions of the SNR among the different path loss regimes, i.e., Line of Sight (LOS), Non Line of Sight (NLOS) and outage. We see that better detection accuracy performance can be achieved when densifying the network and when using larger arrays. In the first case, the endpoints are progressively closer, thus ensuring better signal quality and, in general, stronger received power. In the second case, narrower beams can be steered thus guaranteeing higher beamforming gains. We also notice that, for good SNR regimes, the M gNB = 4, M UE = 4 and M gNB = 64, M UE = 4 configurations present good enough SNR values: in these regions, the channel conditions are sufficiently good to ensure satisfactory signal quality (and, consequently, acceptable misdetection) even when considering small antenna factors. Finally, the red line represents the SNR threshold Γ = -5 dB that we will consider in this work.

Analogous considerations can be deduced from Fig. 3 which illustrates how the misdetection probability monotonically decreases when the gNB density λ b progressively increases or when the transceiver is equipped with a larger number of antenna elements, since more focused beams can be generated in this case. Moreover, we notice that the beamforming strategy in which the UE transmits or receives omnidirectionally, although guaranteeing fast access operations, does not ensure accurate IA performance and leads to degraded detection capabilities. More specifically, the gap with a fully directional architecture (e.g., M gNB = 64, M UE = 16) is quite remarkable for very dense scenarios, and increases as the gNB density increases. For example, the configuration with 16 antennas (i.e., M UE = 16) and that with a single omnidirectional antenna at the UE reach the same P MD , but at different values of gNB density λ b , respectively 30 and 35 [gNB/km 2 ]: the omnidirectional configuration requires a higher density (i.e., 5 [gNB/km 2 ] more) to compensate for the smaller beamforming gain. Finally, Fig. 4 reports the misdetection probability related to λ b , for different subcarrier spacings ∆ f and repetition strategies D. First, we see that, if no repetitions are used (i.e., D = 0), lower detection accuracy performance is associated with the ∆ f = 240 kHz configuration, due to the resulting larger impact of the thermal noise and the consequent SNR degradation. Furthermore, the detection efficiency can be enhanced by repeating the SS block information embedded in the first 240 subcarriers in the remaining subcarriers (i.e., D = 1), to increase the robustness of the communication and mitigate the effect of the noise in the detection process. In fact, if a frequency diversity approach is preferred, the UE (in the DL measurement technique) or the gNB (in the UL measurement technique) has N rep > 1 attempts to properly collect the synchronization signals exchanged during the beam sweeping phase, compared to the single opportunity the nodes would have had if they had not implemented any repetition strategy. We also observe that the ∆ f = 120 kHz with no frequency diversity configuration and the ∆ f = 240 kHz scheme with N rep = 5 produce the same detection accuracy results, thus showing that increasing the subcarrier spacing and increasing the number of repetitions of the SS block information in multiple frequency subbands have almost the same effect in terms of misdetection capabilities. Finally, we observe that the impact of the frequency diversity D and the subcarrier spacing ∆ f is less significant when increasing the array factor, as can be seen from the reduced gap between the curves plotted in Fig. 4 for the M gNB = 4, M UE = 4 and M gNB = 64, M UE = 4 configurations. The reason is that, when considering larger arrays, even the configuration with ∆ f = 240 kHz, with no repetitions, has an average SNR which is high enough to reach small misdetection probability values.

B. Reactiveness Results

For IA, reactiveness is defined as the delay required to perform a full iterative search in all the possible combinations of the directions. The gNB and the UE need to scan respectively N θ,gNB N φ,gNB and N θ,UE N φ,UE directions to cover the whole horizontal and vertical space. Moreover, they can transmit or receive respectively K BF,gNB and K BF,UE beams simultaneously. Notice that, as mentioned in Sec. III, for digital and omnidirectional architectures K BF = min{N θ N φ , M }, for hybrid K BF = min{N θ N φ , M }/ν, where ν is a factor that limits the number of directions in which it is possible to transmit or receive at the same time, and for analog K BF = 1 [START_REF] Sun | MIMO for millimeter-wave wireless communications: beamforming, spatial multiplexing, or both?[END_REF]. Then the total number of SS blocks needed is

S D = N θ,gNB N φ,gNB K BF,gNB N θ,UE N φ,UE K BF,UE . (1)
Given that there are N SS blocks in a burst, the total delay from the beginning of an SS burst transmission in a gNB to the completion of the sweep in all the possible directions is

T IA = T SS S D N SS -1 + T last , (2)
where T last is the time required to transmit the remaining SS blocks in the last burst (notice that there may be just one burst, in which case the first term in Eq. ( 2) would be 0). This term depends on the subcarrier spacing and on the number of remaining SS blocks which is given by

N SS,left = S D -N SS S D N SS -1 . (3)
Then, T last is

T last = N SS,left 2
T slot -2T symb if N SS,left mod 2 = 0 N SS,left 2
T slot + 6T symb otherwise, (4)
The two different options account for an even or odd remaining number of SS blocks. In the first case, the SS blocks are sent in N SS,left /2 slots, with total duration T slot N SS,left /2, but the last one is actually received in the 12th symbol of the last slot, i.e., 2 symbols before the end of that slot, given the positions of the SS blocks in each slot described in [START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF]. If instead N SS,left is odd, six symbols of slot N SS,left /2 + 1 are also used.

A selection of results is presented in the next paragraphs. In Fig. 5 we consider first the impact of the number of SS blocks in a burst, with a fixed SS burst periodicity T SS = 20 ms and for different beamforming strategies and antenna configurations. In particular in Fig. 5a, in which both the UE and the gNB use analog beamforming, the IA delay heavily depends on the number of antennas at the transceivers since all the available directions must be scanned one by one. It may take from 0.6 s (with N SS = 64) up to 5.2 s (with N SS = 8) to transmit and receive all the possible beams, which makes the scheme infeasible for practical usage. A reduction in the sweeping time can be achieved either by using an omnidirectional antenna at the UE or by decreasing the number of directions to be scanned both at the UE and at the gNB. In this case, the only configurations that manage to complete a scan in a single SS burst are those with 4 antennas at both sides and N SS ≥ 16, or that with M gNB = 64, an omnidirectional UE and N SS = 64. Another option is the usage of digital beamforming at the UE in a downlink-based scheme (as displayed in Fig. 5b), or at the gNB in an uplinkbased one (as shown in Fig. 5c). This increases the number of configurations able to complete a sweep in an SS block, even with a large number of antennas at the gNB and the UE. In particular, Fig. 5c shows the performance of an uplink-based scheme, in which the SRSs are sent in the same time and frequency resource in which the SS blocks would be sent, and the gNB uses digital beamforming. It can be seen that there is a gain in performance for most of the configurations, because the gNB has to sweep more directions than the UE (since it uses narrower beams), thus using digital beamforming at the gNB side makes it possible to reduce T IA even more than when it is used at the UE side.

Furthermore, Fig. 6 shows the dependency of T IA on T SS . It can be seen that the highest periodicities are not suited for a mmWave deployment, and that in general it is better to increase the number of SS blocks per burst in order to try to complete the sweep in a single burst.

Impact of Beam Reporting. For IA, in addition to the time required for directional sweeping, there is also a delay related to the allocation of the resources in which it is possible to perform IA, which differs according to the architecture being used. As introduced in Sec. II, the 3GPP advocates the implicit reporting of the chosen direction, e.g., the strongest SS block index, through contention-based random access messages, agreeing that the network should allocate multiple RACH transmissions and preambles to the UE for conveying the optimal SS block index to the gNB [START_REF]Discussion on NR 4-Step Random Access Procedure[END_REF]. When considering an SA configuration, beam reporting might require an additional sweep at the gNB side while, if an MC architecture is preferred, the beam decision is forwarded through the LTE interface and requires just a single RACH opportunity, which makes the beam reporting reactiveness equal to the latency of a legacy LTE connection. Assuming no retransmissions are needed, the uplink latency in legacy LTE, including scheduling delay, ranges from 0.8 ms to 10.5 ms, according to the latency reduction techniques being implemented [START_REF] Takeda | Latency Reduction toward 5G[END_REF].

In Table II, we analyze the impact of the number of SS blocks (and, consequently, of RACH opportunities) in a burst, with a fixed burst periodicity T SS = 20 ms and for a subcarrier spacing of ∆ f = 120 KHz. The results are independent of the antenna configuration at the UE side, since the mobile terminal steers its beam through the previously determined optimal direction and does not require a beam sweeping operation to be performed. It appears clear that the SA scheme presents very good reactiveness for most of the investigated configurations and, most importantly, outperforms the MC solution even when the LTE latency is reduced to 0.8 ms. The reason is that, if the network is able to allocate the needed RACH resources within a single SS burst, then it is possible to limit the impact of beam reporting operations on the overall IA reactiveness, which is dominated by the beam sweeping phase instead. In particular, when considering small antenna factors and when digital beamforming is employed, beam reporting can be successfully completed through a single RACH allocation, thus guaranteeing very small delays.

C. Overhead Results

In this section, we characterize the overhead for IA in terms of the ratio between the time and frequency resources that are allocated to SS bursts and the maximum duration of the SS burst (i.e., 5 ms), or the entire T SS interval.

The total number of time and frequency resources R SS scheduled for the transmission of N SS SS blocks, each spanning 4 OFDM symbols and 240 (or a multiple of 240) subcarriers, is given by R SS = N SS 4T symb 240N rep ∆ f , where T symb is expressed in ms. The overhead for the 5 ms time interval in which the SS burst transmission happens, and with total bandwidth B, is then given by

Ω 5ms = N SS 4T symb 240N rep ∆ f 5B , (5)
while the overhead considering the total burst periodicity T SS is

Ω TSS = N SS 4T symb 240N rep ∆ f T SS B . (6)
Fig. 7 reports the overhead related to the maximum duration of the SS burst (i.e., 5 ms) for different subcarrier spacings and repetition strategies. It can be seen that if no repetitions are used (i.e., D = 0) then the overheads for the configurations with ∆ f = 120 kHz and ∆ f = 240 kHz are equivalent: the OFDM symbols used for the SS blocks have half the duration with the larger subcarrier spacing, but they occupy twice the bandwidth, given that the same number of subcarriers are used. Instead, when a repetition strategy is used (i.e., D = 1), the overhead is higher. As mentioned in Sec. III, we consider 5 repetitions for ∆ f = 240 kHz and 11 for ∆ f = 120 kHz. Therefore, the actual amount of bandwidth that is used is comparable, but since the OFDM symbols with ∆ f = 120 kHz last twice as long as those with the larger subcarrier spacing, the overhead in terms of resources used for the SS burst is higher with ∆ f = 120 kHz. Impact of beam reporting3 . For the SA case, as reported in Table III, the completion of the beam reporting procedure for IA may require additional overhead, due to the need for the system to allocate possibly multiple RACH resources for the reporting operations. Conversely, for the MC case, the beam decision is forwarded through the LTE overlay and requires a single RACH opportunity, with a total overhead of 0.0894 • 10 -3 . Nevertheless, from Table III, we notice that the SA additional reporting overhead is quite limited due to the relatively small number of directions that need to be investigated at this stage, especially when designing digital beamforming solutions.

D. Final Considerations

Overall, it is possible to identify some guidelines for the configuration of the IA framework and the deployment of an NR network at mmWave frequencies. First, a choice of N SS , the RACH resources, the beamforming and the antenna array architectures that allows the completion of the beam sweeping and reporting procedures in a single burst is preferable, so that it is possible to increase T SS (e.g., to 20 or 40 ms), thereby reducing the overhead of the SS blocks.

Second, the adoption of a frequency diversity scheme increases the detection accuracy at the expense of an increased overhead. Nevertheless, the accuracy gain decreases when the antenna array dimension is increased: in those circumstances, it may not be desirable to adopt a frequency diversity scheme which would lead to limited performance improvements.

Third, with low network density, larger antenna arrays can reach farther users and provide a wider coverage but, as λ b increases, it is possible to use a configuration with wide beams for SS bursts (so that it is more likely to complete a sweep in a single burst) during IA and narrow ones for data transmission, to refine the pointing directions and achieve higher gains.

Fourth, when considering stable and dense scenarios which are marginally affected by the variability of the mmWave channel, a standalone architecture is preferable for the design of fast IA procedures, since it enables rapid beam reporting operations, at the expense of a slightly increased overhead. Anyway, we still claim that an MC configuration may be preferable for several other reasons, including:

(i) Reduced overhead: the impact of the reporting operations on the communication performance at mmWave frequencies is almost negligible. (ii) Successful beam reporting: an MC scheme eliminates the need for the UE to send measurement feedback through mmWave connections (which are much more volatile than their LTE-based counterpart) and thereby removes a possible point of failure in the control signaling path. (iii) Centralized beam decision: unlike in traditional attachment policies based on pathloss measurements, by leveraging on the presence of an eNB operating at sub-6 GHz frequencies, an MC-based initial association can be possibly performed by taking into account the instantaneous load conditions of the surrounding cells, thereby promoting fairness in the whole cellular network [START_REF] Giordani | An Efficient Uplink Multi-Connectivity Scheme for 5G mmWave Control Plane Applications[END_REF]. Finally, a downlink configuration is in line with the 3GPP design for NR and reduces the energy consumption at the UE side (since it has just to receive the synchronization or reference signals), but is less reactive because the gNBs have a larger number of directions to sweep with downlink SS blocks.

V. CONCLUSIONS The extreme propagation environment at mmWave frequencies requires the adoption of directional transmissions and beamforming techniques, which increase the achievable data rate but also the latency and overhead required to perform IA. In this paper we evaluated, with an extensive analysis and simulation campaign, the impact of several parameters (specified by the 3GPP for NR) on the performance of multiple IA schemes for NR networks operating at mmWaves. We showed that there exist tradeoffs among better detection accuracy, improved reactiveness and reduced overhead. We therefore provided guidelines for determining the optimal IA strategy in different network deployments, according to the needs of the network operator and the specific environment in which the nodes are deployed.

As part of our future work, we will extend the analysis to the tracking of the beam quality for users in connected state (i.e., users that have successfully completed IA), and investigate the resilience performance of the beam management frameworks when considering radio link failure, outage events and the impact of LTE retransmissions.

Fig. 1 :

 1 Fig. 1: SS block structure. Each blue rectangle is an SS block (with 4 OFDM symbols). Cases (a) and (c) implement a frequency repetition scheme (with Nrep = 5 and 11, respectively) while, for cases (b) and (d), a data solution (i.e., Nrep = 1) is preferred.

MgNB = 4 , 2 Fig. 2 :

 422 Fig. 2: CDF of the SNR, for different antenna configurations. ∆ f = 120 kHz, Nrep = 1. The red dashed line represents the SNR threshold Γ = -5 dB that has been considered throughout this work.

MgNB = 4 ,Fig. 3 :

 43 Fig. 3: P MD as a function of λ b , for different antenna configurations.

M

  Fig. P MD as a function of λ b , for different subcarrier spacings ∆ f and repetition strategies and for different antenna configurations. M gNB = 4, M UE = 4, Γ = -5 dB.

MgNB = 4 ,Fig. 5 :

 45 Fig. 5: T IA as a function of N SS with T SS = 20 ms.

MgNB = 4 ,

 4 Fig. T IA as a function of T SS for the downlink configuration with analog gNB and hybrid UE. N SS = 64

1 Fig. 7 :

 17 Fig.7: Overhead Ω 5ms for IA as a function of N SS , introduced by the transmission of the SS blocks. Notice that the number of repetitions for the different subcarrier spacings ∆ f is chosen to send as many repetitions of the SS blocks as possible.

TABLE I :

 I Relationship between M , θ and N θ , for the azimuth case[START_REF] Giordani | A Tutorial on Beam Management for 3GPP NR at mmWave Frequencies[END_REF].

	M	θ [deg]	N θ gNB	N θ UE
	4	60	2	6
	16	26	5	14
	64	13	10	28

TABLE II :

 II Reactiveness performance for beam reporting operations considering an SA or an MC architecture. Analog or digital beamforming is implemented at the gNB side, while the UE configures its optimal beamformed direction. T SS = 20 ms, ∆ f = 120 KHz.

Ω

  BR,SA •10 -3 ∆ f,RACH = 60 kHz ∆ f,RACH = 120 kHz M gN B

		Analog	Digital	Analog	Digital
	4	0.0894	0.0894	0.0894	0.0894
	16	0.7149	0.0894	0.7149	0.0894
	64	2.2341	0.0894	2.2341	0.0894

TABLE III :

 III Overhead for beam reporting operations considering an SA architecture. Analog or digital beamforming is implemented at the gNB side, for different antenna array structures.

For a complete overview of the most relevant works on beam management we refer to[START_REF] Giordani | A Tutorial on Beam Management for 3GPP NR at mmWave Frequencies[END_REF]. ISBN 978-3-903176-05-8 c

IFIP

We recall that the optimal beam pair for each link can be determined only after a complete scan, since the gNBs have to detect all UEs within their whole angular range.

According to the 3GPP agreements[START_REF] Gpp | NR -Physical channels and modulation -Release 15[END_REF], a bandwidth of about 10 MHz or 20 MHz is reserved for the RACH resources, respectively for ∆ f,RACH = 60 kHz or 120 kHz.