Iacob Juc

Olivier Alphand

Roberto Guizzetti

Michel Favre

Andrzej Duda

Energy Consumption and Performance of IEEE 802.15.4e TSCH and DSME

Keywords: .15.4e, TSCH, DSME, channel hopping, energy efficiency, WSN, LLN

The recent IEEE 802.15.4e standard has introduced two interesting modes of operation: Time Slotted Channel Hopping (TSCH) and Deterministic and Synchronous Multichannel Extension (DSME). Both provide a mix of time and frequency division to improve the performance of the previously available synchronized MAC mode (beacon-enabled 802.15.4). In this paper, we compare the performance of DSME and TSCH with respect to the energy consumption, throughput, and delay through an analysis of their respective ways of operation. We use an energy consumption model coming from our previous experience on the design of recent energy harvesting motes for the GreenNet platform.

Our results show that DSME performs slightly better in terms of the energy consumption spent in data transfers. Both protocols exhibit similar delays for a given duty cycle, nevertheless, TSCH obtains shorter delay and higher throughput for low duty cycles. For higher duty cycles, TSCH results in lower throughput-for applications that send little data, the fixed slot configuration of TSCH results in wasted bandwidth. DSME can allocate shorter slots, which is beneficial for applications that transmit short packets.

I. INTRODUCTION

The IEEE 802.15.4 standard [START_REF]IEEE Standard for Information technology-Local and metropolitan area networks-Specific requirements-Part 15.4: Wireless[END_REF] published in 2003,2006, and 2011 defined the PHY and MAC layers with two operating modes (non-beacon enabled and beacon-enabled) for low-power sensor and actuator networks. In 2012, the 802.15.4e revision [START_REF]IEEE Standard for Local and metropolitan area networks-Part 15.4[END_REF] introduced several new MAC layer modes:

• DSME (Deterministic and Synchronous Multi-channel Extension) for deterministic latency and scalability requirements,

• TSCH (Time-Slotted Channel Hopping) for high throughput requirements, bounded latency, and high reliability.

• LLDN (Low Latency Deterministic Network) for high reliability and low latency,

• RFID Blink (Radio Frequency Identification) for item and people identification, location, and tracking,

• AMCA (Asynchronous Multi-Channel Adaptation) for infrastructure monitoring networks, DSME is an extension of the beacon-enabled mode for better utilization of inactive periods. It retains the principle of periodic beacons of the beacon-enabled mode and takes advantage of channel diversity through channel hopping: devices switch channels according to a predefined sequence for each communication in a reserved time slot. Devices under DSME can also use channel adaptation: they can allocate reserved slots on separate channels, the channel for each slot not changing in time.

TSCH also benefits from channel hopping, but devices do not use beacons for synchronization (except for advertising network information). They rather operate according to a common shared schedule that determines which device may transmit frames on a given channel and during a given time slot. To follow the schedule, devices need to be synchronized, so nodes can benefit from the deterministic behavior and some level of the required quality of service resulting from the schedule allocation.

TSCH has attracted considerable attention from the Wireless Sensor Network community with the establishment of the IETF 6TiSCH Working Group [?] whose goal is to define the operation of Low-power and Lossy Networks (LLN) under RPL routing (Routing Protocol for Low-power and lossy networks) [START_REF] Winter | RPL: IPv6 Routing Protocol for Low-Power and Lossy Networks[END_REF] over TSCH.

DSME and TSCH are the only new modes that support peer-to-peer and multi-hop topologies. In this paper, we compare the performance of the DSME and TSCH protocols with respect to the energy consumption, throughput, and delay through an analysis of their respective ways of operation. We assume two roles of nodes in the test scenario: a leaf node that generates sensor data and a router node that forwards the data in a multihop way to the sink.

From a practical point of view, extending existing beaconenabled 802.15.4 implementations to offer DSME would be easier than implementing TSCH. The comparison was partly motivated by the need to find out which of the two protocols better fits the GreenNet platform [START_REF] Varga | GreenNet: an Energy Harvesting IP-enabled Wireless Sensor Network[END_REF], previously running a beacon-enabled 802.15.4 protocol stack.

We use an energy consumption model coming from the experimental experience on the design of recent energy harvesting motes [START_REF] Varga | GreenNet: an Energy Harvesting IP-enabled Wireless Sensor Network[END_REF] and analyze how two nodes perform when exchanging packets under two protocols. Under our assumptions, we consider that a two-node scenario provides sufficient insight on the functioning of the protocols. Both protocols provide multi-channel operation, thus mitigating multi-path fading. By conveniently configuring them, we highlight their similarities and simplify the test scenario. Our results show that DSME performs slightly better in terms of the energy consumption spent in data transfers. Both protocols exhibit similar delays for a given duty cycle, nevertheless, TSCH obtains shorter delay and higher throughput for low duty cycles. For higher duty cycles, TSCH results in lower throughput-for applications that send little data, the fixed slot configuration of TSCH results in wasted bandwidth. DSME can allocate shorter slots, which is beneficial for applications that transmit short packets.

We start the paper with a presentation of DSME and TSCH in Section II. In Section III, we discuss parameter configurations that we adopt for the protocols. Then, in Section IV, we present the energy consumption model and the estimated energy costs for the protocols. Then, we compare the protocols in terms of throughput and delay. Section V discusses related work and Section VI presents conclusions and the future work.

II. BACKGROUND ON DSME AND TSCH

A. DSME

As an extension of the 802.15.4 beacon-enabled mode [START_REF]IEEE Standard for Information technology-Local and metropolitan area networks-Specific requirements-Part 15.4: Wireless[END_REF], DSME inherits some of its features such as beacons that synchronize data transfers, the basic superframe structure with time slots, and two types of devices: Full-Function Devices (FFDs) and Reduced-Function Devices (RFDs) [START_REF]IEEE Standard for Local and metropolitan area networks-Part 15.4[END_REF]. FFD devices transmit beacons and act as coordinators while RFD only wake up at beacons to transmit data. Intermediary nodes act as routers to forward packets-they act as RFD devices towards their coordinators and as FFD towards their child nodes. DSME extends the 802.15.4 beacon-enabled superframe structure with the notion of a multi-superframe (cf. Fig. 1):

• a superframe is composed of 16 slots of aBaseSlotLength = 960 * 2 SO µs and the Superframe Duration is SD = aBaseSuperframeDuration * 2 SO , where SO is the Superframe Order,

• 2 (M O-SO) superframes are grouped in a multisuperframe, where M O is the Multi-superframe Order,

• 2 (BO-M O) multi-superframes are contained in a Beacon Interval BI = aBaseSuperframeDuration * 2 BO , where BO is the Beacon Order. The Beacon Interval contains 2 (BO-SO) superframes.

In DSME, the Contention Access Period (CAP) is reduced to 9 slots (grey slots in the figure) and the remaining 7 slots are reserved for allocating Guaranteed Time Slots (GTS). Slot 0 is always reserved for Enhanced Beacons emission. In contrast with beacon-enabled 802.15.4, DSME can allocate GTS slots to any device in any GTS slot inside a multisuperframe (Fig. 1). By varying M O, we can adjust the repetition period of GTS slots inside the Beacon Interval.

Enhanced Beacons contain Information Elements (rather than a superframe specification) to describe various properties of the network, such as a bitmap to indicate the allocation of superframes inside the Beacon Interval. This mechanism for superframe allocation solves the problem of the multi-hop network construction in 802.15.4 beacon-enabled networks [START_REF] Vucinic | Topology construction in RPL networks over beacon-enabled 802[END_REF]. The maximum number of routing devices, including the PAN Coordinator is given by M axRouter = 2 (BO-SO) , the number of Superframes in the Beacon Interval. DSME also introduces CAP Reduction: with CAP Reduction, only the first superframe in a multi-superframe has the CAP period and the CAP slots for the remaining superframes are available for GTS allocation. This mechanism reduces the energy consumption, since nodes do not need to wake up for the unused CAPs and the extra GTS slots allow for a better distribution of bandwidth. With CAP Reduction enabled (cf. Fig. 1-B), nodes can communicate with their coordinator in the remaining CAP.

During CAP, nodes proceed in four steps:

• beacon transmission, • coordinator broadcast transmission, • coordinator unicast transmission,

• device unicast transmission to coordinator.

As in beacon-enabled 802.15.4, coordinators announce frames pending for devices in beacons. To retrieve a data frame, a device polls the coordinator with a Data Request and the coordinator sends the corresponding data frame. Nodes transmit both Data Requests and data frames using the slotted CSMA/CA algorithm. The frames are acknowledged by ACK frames. of each protocol. They both provide mechanisms to reserve communication slots between pairs of nodes, the slots being grouped in superframe structures that repeat periodically. We shall propose configurations for the two protocols so that the resulting superframes are similar. We configure both protocols for a default check interval T of 1 s. Thus, by the addresses, and no security). In the worst case, if using long addresses, the header is 23 byte long without security and 37 byte long with security [START_REF]IEEE Standard for Information technology-Local and metropolitan area networks-Specific requirements-Part 15.4: Wireless[END_REF]. We consider the most common case of the header without security. We assume that applications generate packets that do not require 6LoWPAN fragmentation. In the case of fragmentation, the overhead added by 6LoWPAN would be 7 bytes, which would sum up to 18 bytes with the MAC header. The minimal CoAP [START_REF] Shelby | The Constrained Application Protocol (CoAP)[END_REF] packet size is 4 bytes (the header without payload).

We consider three packet sizes: 30, 60 and 90 bytes and we take into account Enhanced ACK frames used by TSCH and described in Table II. DSME uses 5 byte long ACK frames as shown in Table III. The chosen values for TSCH slots are long enough to accommodate all packet sizes. DSME GTS of 6 ms duration can also accommodate a data exchange, including the ACK, with a maximal size packet.

B. Communication Patterns

We consider frame exchanges in both protocols that follow the patterns shown in Fig. 4. We adopt the parameters of the TSCH slot according to the 6TiSCH minimal configuration draft [START_REF] Vilajosana | Minimal 6tisch Configuration[END_REF]. Inside a TSCH slot, nodes delay a transmission with respect to the beginning of the slot by an offset and the guard time defined in the TSCH timeslot structure. The default tsTxOffset is 2120 µs and the default guard time is 2000 µs. We consider that on the average, the receiver listens for the half of the guard time. Clear Channel Assessment (CCA) is used in TSCH before a packet transmission, to prevent nodes from transmitting on a busy channel. CCA is optional, but we have chosen to take it into account.

After CCA, the radio needs 192 µs to switch from Rx to Tx mode. Note that CCA is useful when several networks coexist, otherwise, CCA cannot detect and prevent multiple transmissions inside the same slot if the transmissions are synchronized.

In DSME, the transmission may be aligned with the beginning of a GTS slot. The ACK frame is transmitted 192 µs after the end of the received frame. The guard time is implementation dependent: when using a 10 ppm oscillator on the MS1.0 platform (GreenNet Project) and a Beacon Interval of 1 second, the drift should be less than 10 µs, while a radio symbol is 16 µs long. The guard time can be adjusted locally by each node, based on the interval between synchronizations, for example, doubled if a node missed a beacon.

IV. ENERGY CONSUMPTION COMPARISONS

In this section, we first discuss the energy consumption model used for comparing energy consumption and then present the results of these comparisons.

A. Energy Consumption Model

We follow the recent work of Vilajosana et al. who proposed a simple energy consumption model for TSCH networks [START_REF] Vilajosana | A Realistic Energy Consumption Model for TSCH Networks[END_REF]. We also build on our previous work in which we have performed extensive evaluations of the energy consumption in GreenNet, an energy harvesting IP-enabled wireless sensor network [START_REF] Varga | GreenNet: an Energy Harvesting IP-enabled Wireless Sensor Network[END_REF]. We adopt the definition of a consumption profile as a sum of energy consumption contributions from each running peripheral. The radio and the micro-controller are the most energy consuming devices, thus we can obtain the total energy consumption by summing the time they are ON and considering how much power (or current intensity) they require in that state. Note that the radio consumes almost the same energy in reception as in transmission. Table IV presents the current intensity drawn in different states for various types of motes (data sources: MS1.0 [START_REF] Varga | GreenNet: an Energy Harvesting IP-enabled Wireless Sensor Network[END_REF], OpenMoteSTM, GINA [START_REF] Vilajosana | A Realistic Energy Consumption Model for TSCH Networks[END_REF]).

B. Energy Consumption Evaluation for Reserved Slots

In this section, we use the figures of the current consumption on the STM MS1.0 platform. We consider V Bat = 3 V and constant. Table V presents the energy consumption for a DSME GTS slot, and a TSCH Timeslot, based on two slot configurations: the default slot [START_REF]IEEE Standard for Local and metropolitan area networks-Part 15.4[END_REF], [START_REF] Vilajosana | Minimal 6tisch Configuration[END_REF] and the slot with reduced Rx Guard Times, based on the work of Stanislowski et al. on adaptive synchronization in a TSCH network [START_REF] Stanislowski | Adaptive Synchronization in IEEE802.15.4e Networks[END_REF].

DSME obtains lower energy consumption than TSCH because synchronization before reception in TSCH adds a significant part to the overall energy consumption. Stanislowski et al. proposed a synchronization procedure that would allow keeping the clock drift in a controlled range of ±100 µs in an experimental setup [START_REF] Stanislowski | Adaptive Synchronization in IEEE802.15.4e Networks[END_REF], which would mean that the average tsRxW ait would be reduced ten times. The procedure would also allow considering shorter synchronization times for ACK reception.

Figure 5 summarizes the breakdown of the energy consumption over different phases during transmission and reception. The data is obtained for a packet size of 30 bytes. For bigger packets, the relative overhead becomes less important. We note that using Enhanced ACKs adds a significant penalty to the energy consumption. DSME is more efficient from this point of view.

C. Throughput and Delay

We evaluate throughput and expected delay for two classes of devices: router nodes and leaves. Leaves need one slot to transmit a packet, whereas routers need two slots: one for receiving a packet and another for forwarding it to another node. In a DSME network, router nodes (coordinators) must wake up for two superframes during a Beacon Interval: one for communicating with their associated devices and another one for forwarding a packet to their own coordinator. We will take into account the two active periods in the superframes for forwarding one packet in the total measurement of throughput.

In a TSCH network, the routing structure does not imply differentiated behaviors inside shared slots. We still need to consider two slots inside a superframe for routers to account for packet forwarding. For the delay, we consider that active slots are evenly distributed across the measurement period (the Beacon Interval in case of DSME and the slotframe in the case of TSCH), which corresponds to the best case scenario.

Figs. 6 and7 show total throughput and delay for router and leaf nodes in DSME and TSCH networks for the parameters described in Section III and the duty cycle computed for packets 90 bytes. We can observe that both protocols exhibit similar delays for a given duty cycle, nevertheless, TSCH routers obtain shorter delay and higher throughput for low duty cycles. The CAP in DSME contributes significantly to the duty cycle of the device. As more slots are allocated, DSME benefits from a better slot organization.

Then, we look at lower duty cycles under 1%. For DSME, we increase BeaconOrder to 10, which gives a BeaconInterval of 15.728 ms, roughly 16 s. For TSCH, we increase the slotframe to 1570 timeslots, or 15 700 ms. Neither the Superf rame Order nor the T imeslot Length do not change so the analysis concerning the packet transfer in reserved slots is still valid for this second scenario. Figs. 8 and9 present the results and show similar effects. [START_REF] Shabro | Comparison of IWSN MAC Protocols for IEC 61850 Applications[END_REF], among other protocols, to Condition Monitoring Diagnosis in Smart Grid applications in the context of IEC 65850 [START_REF]IEC 61850 standard[END_REF]. It is the only comparison between DSME and TSCH that we are aware of and still, the paper does not provide performance comparisons.

Several authors have analyzed the individual performance of TSCH, DSME, and beacon-enabled 802.15.4. Koubaa et al. applied the network calculus to analyze the limitations of a cluster-tree network of a given structure (width and depth) and transposed the model to a 802.15.4 beaconenabled network [START_REF] Koubaa | Modeling and Worst-Case Dimensioning of Cluster-Tree Wireless Sensor Networks[END_REF]. The proposed model can be easily adapted for DSME.

In our previous work, we studied the problem of duty cycle adaptation for an energy harvesting beacon-enabled 802.15.4 network [START_REF] Varga | GreenNet: an Energy Harvesting IP-enabled Wireless Sensor Network[END_REF]. The choice of the duty cycle relies on a proper combination of BO-SO, the beacon and superframe order, since GTS slots in the 802.15.4 beacon-enabled mode can only be allocated by the PAN Coordinator. Both DSME and TSCH allow for a finer adjustment of the duty cycle by managing reserved slots. Tinka et al. proposed a solution for connecting mobile TSCH nodes [START_REF] Tinka | A Decentralized Scheduling Algorithm for Time Synchronized Channel Hopping[END_REF]. Because of the highly instable nature of the network, the TSCH synchronization mechanism is not suited, and instead, nodes rely on a GPS signal that synchronizes all nodes each 1s. The energy cost of the synchronization is not discussed.

Duquennoy et al. [START_REF] Duquennoy | Orchestra: Robust Mesh Networks Through Autonomously Scheduled TSCH[END_REF] recently proposed a new scheduling algorithm for TSCH. The algorithm separates the traffic in categories (application, routing, MAC) and allocates different schedules for each traffic plane. This approach narrows the gap between TSCH and DSME, since DSME provides a similar separation, for example, with the reserved slots for the Enhanced Beacon emission.

VI. CONCLUSIONS

The contribution of this paper is twofold: we have presented side-by-side the DSME and TSCH modes introduced in the 802.15.4e standard [START_REF]IEEE Standard for Local and metropolitan area networks-Part 15.4[END_REF] and compared their respective performance. Under certain configurations, both protocols operate similarly in terms of the medium access: time division multiplexing with channel diversity.

Our analytical results have underpinned a slight advantage of DSME in terms of the energy consumption during data transfers. The reason for this difference is the synchronization method used in TSCH networks. As a consequence, a TSCH network also exhibits worse performance in terms of the total throughput for higher duty cycles. For applications that send little data, the fixed slot configuration of TSCH results in wasted bandwidth. DSME can allocate shorter slots for applications that transmit short packets. With respect to delay, TSCH obtains shorter delay and higher throughput for low duty cycles.

The future work will consist of validating the results by running both protocols on a real platform and comparing other aspects of the network lifecycle: network discovery, scheduling, node mobility, and synchronization.

Figure 1 .

 1 Figure 1. Example of DSME multi-superframes for different parameters: A) normal mode, B) CAP Reduction enabled.

Figure 3 .

 3 Figure 3. 6TiSCH minimal configuration: TSCH slotframe vs. DSME beacon interval

Figure 4 .

 4 Figure 4. Data exchange patterns inside DSME GTS and TSCH shared slots.

Figure 5 .

 5 Figure 5. Energy consumption breakdown for different phases

Figure 6 .Figure 7 .

 67 Figure 6. Throughput and delay of routers in function of duty cycle

Figure 8 .Figure 9 .

 89 Figure 8. Throughput and delay of routers in function of duty cycle, for low duty cycles

ACKNOWLEDGEMENTS

This work was partially supported by the French Ministry of Research project IRIS under contract ANR-11-INFR-016.

DATA DATA

ACK TsTxAckDelay


Gabriele Romaniello

Olivier Alphand

Roberto Guizzetti

Andrzej Duda

Sustainable Traffic Aware Duty-Cycle Adaptation in Harvested Multi-Hop Wireless Sensor Networks

Sustainable power management techniques in energy harvesting wireless sensors currently adapt the consumption of sensors to their harvesting rate within the limits of their battery residual energy, but regardless of the traffic profile. To provide a fairer distribution of the energy according to application needs, we propose a new sustainable traffic aware duty-cycle adaptation scheme (STADA) that takes into account the traffic load in addition to previous factors. We evaluate our protocol in the specific context of multi-hop IEEE 802.15.4 beacon-enabled wireless sensor networks powered by solar energy. Simulations show that our solution outperforms traffic-unaware adaptation schemes while minimizing the variance of the quality of service provided to applications.

I. INTRODUCTION

Wireless Sensor Networks powered by ambient energy harvesting (WSN-HEAP) may substantially extend their lifetime by taking advantage of ambient sources of energy to recharge the sensor battery. If nodes achieve a proper energy balance between all energy consuming activities and the energy harvesting intake, the network could even last for ever.

To perform energy balance, advanced consumption adaptation schemes currently rely on the energy harvesting rate and the battery residual energy regardless of the traffic load. Therefore, the supplied energy is not always consistent with the traffic profile leading to an irregular quality of service and a non-optimal use of energy. For instance, a high duty-cycle when traffic is low does not bring much in terms of throughput, but leads to a waste of energy that could have been better used later in case of a traffic increase or a decreasing harvesting rate.

Moreover, we have decided to focus on indoor scenarios and choose light (natural and artificial) as the ambient source of energy, because it is abundant, easy to access, and benefits from a proper power density. Unlike solar profiles which diurnal and seasonal variations can be predicted, indoor light profiles may be quite unpredictable because of the fluctuation of its artificial component. Therefore, we favor a predictionless approach to estimate the energy harvesting rate.

At last, we propose to address the adaptation issue in a specific highly constrained context of multi-hop 802.15.4 networks operating in the beacon-enabled mode. Maintaining energy balance while still meeting good network performance is difficult, because harvested energy and traffic load are unevenly distributed in space and in time. Thus, nodes may obtain different solar energy at different places and, for instance in a convergecast scenario, the traffic load is heavier for the nodes closer to the sink. An additional difficulty is that, when each node independently adapts its duty-cycles to local conditions, it may influence the operation of other nodes on the path to the sink.

For all these reasons, we propose a new sustainable traffic aware duty-cycle adaptation algorithm (STADA) that fits the constraints of multi-hop energy harvesting wireless sensor networks. It takes into account the traffic load in addition to the harvesting rate and the battery level. We perform extensive simulations to analyze the performance of our algorithm in terms of delay and packet delivery ratio as well as a fairer distribution of energy in function of the traffic needs. We also compare our solution to a traffic unaware algorithm [START_REF] Yoo | Dynamic duty-cycle scheduling schemes for energy-harvesting wireless sensor networks[END_REF].

The rest of the paper is organized as follows. Section II recalls the principles of the 802.15.4 operation and energy harvesting. Section III presents the proposed adaptation algorithm and Section V reports simulation results. Finally, Section VI discusses the related work and Section VII concludes the paper.

II. BACKGROUND

A. IEEE 802.15.4 Networks

The IEEE 802.15.4 standard for Low-Rate Wireless Personal Area Networks (LR-WPANs) [2] defines the physical and the MAC (Medium Access Control) layers and two operating modes. In the beacon-enabled mode, a coordinator node periodically sends a beacon to delimit its superframes and invites neighboring associated nodes to send their frames during the Contention Access Period (CAP). To avoid collisions during the CAP, all children use the slotted CSMA-CA method to access the medium.

In the beacon-enabled mode, two parameters determine the duty-cycle: Beacon Order (BO) and Superframe Order (SO) with integer values satisfying 0 ≤ SO ≤ BO ≤ 14. They define the time between two successive beacons (BI, Beacon Interval):

BI = aBaseSuperf rameDuration • 2 BO (1)
and the duration of the active phase (SD, Superframe Duration):

SD = aBaseSuperf rameDuration • 2 SO . ( 2
)
Incoming Active Period (received)

Received Beacon

Outgoing Active Period (transmitted)

Beacon Interval (BI)

Fig. 1: Outgoing and incoming superframes

To support multi-hop topologies (i.e. cluster-trees), the 802.15.4 working group defined an Outgoing Superframe (SF out. ) dedicated to communications of a node with its child nodes and an Incoming Superframe (SF inc. ) for communications with its parent node interspaced by STARTTIME (cf. Fig. 1). Nodes may sleep during the inactive parts of the superframe. Nodes may additionally sleep during SF inc. if they have no traffic to send to their coordinator. On the contrary, during SF out. , nodes have to listen during the whole superframe to possible transmissions coming from their sons. A particular care has to be taken for the scheduling of superframes among the coordinators in the two-hop neighborhood, because they may overlap and in this case, beacons and frames may collide. We use a static multichannel allocation scheme of superframes over 16 channels to avoid beacon collisions.

Another limitation of the standard is that SF out. and SF inc. share the same duration. Therefore, the duty-cycle of all coordinators belonging to the same Personal Area Network (PAN) is fixed (in time) and homogeneous (in space). However, in our multi-hop harvesting context, nodes do not necessarily face the same traffic and light conditions. Thus, each coordinator should be able to dynamically adapt its own duty-cycle to its local light conditions and traffic load.

B. Energy Harvesting

Regarding harvesting, we consider sensors that convert light energy to electrical energy through small solar panels of 5 × 4cm. Their efficiency is around 3-5% and the maximum power they generate is 3.8mW if we refer to both indoor light profiles we consider in Section V. Even at this power, the solar panel does not generate enough power to cope with the instantaneous consumption of a sensor node. Consequently, the energy coming from the panel is first used to recharge the battery and then the sensor draws power from the battery as soon as a minimum level is reached. Finally, we assume an ideal non-leaking battery that supports a (virtually) unlimited number of recharge cycles and therefore does not suffer from degradation issues like the reduction of storage capabilities. Thanks to those assumptions, the battery can be easily included in the model that we use to analyze the harvesting nodes detailed in Section III.

III. HARVESTING SYSTEM MODEL

The model depicted in Figure 2 gives an overview of our harvesting model and the different constraints taken into account by our duty-cycle adaptation scheme.

First, we propose to model the couple battery-solar panel as a modified token-bucket that we call an energy-bucket (cf. Figure 2). The solar panel operation is represented by the recharging rate λ, the intake power. The energy consumption is characterized by δ (i.e Outgoing Power), the average energy consumption rate that relies on the decision of the Duty-cycle Manager detailed later in Section IV. Thus, the instantaneous battery level B(t) directly depends on λ and δ. At last, we define 3 specific battery levels : B max , B min and B surv . B max and B min represent the maximum and minimum energy values storable in the battery. If B(t) > B max (i.e. the battery is full), the energy coming from the solar panel is discarded.

If B(t) <= B min , the sensor stops working and needs to be recharged and rebooted manually. B surv is the minimum level of battery required to survive at an a priori fixed low dutycycle during long predefined dark periods based on predictable light profiles (nights) or computed from previous observations. The last element is the duty-cycle manager in charge of maintaining energy balance and leading to an unlimited lifetime. In other words, it has to adapt the outgoing dutycycle so that the equation 3 is always satisfied.

T 0 δ(t) ≤ B 0 + T 0 λ(t) ∀ T ∈ [0, ∞), (3)

IV. DUTY-CYCLE MANAGER

The main issue our new duty-cycle adaptation scheme addresses is the waste of energy resulting from an adaptation of duty-cycle not taking into account dynamic application needs. For instance, allocating high duty-cycles when there is no traffic is counter-productive since this energy could be better used later. Similarly, decreasing the duty-cycle when the traffic is moderate is not always the best option as local contention will rise leading to expensive retransmissions and significant performance degradations.

For better understanding, we give an overview in Figure 2 of the set of parameters taken into account by the duty-cycle manager and we detail them subsequently.

We first introduce a division of time into 5-minute slices (e.g. n = 288 per day) and assume that during a slice, a node will harvest a similar amount of energy to the previous slice, because of slow light variations. Let E n be the energy to allocate for the slice n, H n the energy harvested during slice n (dereived from the light sensor and the battery charge), L B ∈ (0, 1) the proportion of the battery level, and L T ∈ (0, 1) the proportion of the traffic level measured in function of the number of packets in the buffers of nodes associated with the coordinator 1 .

At the end of each slice, the duty-cycle manager computes the energy to allocate for the next slice as shown in Eq. 4.

E n = β • H n-1 + γ • H max • L B + δ • H max • L T , (4)
where β, γ, δ are respectively, the weight factor of each component that satisfy the following condition β + γ + δ = 1 except when the battery is full (in this case, β is set to 1 to completely consume the scavenged energy). H max is the maximum energy harvested during a slice (H max = 1.08J on our platform). H max is updated using an Exponentially Weighted Moving Average carried out over past days.

The duty-cycle manager provides the outgoing duty-cycle that defines the length and frequency of SF out. for the next slice. To obtain it, we first derive the duty-cycle for the next slice according to the following formula:

DC n = (E n -E pn )/E 0 , (5)
where E 0 is the energy consumed during a slice by an alwayson node and E pn represents the energy consumed during the incoming active period. E pn is updated according to the expression:

E pn+1 = α • [E pn + (1 -α) • E pn-1 + (1 -α) 2 • E pn-2 ] (6)
where E p0 is 0.

Then we transform DC n into a combination of BO and SO that results in DC n with Algorithm 1.

Algorithm 1 Duty cycle adaptation and BO out choice

SO out ← SO def ault BO out ← BO init DC ← ComputeDC(BO out , SO out ) while DC > DC out do BO out ← BO out + + DC ← ComputeDC(BO out , SO out ) end while
For the sake of simplicity, we have decided to fix SO. First, the algorithm fixes SO out to the default value and adjusts BO out starting from an initial low value. In the while loop, the node increases BO out until the resulting duty-cycle is less than the outgoing duty-cycle. In IEEE 802.15.4 beacon-enabled mode, several combinations of BO and SO correspond to the same duty-cycle. We privilege the smaller values of BO that result in shorter delays.

If L B ≤ L min B
(the proportion of the battery level at B surv ), the node automatically adopts the night configuration for BO and SO (BO survive and SO survive ) for its outgoing superframe. BO survive and SO survive represent the minimum level of required quality of service.

V. PERFORMANCE EVALUATION We used the WsNet simulator [START_REF]An event-driven simulator for large wireless sensor networks[END_REF] designed for Wireless Sensor Networks. We have integrated the accurate beacon-enabled implementation of IEEE 802.15.4 [START_REF] Abdeddaim | Implementation of a wsnet module to simulate the ieee 802.15.4 beacon-enabled mode in multihop topologies[END_REF] that supports multihop topologies, multichannel superframe scheduling, and single duty-cycle networks. We have implemented the proposed dutycycle adaptation algorithm and extended the module to support heterogeneous duty-cycles. We developed a module for a rechargeable battery and a module that simulates the solar panel.

We have set up all simulation parameters of energy consumption and scavenging behavior to the values corresponding to STM GreenNet tag, the new generation of harvesting sensor nodes manufactured by STMicroelectronics (STM). A GreenNet tag is composed of a 32 bit microcontroller, a rechargeable battery, a 802.15.4 beacon-enabled radio, a solar panel (∼ 4 × 5cm), and the Contiki network stack. Table I shows the STM node power consumption in each operational state. We simulate the topology shown in Figure 3, a cluster-tree with maximal depth 4 and 23 nodes representing a Home Automation or Office Automation scenario.

Fig. 3: Example topology

The sink (Edge Router) is main powered and uses a fixed duty-cycle (BO = 4 and SO = 1). We use all of the 16 available channels provided by standard in order to avoid active period overlapping during dynamic changes of duty-cycles.

Once the battery level is below L min B , we fix the surviving outgoing duty-cycle (SF out. ) to BO survive = 9 and SO survive = 1. This duty-cycle is also the minimum dutycycle that can be chosen by the duty-cycle Manager.

We fix BO Init = 4 and SO def ault = 1 to speed up the network bootstrap at the beginning of the simulation. This duty-cycle also provides a satisfactory quality of service for a typical traffic data rate in Home or Office Automation.

We fix the duty-cycle manager parameter with β = 0.5, γ = 0.25, and δ = 0.25, because in our case, we want an algorithm that principally makes its decision based on the harvesting rate.

Table II summarizes all the parameters of the simulations. In all simulations each data point is derived from the average of five 72-hour simulations each using different seeds.

We consider two light profiles: a predictable profile and an unpredictable light.

The predictable light profile is shown in Figure 4. It is the power profile of three regular sunny days with the maximum around midday with 3.8mW . We have compared the result of STADA with Duty-cycle Scheduling based on Prospective increase in residual energy (DSP) [START_REF] Yoo | Dynamic duty-cycle scheduling schemes for energy-harvesting wireless sensor networks[END_REF].

In DSP, sensor nodes adjust their duty-cycle proportionally to the residual energy in the battery and the prospective increase (or decrease) linked to their energy harvesting rate. DSP is designed for the asynchronous RI-MAC access protocol [START_REF] Sun | RI-MAC: A receiver-initiated asynchronous duty cycle mac protocol for dynamic traffic loads in wireless sensor networks[END_REF] so we have to adapt it to beacon-enabled 802.15.4 networks to be able to compare it with STADA.

To exhibit the substantial differences between the two algorithms, Figure 5 shows the packet delay at the second hop in the topology shown in Figure 3. DSP in the first 10 hours is in the warm up phase. It provides high duty-cycles even without intake energy because in the beginning the battery level is high. We can notice that packets experience a larger delay and jitter with DSR than with STADA during the night period. On one hand, by reacting immediately to the change of light, STADA is able to spare energy at the beginning of the night and to redistribute it more equally over the whole night duration. On the other hand, DSP is not able to take into account the harvesting rate, so it continues to make its decision based on the battery level. The consequence is that it wastes energy in the first night phase. Then, the battery level rapidly decreases and the algorithm is forced to schedule larger BO leading to higher delays.

Figure 6 shows the cumulative energy consumptions of both STADA and DSP against the cumulative harvested energy. The recharged energy starts from 100 J, which is the initial battery level. The distance between the harvested energy curve and the energy consumed one represents the instantaneous battery level. The shaded regions correspond to the period when there is no light (also indicated by a plateau in the cumulative harvested energy curve).

We can notice again that the energy consumption of STADA better follows the harvested energy curve. Moreover, its consumption curve is always below the DSP curve, which leads to higher battery levels during the whole simulation for STADA. Thus, for a similar (or even better) quality of service as explained later, STADA consumes less energy than DSP. Another interesting consequence is that the battery lifetime is correlated with the depth of discharge [START_REF]Hitachi Maxell lithium manganese dioxide rechargeable battery -technical report[END_REF]. In other words, STADA may safeguard more recharge cycles than the DSP algorithm. Fig. 6: Energy profile Figure 7 shows the Cumulative Distribution Function for the delay of all packets for each algorithm. We have simulated the network with a traffic pattern set to one packet every 6 and every 12 seconds. In either cases, STADA provides better performance, even if in the configuration with the traffic set to a packet every 12 seconds the profiles are quite similar. By increasing the data rate up to one packet every 6 seconds, the difference is even more salient and packets experience shorter delays with STADA during the whole simulation as well as a better PDR. We reproduce the same experiments with a non predictable profile as shown in Figure 8, which is an interpolation of real traces [START_REF] Gorlatova | CRAWDAD data set columbia/enhants (v. 2011-04-07)[END_REF].

Figure 9 shows the Cumulative Distribution Function of the simulation with an unpredictable profile. STADA also provides better performance under both traffic patterns in terms of delay and packet delivery ratio. By taking taking into account the Several authors proposed algorithms to adapt the duty-cycle to traffic in 802.15.4 beacon-enabled, battery powered WSN but the most advanced one is DCLA [START_REF] De Paz Alberola | Duty cycle learning algorithm (DCLA) for ieee 802.15.4 beacon-enabled wireless sensor networks[END_REF]. It is an efficient learning algorithm that jointly changes BO and SO according to an advanced traffic estimation based on the superframe utilization (observed by the coordinator), buffer occupancy, and queuing delays (transmitted to the coordinator by each node). An exhaustive comparison with other solutions is done and DCLA clearly outperforms them under various traffic patterns.

Nevertheless, all the proposals share the same drawback: they only consider star topologies. duty-cycle adaptation in multi-hop topologies requires taking into account additional parameters: heterogeneous duty-cycles, the additional queued traffic that a coordinator needs to relay to its parent, or the superframe allocation conflicts.

Distributed Duty Cycle Management (DDCM) [START_REF] De Paz Alberola | Distributed duty cycle management (DDCM) for ieee 802.15.4 beacon-enabled wireless mesh sensor networks[END_REF] tackles those issues but it relies on the new 802.15.4e standard [START_REF][END_REF] which supports mesh topologies as well as the allocation/deallocation of extra superframes (in addition to the traditional outgoing superframe), which provides a finer granularity and a higher flexibility not possible in the original 802.15.4.

B. Duty-cycling in sustainable wireless sensor networks

Several research papers are published to make the WSN-HEAPs auto-sustainable and increase their performances. Kansal et al. [START_REF] Kansal | Power management in energy harvesting sensor networks[END_REF] dynamically adapt the duty-cycle according to the deviations from the expected energy input learned from historical observations. They assume a periodic and predictable light profile and use a prediction mechanism in order to estimate the future energy supply. Prediction tools suffer of prediction errors and require a non negligible storage for low power sensor nodes. Vigorito et al. proposed an alternative model-free approach to solve the duty-cycle problem in the HEAP context (energy harvesting) using techniques from adaptive control theory [START_REF] Vigorito | Adaptive control of duty cycling in energy-harvesting wireless sensor networks[END_REF]. The proposed solution does not make any assumption about the nature and dynamics of the energy source, making their approach more easily implemented in real systems. Their approach makes use of a batterycentric objective function which requires a precise knowledge of the battery level. This information is not always realistic or accurate and it is better use it in a complementary manner [START_REF] Michelusi | Correlated energy generation and imperfect state-of-charge knowledge in energy harvesting devices[END_REF]. Another contribution of their work is the consideration of duty-cycle stability, the issue addressed for the first time. The authors change the duty-cycle using a smoothing system to reduce the duty-cycle variability. The approach may be a good solution for wireless sensor networks in general, but not for the IEEE 802.15.4 beacon-enabled mode in which the dutycycle is bounded to specific values of BO and SO.

Yoo et al. evaluated two adaptive duty-cycle schemes in a harvesting and multi-hop context [START_REF] Yoo | Dynamic duty-cycle scheduling schemes for energy-harvesting wireless sensor networks[END_REF]. The first algorithm computes its duty-cycle in an inverse proportion to the battery residual energy. The second one also benefits from an estimation of the residual energy increase allowing for more aggressiveness. However, this evaluation is based on an asynchronous duty-cycle protocol (when 802.15.4 belongs to synchronous ones) and does not consider dynamic harvesting profiles.

With respect to the related work, our adaptation scheme presents the advantage of taking into account the general multi-hop topology of the network as well as the complex interaction between the BO and SO values of parent nodes and possible values of the BO and SO at a given node.

VII. CONCLUSION

In the present paper, we propose a novel adaptation scheme that takes into account the energy harvesting rate, the battery level and local traffic conditions. It provides the best quality of service for the available level of energy in an IEEE 802.15.4 beacon-enabled multi-hop harvested WSN. The scheme uses an analogy of the token bucket applied to the harvested intake energy, the model we call an energy bucket. The adaptation scheme takes into account the intake energy, stored energy, the buffer status of son nodes, and finds the best duty-cycle that leads to high throughput and low delay. It also reserves some energy for surviving the periods without energy intake, and energy to face eventual buffer queuing avoiding packet drop.

Our evaluation through simulations has shown that the proposed scheme leads to good performance in terms of packet delay and packet delivery ratio as well as to an efficient use of harvested energy. As a future direction of this work, we plan to deploy a network of STM solar harvested nodes with the adaptation scheme and measure its performance in real conditions. Moreover we are interested in studying how to dynamically adapt α, β and γ to different network situations (traffic and light pattern). This experience will also help us to empirically characterize the battery behavior and charging times of the STMicroelectronics sensor node in time and space.

Fig. 2 :

 2 Fig. 2: Energy bucket model

Fig. 4 :

 4 Fig. 4: Incoming power during three sunny days.

Fig. 5 :

 5 Fig. 5: Packet delay during three sunny days.

Fig. 7 :

 7 Fig. 7: CDF of packet delay during three sunny days.

Fig. 8 :Fig. 9 :

 89 Fig. 8: Incoming power during three unpredictable days.

TABLE I :

 I Typical Operating Conditions of STM nodes.

	Operational state 1: MCU On, Radio Rx	30 mW
	Operational state 2: MCU On, Radio Tx	30 mW
	Operational state 3: MCU Off, Radio Off 8.4	µW

TABLE II :

 II Simulation Parameters.

	Starting BO	4
	Starting SO	1
	Number of nodes	23
	Traffic rate	10 up to 21 bytes per second
	Traffic type	CBR converge-cast toward sink
	Data packet size	127 bytes
	Radio transmission range	50m
	Radio sensing range	90m
	Shadowing Model	Log-normal

β (weight for energy harvesting rate) 0.5 α (weight for residual battery level) 0.25 γ (weight for sons' traffic load) 0.25

To provide traffic status, additional information on the queuing occupancy of son nodes are sent in the reserved field of the MAC header (3 bits). The algorithm just considers the worse queuing occupancy among the sons.


Liviu-Octavian Varga

Martin Heusse

Roberto Guizzetti

Andrzej Duda

Why is Frequency Channel Diversity so Beneficial in Wireless Sensor Networks?

Keywords: 802.15.4, coherence band, channel hopping, radio propagation

In dense wireless sensor networks, a multichannel MAC is a good means to reduce channel contention and increase frame reception probability. In this paper, we report on experiments with transmissions on various channels in the 2.4GHz ISM band and find more channel diversity than expected: this effect is particularly exacerbated at a short range, but it also has a significant impact at any distance. Moreover, we find that wireless sensor nodes have a radiation pattern that changes significantly with the frequency channel. This feature is inherent to the size of the sensor node, in which the antenna necessarily interferes with other components. The first consequence of this finding is that frequency diversity in sensor networks is even more effective than generally thought, and conversely, single channel communication schemes should be avoided as long as the power budget is not very comfortable.

I. INTRODUCTION

In the context of a growing number of connected devices forming potentially dense wireless networks, using the whole available spectrum becomes unavoidable. IEEE 802.15.4 defines 16 channels in the 2.4GHz band with the width of 2 MHz and 5 MHz interchannel spacing. Besides segregating the transmissions, changing the channel allows to benefit from the diversity due to the sensitivity of multipath fading to the central frequency. In other words, there can be a channel between two nodes that works well, but during the same time frame, this channel gives very bad performance with other nodes. For all these reasons, the IEEE 802.15.4e-2012 amendment [1] specified channel hopping protocols such as TSCH (Time Synchronized Channel Hopping) or DSME (Deterministic and Synchronous Multi-channel Extension).

Even though a lot of research aims at harnessing channel diversity, most of the studies invoke multipath fading as the reason of bad communication on certain channels between two given nodes. Two solutions exist to improve performance: either change the position of a node or the antenna, or change the frequency. The first solution is inapplicable in most cases because access to the node might not always be possible. Taking advantage of antenna diversity is also challenging to implement for cost and space constraints.

Fortunately, even for short range and line of sight communications, our experiments show that there is a lot of diversity when changing channels, more than multipath fading itself can explain. We posit that the entire wireless sensor board has a role in radio propagation. On certain frequencies and in many directions, its presence either attenuates the radio signal or amplifies it. This effect is unavoidable for compact nodes and it has a noticeable impact within the band of interest.

We start the paper with a simple radio propagation model and present selected real world measurements of commu-nications involving GreenNet nodes (Fig. 1) developed by STMicroelectronics [START_REF] Varga | Greennet: An energy-harvesting ip-enabled wireless sensor network[END_REF]. The board is based on a System on Chip STM32L low power microcontroller with a test-chip RF200 radio and a ceramic RainSun antenna [START_REF]RainSun[END_REF].

B c = C 2 • δ d [4]
. This expression is only relevant for a pair of paths with similar incident power at the receiver: in fact, if the difference is of the same order of magnitude as the shortest path length, then free space attenuation lessens the impact of the secondary path.

Consequently, the coherence band for short distances is inherently larger than the band for longer distances, where larger δ d corresponds to similar received powers on the considered paths. For instance, with 1m between the sender and the receiver, a reflection on a wall 1m behind the receiver reaches the receiving antenna with a power at most one 9 th of the power on the direct path, so it will not hurt much the direct path wave. Conversely, at e.g. 5m or more, the reflected signal may mostly cancel out the direct wave [START_REF] Sexton | Radio channel quality in industrial wireless sensor networks[END_REF]. When the sender and the receiver are further and further apart, the coherence band eventually shrinks well below 0.1MHz at distances of the order of 1km [START_REF] Cox | Correlation Bandwidth and Delay Spread Multipath Propagation Statistics for 910-MHz Urban Mobile Radio Channels[END_REF].

For δ d = 1m (think of a reflection on a wall 50cm behind the sender or the receiver) the coherence band is 150MHz, or 30 times the 802.15.4 channel spacing (5MHz), whereas the ISM band is "only" 80MHz wide. In this case, the whole range of the available transmission frequencies is too small to exploit the diversity from varying multipath recombinations. From this simple analysis, it appears unlikely that a frequency shift by 5MHz brings any change due to multipath fading at a short distance. The next section considers a more complex synthetic model that captures with more accuracy how the combination of multiple radio waves changes with the channel center frequency. A. Considering more than two propagation paths With more paths, the recombination at the receiver is harder to predict but, in general, it is expected that the coherence band shrinks. To assess the influence of a channel change, we consider a simple model with one direct (dominant) path and several scatterers or reflectors (for a total of 8 waves, in this section) placed at random positions from the immediate vicinity of the sender or the receiver up to 600% of the direct path length. Each path receives varying amounts of power, and all paths except the direct one, are attenuated by 3dB, which is rather typical for a reflected wave [START_REF] Landron | A comparison of theoretical and empirical reflection coefficients for typical exterior wall surfaces in a mobile radio environment[END_REF]. The histograms of the gain variations for a direct path of 1m appear in Figure 2a, respectively, for a frequency shift of 4 channel spacing gaps (20MHz). Multipath propagation is only modeled for the top histogram, whereas random gain variations of up to 5dB at the sender and the receiver are applied for the bottom histogram.

At 1m, much like previously experienced at a few meters in the 433MHz band [START_REF] Tuset-Peiró | On the suitability of the 433 mhz band for m2m low-power wireless communications: propagation aspects[END_REF], we do not expect that changing frequency would have much effect: accordingly, there is hardly any gain variation above 6dB in the histogram at the top in Figure 2a. However, Figure 2b shows a different behavior: at 1m indoors, gain changes of 6 dB or above are common. So, there is something more: in the model, we need to randomly change the channel gains over the various paths by e.g. 5 dB at the sender and the receiver when shifting the channel frequency to get gain variations reaching this magnitude, in the histogram at the bottom of Figure 2a. This last gain distribution significantly differs from the measurements presented in Figure 2b: in the real world conditions, a frequency change does not change the gains randomly, but there is a general improvement when going from channel 15 to 11, with some exceptions.

Our point is that multipath fading is insufficient by itself to explain these gain variations when changing channels. In the next section, we consider the case with a single path to get insight into another possible cause for the gain variations.

III. OUTDOOR MEASUREMENTS: RADIATION PATTERNS

vs. THE TRANSMISSION FREQUENCY The experiment takes place at a large empty parking lot with the receiver node in the middle, one meter above the ground and the sender on a robot that circles around the receiver. The constant distance between the two nodes is maintained using a string between the center of the circle and Fig. 3 shows the average RSSI (Received Signal Strength Indicator) for 20 packets/channel at each robot position. We can observe that the signal strength notably varies with the aspect angle. The pattern in Figure 3b is expected-it corresponds to a typical dipole radiation pattern. What is less expected, though, is the difference of up to 10dB from one channel to another in many directions. Furthermore, channel 11 has a higher signal reception strength in many, but not all, directions, which matches the bias already noticed at a short range in Figure 2b.

A. Origin of the phenomenon

We consider a board that integrates the antenna, the circuit board, and a solar panel. So, the transmitted radio signal is in fact the combination of the antenna radiation with the radio waves scattered and reflected by the other components, which is unavoidable. Even with a single path in the environment, the receiver gets a combination of waves from the transmitter, and actually creates itself a set of secondary radio waves. It turns out that the combination of scattered waves is sensitive to the transmission frequency at the granularity of the 802.15.4 channel spacing.

If this effect is better understood, and taking for granted that advanced sensor network MAC layer will include some form of channel agility, one can imagine designing a sensor board in such a way that the difference from one channel to the next is exacerbated, to increase the diversity.

IV. INDOOR MEASUREMENTS

In this experiment, the sender is static and the receiver is attached to a small robot. The sender sends three groups of packets on different channels [START_REF] Giorgetti | Exploiting Low-Cost Directional Antennas in 2.4 GHz IEEE 802.15.4 Wireless Sensor Networks[END_REF]18,26) and the receiver sends back statistics. Then, the sender commands the robot to move forward etc. In the first part of the experiment, nodes are in line of sight, whereas after four meters, they are not in the direct view any more, as the robot moves out of the room. In each position, the sender sends 20 packets on each of the three channels (so 60 packets/position) and waits for the receiver to send back the RSSI measured for each received packet. The emission power is set to 0dbm and there is no retransmission when the hardware acknowledgement is not received.

Figure 4a shows the RSSI measured on each channel over the 10m course of the robot. The RSSI follows a general trend: it goes down as the robot moves away. Nevertheless,

RSSI of received packets

Position (cm)

q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 200 400 600 800 1000 -115 -100 Figure 4: Indoor evaluation locally, the RSSI varies considerably even when the sender and the receiver are in the same room, and clearly differs from one channel to another: signal fadings on each channel are rather uncorrelated although the measurements were taken at very near instants. Obviously, in the same room, RSSI is high enough to warrant successful reception, whereas it gets more challenging at the other end of the corridor.

V. RELATED WORK Watteyne et al. [START_REF] Watteyne | Mitigating Multipath Fading through Channel Hopping in Wireless Sensor Networks[END_REF] considers that deep fading caused by destructive interference can be overcome by switching the frequency or the location of a node. They estimate that the coherence band for 2.4GHz varies from 5MHz for long ranges up to 15MHz for extremely short links, and we suspect that this finding is also due to the physical configuration of the sender and receiver used in experiments.

In the experiments made by Varela and Sánchez [START_REF] Varela | RMS Delay and Coherence Bandwidth Measurements in Indoor Radio Channels in the UHF Band[END_REF], they find that the 90% coherence band is of the order of 5 to 10MHz at 10m, and 10MHz or above at 3m. This coherence band corresponds to B 0.9 = 1 50στ , where σ τ is the mean delay among the paths weighted by the received power, which results in 50MHz and more for the 50% coherence band (3dB variation) (B 0.5 = 1 5στ ). This value is much larger than what we observe with our nodes. Besides, they also set out that the coherence band is generally larger for the copolar component than for crosspolar one whereas in most other studies, only the copolar antenna positions are considered. This is not surprising as the crosspolar setup reduces the gain on the direct path.

Wysocki and Zepernick [START_REF] Wysocki | Characterization of the Indoor Radio Propagation Channel at 2.4 GHz[END_REF] presented a characterization of the indoor radio propagation in the 2.4 GHz band with measurements of fading characteristics, multipath parameters, and background interference. In a room of 10m by 8m, they find lower coherence bands than Varela, which may be due to an environment that contains many scatterers.

Giorgetti et al. [START_REF] Giorgetti | Exploiting Low-Cost Directional Antennas in 2.4 GHz IEEE 802.15.4 Wireless Sensor Networks[END_REF] proposed an approach based on directional antennas placed on different sides of a node, using specific 802.15.4 antennas. This solution can be used to overcome the imperfection of a board with a ceramic antenna, but the main drawback is the size of the device-GreenNet nodes are only 4 mm thick.

VI. CONCLUSIONS

In this paper, we have provided an experimental evidence of the fact that changing channels can have a significant influence on the radio propagation and consequently, on the quality of the link between two or more devices. However, in the case of close range communications in line of sight, channel diversity is not only due to multipath, but also to other phenomena. It is hard to believe that just multipath fading can have an impact of up to 10dB when changing channels in line of sight at a short distance. We postulate that the difference most probably comes from the board construction. As the antenna interferes with the board, its ground plane and, in our case, the solar panel, it strongly affects the radiation pattern and renders it sensitive to the transmission frequency.

This fact may become an issue for the basic 802.15.4 scheme that do not support channel hopping. In this case, nodes need to be laid out with a comfortable range margin to compensate for the channel gain uncertainty. Even with stable omnidirectional antennas and a copolar placement of nodes, multipath fading is unavoidable, and may only be overcome with antenna diversity, which in turn imposes a much larger footprint. On the contrary, 802.15.4 channel hopping schemes may significantly benefit from the gain variability with respect to the transmission channel, so we can actually design boards to increase the level of diversity.

Figure 1 :

 1 Figure 1: GreenNet board

Figure 2 :

 2 Figure 2: Fig. 2a: Computed RSSI variations at 1m with one dominant path, when changing the frequency by 20MHz (4 channels or a 0.8% wavelength variation). Top: variations solely due to the phase changes at the receiver; bottom: with additional random gain changes among the paths; Fig. 2b: Experimentally measured RSSI variations at 1m

Figure 3 :

 3 Figure 3: Reception patterns for a GreenNet board

  RSSI value for each position for channels[START_REF] Giorgetti | Exploiting Low-Cost Directional Antennas in 2.4 GHz IEEE 802.15.4 Wireless Sensor Networks[END_REF] 18, 26