FAVOR: Frequency Allocation for Versatile Occupancy ofspectRum in Wireless Sensor Networks

Feng Li? Jun Luo? Gaotao Shi† Ying He??School of Computer Engineering, Nanyang Technological University, Singapore

†School of Computer Science and Technology, Tianjin University, China{fli3, junluo, yhe}@ntu.edu.sg, shgt@tju.edu.cn

ABSTRACTWhile the increasing scales of the recent WSN deploymentskeep pushing a higher demand on the network throughput,the 16 orthogonal channels of the ZigBee radios are inten-sively explored to improve the parallelism of the transmis-sions. However, the interferences generated by other ISMband wireless devices (e.g., WiFi) have severely limited theusable channels for WSNs. Such a situation raises a need fora spectrum utilizing method more efficient than the conven-tional multi-channel access. To this end, we propose to shiftthe paradigm from discrete channel allocation to continuousfrequency allocation in this paper. Motivated by our ex-periments showing the flexible and efficient use of spectrumthrough continuously tuning channel center frequencies withrespect to link distances, we present FAVOR (Frequency Al-location for Versatile Occupancy of spectRum) to allocateproper center frequencies in a continuous spectrum (hencepotentially overlapped channels, rather than discrete orthog-onal channels) to nodes or links. To find an optimal fre-quency allocation, FAVOR creatively combines location andfrequency into one space and thus transforms the frequencyallocation problem into a spatial tessellation problem. Thisallows FAVOR to innovatively extend a spatial tessellationtechnique for the purpose of frequency allocation. We imple-ment FAVOR in MicaZ platforms, and our extensive exper-iments with different network settings strongly demonstratethe superiority of FAVOR over existing approaches.

Categories and Subject DescriptorsC.2.1 [Computer-Communication Networks]: NetworkArchitecture and Design—Network topology

General TermsAlgorithms, Design, Performance

KeywordsContinuous Frequency Allocation, Wireless Sensor Networks,CC2420 Radio, Spatial Tessellation.

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1. INTRODUCTIONDeeply exploited as an emerging technology, Wireless Sen-

sor Networks (WSNs) have the potential to be widely de-ployed to support a variety of applications. In many recentapplications, both the scale of WSN deployments and the de-mand in data rate for individual sensor nodes keep increas-ing [3,6]. However, such a development is severely hamperedby the co-channel interference produced by the ever increas-ing wireless transmissions and their intensity. Moreover, co-channel interference may come from not only the ZigBee [2]devices involved in a WSN, but also other 2.4GHz ISM bandoccupants such as WiFi and Bluetooth [11,12].

As ZigBee compatible radios (e.g., CC2420 of MicaZ Motes[1]) may operate on up to 16 channels, common wisdom sug-gests that one can make use of the multi-channel ability toprevent WSN links from interfering each other. This hasled to quite a few research proposals, including prominentlymulti-channel scheduling for multi-hop transmissions (e.g.,[24]) and multi-channel MACs (e.g., [21]). However, thenumber of channels available to a WSN is much lower thanwhat ZigBee radios can offer, mainly due to the strong inter-ference from other occupants in the 2.4GHz ISM band [11].In our case (as shown in Figure 1), the experimental fieldis occupied by many WiFi testbeds, which effectively con-strains the “clean” spectrum1 to 2473–2483MHz where onlytwo ZigBee channels can fit in [2].

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Am

plit

ud

e [

dB

m]

Figure 1: We overlap the WiFi signal strength ob-served through inSSIDer with the 16 channels ofZigBee. It is easy to spot that, apart from channels25 and 26, other channels can be heavily interferedby multiple WiFi hotspots.

1Though avoiding WiFi interference temporally [12] or infrequency [28] is possible, directly incorporating these algo-rithms may severely complicate the system design, so weleave the ZigBee-Wifi coexistence issue as a future work.

By intensively experimenting (to be reported later) on ourMicaZ Motes and their CC2420 radios, we have discoveredthat it would be more efficient to use the spectrum resourcein a continuous manner. In other words, we should allocatechannels to nodes or links in terms of their center frequencies(rather than a finite set of channel IDs). As it is well knownthat interference attenuates with distance and the distancebetween two interfering nodes/links is a continuous vari-able in Euclidean space, it is bounded to be more flexibleand efficient (in term of spectrum utilization) to tune thefrequencies of the nodes/links in a continuous manner, com-pared with the conventional graph coloring approach [18]where discrete channels are allocated based on the conceptof (discrete) graph distance. Therefore, if one could allocatespectrum resource by jointly taking into account frequencyand distance in a continuous manner, there is still a great po-tential to improve the performance of WSNs. For practicalimplementation, the ability of CC2420 radio in adjusting itschannel center frequency at a granularity of 1MHz [1] doesoffer a good approximation of frequency fine-tuning.

Based on the above discovery, we first propose to shiftthe paradigm from channel allocation to (center) frequencyallocation in utilizing frequency spectrum for WSNs. Al-though continuously allocating channel center frequenciesto different links may lead to partially overlapped channelsbeing operating simultaneously, we can combat the result-ing interference by spacing them with a proper distance.In order to find the optimal frequency allocation for a setof spatially distributed nodes (or links), we further proposeFrequency Allocation for Versatile Occupancy of spectRum(FAVOR) as a novel framework for frequency allocation inWSNs. FAVOR consists of two main components: i) a met-ric that unifies frequency and distance, which allows us totransform the frequency allocation problem into a spatialtessellation problem in a higher dimensional space, and ii)an algorithm that innovates on the Centroidal Voronoi Tes-sellation (CVT) method [8] to search for the local but nearlyoptimal frequency allocations.

Roughly speaking, FAVOR results in a frequency alloca-tion such that nodes/links that are closer to each other indistance are further away from each other in frequency, whilethose far from each other in distance are allowed to be closein frequency. While FAVOR can be viewed as a continu-ous version of the conventional graph coloring approach, itoffers a much greater freedom due to the relaxation fromdiscrete sets to continuous spaces. The improved spectrumefficiency is bounded to favor WSN performance in through-put. Moreover, the FAVOR algorithm can be performed ina distributed manner using only local information. In orderto verify the efficacy of FAVOR, we perform extensive ex-periments on a set of arbitrary links, as well as on two datacollection trees. Our experiments demonstrate that FAVORoutperforms conventional graph coloring channel allocationsand a recent overlapped channel allocation mechanism [29]in terms of throughput, given a stringent spectrum resource.In summary, our main contributions are:

• We propose to replace channel allocation with (center)frequency allocation, representing a paradigm shift inutilizing the scarce frequency spectrum.

• We define an optimization objective unifying frequencyand distance; it enables us to formulate a frequency

allocation problem into a spatial tessellation problemin a high dimensional space.

• We propose a new algorithm inspired by CVT to searchfor the (local) optimal frequency allocations; the algo-rithm entails an easy distributed implementation witha need for only local information.

• We perform extensive experiments, both to investigatethe frequency-distance tradeoff and to verify the effi-cacy of our proposed FAVOR framework.

In the remaining of our paper, we first report the exper-iments that lead to our discovery of the distance drivingfrequency allocation method in Sec. 2. Then we presentour FAVOR framework in Sec. 3. Further experiments indemonstrating the superiority of FAVOR are reported inSec. 4. We also discuss the related work and possible ex-tensions of FAVOR to general wireless networks in Sec. 5,before concluding our paper in Sec. 6.

2. MOTIVATION AND MATHEMATICALBACKGROUND

In this section, we first motivate the design of FAVOR, byreporting our experiment results that exhibit an almost con-tinuous tradeoff between (center) frequency and (Euclidean)distance for two competing wireless links. We also brieflydiscuss the mathematical background needed for the devel-opment of FAVOR optimal frequency allocation algorithm.

2.1 Frequency–Distance Tradeoff for 2 LinksOur simple experiment setting involves two parallel wire-

less links, l1 and l2, operated by four MicaZ nodes. Theconfiguration is illustrated in Figure 2: we fix the locationof transmission link l1, and change the location of l2 withthe distance to l1 ranging from 1.2 m to 4.8 m. We makethe transmitters of the two links to send packets persistentlyas fast as possible, and measure the throughput of the twolinks, i.e., how many packets can be received correctly.

0 1.2 2.4 3.6 4.8m

1l 2l ... ... ...

Figure 2: Experiment configuration. Each link has alength (the distance from its sender to its receiver)of 3.6m.

2.1.1 The Anomaly of MicaZ with CSMAWe first report an anomaly of MicaZ motes to better mo-

tivate our case.2 It is well known that, though the nominaldata rate of CC2420 is 250kbps, the maximum stable datarate one may squeeze from it is much lower (it is only about50kbps for TelosB [22]). In our experience with MicaZ, wecan only push one packet (45 bytes in total including 26 byes

2This anomaly also exists for other nodes using CC2420 ra-dio, such as TelosB motes. However, we will not reportresults for other platforms due to the space limit.

pay load and 19 bytes header) through a ZigBee channel ev-ery 9ms, which achieves a data rate of 40kpbs (equivalent toa throughput of 0.16 with respect to the nominal data rate).In the following, we say a link achieving full data rate (orthroughput) if it has a performance comparable to a singlelink. One would expect that operating two links simultane-ously in the same channel would result in much lower (atleast halved) data rate for each link. The results in Fig-ure 3, nevertheless, show very different outcome, where wemeasure the throughput as the ratio between receiving ratesat the receivers and the nominal data rate.

An amazing observation is that both links roughly achievethe full throughput of 0.16. The reason accounting for this

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Figure 3: The throughput for two co-channel linkswith different distances.

anomaly is that the MCU (Atmel AVR Atmega 128L) usedby MicaZ spends a certain amount of time moving packetswithin the protocol stacks and, most prominently, perform-ing CSMA, the radio interface is left in an unsaturated mode.Consequently, CSMA may perfectly coordinate the two linkssuch that they both achieve nearly full throughput. Actu-ally, as we will show later, even adding up to 5 links will notdrastically decrease the throughput of individual links. Soone important message we have here is the follow:

Testing a channel allocation mechanism on CSMA-enabled platforms can lead to wrong conclusion,as even co-channel links may NOT conflict if weobserve the outcome only in terms of throughput.

2.1.2 Frequency vs. Distance without CSMAIn light of the results presented in Sec. 2.1.1, we test the

throughput of two links under different (center) frequencyand distance with CSMA disabled. While the four dis-tances are shown in Figure 3, we also vary the frequencyof l1 from 2475MHz to 2480MHz but keep the frequencyof l2 at 2480MHz. When CSMA is disabled, a single linkcan carry a packet as fast as every 2ms, resulting in a datarate of 180kbps and a throughput (against the nominal datarate) of 0.72. Therefore, the full data rate in this case is4.5 times higher than a CSMA-enabled link. The through-puts for all the frequency–distance combinations are shownin Figure 4. The figure clearly shows a throughput trade-off surface we may achieve by extending from a 1D discretefrequency space (for conventional channel allocations) to ahigher dimensional spatial-frequency space.

We also plot the two sets of results in 2D figures in Fig-ure 5, with Figure 5(a) fixing the distance at 1.2m and Fig-ure 5(b) fixing the frequency of l1 at 2479MHz. It is clearfrom Figure 5(a) that even a frequency interval of only 1MHzis rather usable at the minimum distance: while the higher

Figure 4: The lower throughput for two links withdifferent frequency–distance combinations. CSMAis disabled for both links.

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(a) Throughput vs. frequency (b) Throughput vs. distance

Figure 5: The throughput of both links as functionsof frequency interval (a) and distance (b).

throughput is almost full (beyond 0.7), the lower through-put still offers a reasonable data rate of about 50kbps (evenhigher than the full rate of a single link with CSMA en-abled). Figure 5(b) further shows that, by increasing thedistance between two links, both links may achieve a nearlyfull throughput. Remember that, if we follow the IEEE802.15.4 standard, only two independent channels are avail-able for the spectrum we can use (due to the heavy inter-ference from WiFi hotspots, see Sec. 1), whereas we almostget six usable but overlapped channels by varying center fre-quencies and distances in a continuous manner.3 Therefore,another important message we get is this:

Continuously tuning frequencies allocated to linkswith respect to the distances between them allowsfor a more flexible and efficient use of spectrum.

Note that a byproduct is that CSMA can be disabled as soonas the center frequencies of all links are slightly misaligned,reducing overhead and hence further improving throughput.

Now the question is, given a set of wireless nodes or links(whose locations are already fixed), how can we find the op-timal (center) frequency allocation for them? Our FAVORframework is exactly proposed to address this question. Be-fore diving into the details of our proposal, we need to brieflydiscuss the mathematical background relevant to our algo-rithm designed for FAVOR.

3We are still confined by the current implementation ofCC2420 radio, whose center frequency can be tuned onlyat a granularity of 1MHz. With more flexible radios devel-oped in the future, we will have more channels available.

2.2 Mathematical Background on Spatial Tes-sellation and CVT

Given a regionA ⊆ Rn, the set {Ai} is called a tessellationof A if Ai ∩ Aj = ∅ for i 6= j and ∪iAi = A. Let ‖ · ‖`2denote the Euclidean norm on Rn. For a set of points {ui}belonging to Rn, the Voronoi region Vi corresponding to thepoint ui is defined by

Vi ={v ∈ A|‖v − ui‖2`2 ≤ ‖v − uj‖

2`2 , ∀j 6= i

}.

The set {Vi} is termed Voronoi tessellation of A, with points{ui} called generators and each Vi referred to as the Voronoicell corresponding to ui.

For a fixed number of generators, varying their locationsresults in different tessellations of A. One way to identifythe“best” tessellation is to define a metric that measures thequality of a tessellation, and a typical metric is the “impact”of the generator ui to a point v in its cell,4 represented oftenby ‖v − ui‖`2 for v ∈ Vi. This ends up with an objectivethat represents the total impact of the generators to theirindividual cells:

I({Ai}, {ui}) =∑i

∫Ai

‖v − ui‖2`2Φ(v)dv, (1)

where Φ(v) indicates the density at location v. This objec-tive is neither convex nor concave, so optimizing this objec-tive may lead to many local minima (or maxima). Accordingto the theory of Centroidal Voronoi Tessellations (CVT) [8],we have the following four basic conclusions:

• The Voronoi tessellation is optimal for a fixed set ofpoints {ui}.

• A (good) local optimal solution is when every ui coin-cides with the gravity center (centroid) of its cell Vi.

• Lloyd’s method [14] that moves each ui to the centroidof its current cell in every iteration terminates at thislocal optimal solution with a linear convergence rate.

• Lloyd’s method outputs {ui} that are uniformly dis-tributed in A and, if A ⊆ R2, the cells that are almostall regular hexagons.

The interesting observation of the outcome of CVT isthat {ui} at termination are uniformly distributed in thespace, which is intuitively related to our need of “spreading”nodes/links over the available frequency spectrum. In fact,our FAVOR framework is a non-trivial extension of CVT toa space involving both frequency and distance (or location).

3. FAVOR: A LOCATION-AWARE FRE-QUENCY ALLOCATION SCHEME

In this section, we first discuss our system model, then wepresent our FAVOR framework in terms of the optimizationobjective and the algorithm to find a local optimal solution.Finally, we discuss how the algorithm can be implementedin practical scenarios.

4There are many interpretations to this metric [8], we choosethe one that is relevant to our design later.

3.1 System ModelWe assume a WSN consisting of a set of sensor nodes N ={n1, n2, ..., nN} with |N | = N , which are deployed on a 2Dplane. Although our proposal can be readily extensible to3D volume deployments in theory, we confine our scenariosto 2D deployments due to the limitations imposed by ourexperimental conditions. Let {ui}i=1,...,N be the locationsof the sensor nodes, where ui ∈ R2. Given a frequencyband B = [fmin, fmax] and the channel width fw, we assigneach sensor node ni a channel with center frequency fi ∈B′, where B′ = [fmin + fw

2, fmax − fw

2].5 Combining the

node’s location and frequency, a node ni now has a new“coordinate” (ui, fi) ∈ R2 × B′. We denote by N (ni) theone-hop neighbors of node ni: the nodes with whom ni cancommunicate directly given a common channel and a fixedtransmit power.

3.2 FAVOR Objective: Balancing Distance andFrequency

According to our observation in Sec. 2.1.2, a good fre-quency allocation scheme should assign very different fre-quencies to nodes that are close to each other but arbitraryfrequencies to nodes that are far from each other. We illus-trate such a possible location-dependent frequency alloca-tion scheme in Figure 6. However, as there are many possi-

freq

uen

cy

x y

Figure 6: Allocating center frequencies based on thenodes’ locations. While the black points indicate thesensor nodes, the “poles” on the points (with theirdifferent heights) represent different center frequen-cies allocated to the nodes.

ble allocations given a certain WSN deployment, we need tofind the best possible allocations, for which we need a metricto evaluate different allocations.

To this end, we define the impact metric as

‖v − uj‖`2 + β‖f − fi‖`2 ,

where v ∈ R2 and f ∈ B′, β is a weight to tune the tradeoffbetween frequency and distance, and we aim at a “tessella-tion” of the subset A = R2×B′ in R3 such that the followingFAVOR objective is minimized:

F({Ai}, {fi}) =∑i

∫Ai

(‖v − ui‖2`2 + β‖f − fi‖2`2

)dz, (2)

where z = (u, f) ∈ A. It is obvious that (2) differs from (1)mainly in that part of the coordinates are fixed: we do notget the freedom to move nodes around, only the frequenciesallocated to them are variables. Intuitively, F({Ai}, {fi})represents the total“impact”from nodes to their cells. Given

5Channels can also be assigned to links rather than nodes;we will discuss this later in Sec. 3.4.

fixed locations, minimizing the objective has the effect ofminimizing interference to some extent: according to whatwe discussed in Sec. 2.2, an optimal solution tends to spreadout the generators (nodes’ locations in this case). Since thelocations in R2 are fixed, frequencies for two close-by nodeswill be pushed further from each other. Another (relativelyminor) difference is that we let Φ(v) = 1 in (2), as bothEuclidean and frequency spaces are assumed to be homoge-neous for now. We could make use of Φ(·) to characterizethe non-homogeneity in space for our future development.

3.3 FAVOR: A CVT-based ApproachGiven the similarity between (1) and (2), it is natural that

one would propose to apply CVT to find a local optimal so-lution. Without loss of generality, we let β = 1 to simplifyour derivation. The problem we face now is twofold: i) as weneed to perform CVT at least in a 3D space (it can be 4Dif nodes are distributed in a 3D Euclidean space), we needan algorithm more efficient than the Lloyd’s method [14];otherwise nodes with limited computation resource cannotafford it,6 and ii) part of the coordinates for each ui ∈ Aare fixed, whereas CVT requires all the coordinates to bevariables. To tackle these issues, we first propose Approxi-mate CVT (A-CVT) to transform the problem into a moretractable and implementable form, then we apply gradientprojection method to handle the fixed coordinates.

Given a region A = R2 × B′ ⊆ R3 and suppose we applyVoronoi tessellations to partition A, we may re-write theobjective (2) as the following.

F({Ai}, {fi}) =

∫A

mini

(‖v − ui‖2`2 + ‖f − fi‖2`2

)dz (3)

The equivalence between (2) and (3) is obvious: for eachgenerator (ui, fi), integrating over its own cell Vi impliesan integration over all the points in A that are closer to(ui, fi) than to any other generators (by the definition of aVoronoi cell shown in Sec. 2.2). Now we get a global inte-gration over A, eliminating the need for re-computing theVoronoi tessellations in every iteration, but we have to facethe non-differentiable function min(·). To make the problemtractable, we apply an approximation to the min(·) functionto “smooth” it, leading to the following A-CVT objective.

F({Ai}, {fi})=

∫A

[∑i

(‖v − ui‖2`2 + ‖f − fi‖2`2

)λ] 1λ

dz (4)

Due to page limit, we omit the proof of (4) converging to(3) when λ→ −∞. In practice, we take λ ∈ [−40,−20].

As minimizing the A-CVT objective (4) is a typical non-linear optimization problem, we apply a gradient-descentmethod with gradient projection to search for a local mini-mum. The pseudocodes of the algorithm are shown by Al-gorithm 1. Roughly, the algorithm proceeds in rounds andtakes the following three steps in each round:

6Lloyd’s method requires to recompute the Voronoi tessel-lation in every iteration (due to the modified locations ofthe generators and the need to find the centroids of thecells), entailing high computational cost in Rn for n > 2.In fact, the complicated data structures required to modela R3 Voronoi tessellation cannot be easily implemented insensor nodes, and no algorithm for CVT in Rn, n > 3 hasbeen implemented even for common CPUs.

1. Compute gradient for each generator zi as (line 2)

g(zi) =

∫A

2(‖z − zi‖2`2

)λ−1(zi − z)

(∑j

‖z − zj‖2λ`2

)1−λλ

dz.

In order to facilitate localized computation and alsoto reduce the complexity, the summation in the thirdterm can be applied only for j : nj ∈ N (ni) and theintegration can be done only for z in the neighborhoodof zi. This is possible because the terms introduced bythose far-away locations contribute only insignificantlyto g(zi), due to λ→∞. This is also intuitively correctas the change in zi for CVT is only affected by zjwhose cell shares boundaries with that of zi. For aWSN, we can use the communication neighborhood toapproximate the tessellation neighborhood.

2. As ui is fixed and we can change only fi, we take gf (zi)as the projection of g(zi) on the frequency axis (line 3).

3. A tentative update is applied to the frequency by f+i =

fi − α · gf (zi) where α is a step size. If both |gf (zi)|and |f+

i −fi| become sufficiently small, the algorithm isterminated, returning the optimal frequency allocation(line 8); otherwise, the frequency of each ni is updatedby fi ← f+

i , the outcome is exchanged among neigh-boring nodes (line 6), and further compuation will beconducted during the next round.

Algorithm 1: FAVOR

Input: For each ni ∈ N , location ui, initial frequencyf0i ∈ B′, stopping tolerance ε1 and ε2

Output: f∗i for each ni1 For every node ni ∈ N in each round (every τ ms):2 Compute the gradient g(zi) of (4)3 Project g(zi) on fi to get gf (zi)

4 f+i = fi − α · gf (zi) /*α is the step size*/

5 if |gf (zi)| > ε1 ∨ |f+i − fi| > ε2 then

6 fi ← f+i ; Broadcast(fi) to nodes in N (ni)7 else

8 f∗i ← f+i

We omit the convergence analysis as it follows directlyfrom the basic theory of gradient-descent methods [4]. Theconvergence can be even faster if a centralized Quasi-Newtonmethod is used to solve (4). We illustrate the results ofour FAVOR algorithm in Figure 7. It is shown that, whilethe frequency allocation is initially ascending from left toright (with small frequency separations between neighbor-ing nodes), the outcome of FAVOR exhibits much betterseparation in frequency for nodes close to each other. Tofacilitate visual illustration, we use only a 1D deployment(nodes on a line) as an example, which leads to easily dis-cernable Voronoi tessellations in R2. However, our FAVORalgorithm works for any dimension higher than 2, while ourexperiments in Sec. 4 will be done for 2D deployments.

3.4 FAVOR for Disjoint Link SetAs FAVOR relies on a set of (point) locations {ui} to per-

form allocation, an obvious difficulty it may face is what ifno obvious points exist in a networking scenario. In particu-lar, a network may consist of several point-to-point wireless

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(a) Initial frequency allocation (b) Outcome of FAVOR

Figure 7: Frequency allocation based on Voronoi tes-sellations. With a regular (ascending) initial alloca-tion (a), our FAVOR algorithm outputs a much bet-ter allocation (b). In both cases, the correspondingVoronoi tessellations are also shown using red linesegments as cell boundaries.

links [29]. We propose two possible solutions for central-ized and distributed computing separately. If a centralizedcomputing is feasible, we may apply the extended Voronoidiagram where generators are not points but line segments(representing the links) [5]. Whereas this method may resultin rather accurate frequency allocation, computing Voronoitessellation with line segments as generators is quite timeconsuming. Therefore, we pick one point to represent eachlink in a distributed computing environment. This point canbe either the source or the destination of the link, or it caneven be the middle point of the link. If a point is chosen asthe source or the destination, the computation is performedby that node. If the middle point is chosen, the computationcan be done by either of the two nodes. Our experimentsreported in Sec. 4.2 show that replacing line segments bypoints still leads to very good performance in throughput.

3.5 FAVOR For Tree-based Data CollectionOne typical communication pattern in WSNs is the con-

vergecast. More specifically, nodes of a WSN are organizedinto a data collection tree with a root at sink ns, and ev-ery other node ni sends data directly or indirectly (throughmulti-hop routing) to ns [9]. In this case, frequency alloca-tion itself is not sufficient to tackle the conflicts in media ac-cess: it cannot avoid conflicts for either multiple links endingat the same node or one node having both incoming and out-going links, as such conflicts are the consequence of equip-ping a node with only one radio. Therefore, we need to per-form both the frequency allocation and a TDMA-like timeschedule. While a joint frequency allocation and schedulingproblem is beyond the scope of our paper, we simply adaptthe minimum latency scheduling mechanism [23].

We basically order the nodes into layers according to theirhop-distances to the sink on the collection tree T , then usea similar labeling mechanism as proposed in [23]. The ideaof this labeling is twofold: i) to guarantee that the num-ber of labels assigned to an outgoing link of node ni shouldbe 1 plus the number of descendants of ni in T , and ii)to assign different labels for links sharing the same node.Whereas the proposal in [23] adopts (orthogonal) channelallocation to enable parallel transmissions, our frequency al-

location potentially allows more parallel transmissions. Forthe convenience of deriving bounds, channels are allocatedusing a first-fit distance-(ρ + 1) graph coloring in [23], butwe allocate different frequencies using FAVOR. As a nodenj needs to tune to the frequency fi when transmitting toa receiver ni, leaf nodes (being receivers to no one) do notneed their own frequencies. We will show an example of ourfrequency allocation and scheduling in Sec. 4.3.

A similar frequency allocation and scheduling method alsoworks for other types of communication patterns, such asbroadcast (disseminating commands from the sink to thenetwork) and aggregation (each relay node may send outless data then it receives). However, we focus only on datacollection in our paper.

3.6 Time SynchronizationTime synchronization severs as a fundamental infrastruc-

ture for the TDMA scheduling used by FAVOR. Unfortu-nately, the existing synchronization protocols (e.g., FTSP[17]) rely on periodically flooding, resulting in a heavy trafficload that may significantly compromise the network through-put. In this paper, we employ a link-based approach thatpiggybacks control information with data traffic: for eachtransmission link, the transmitter synchronizes its transmit-ting schedule with that of the receiver based on the infor-mation piggyback with the acknowledgements sent by thereceiver. To further suppress the control traffic, the trans-mitter may require acknowledgement only for the first trans-mission in each transmission schedule that consists of severaltransmissions as shown by Figure 11(b). In effect, non-rootnodes report data to their respective parents while gettingsynchronized with the latter. Therefore, running this proto-col within a data collection tree simply forces every node tostay synchronized with the root.

4. EVALUATIONWe have implemented FAVOR in our MicaZ platforms

and performed extensive experiments on them. The excitingexperimental results are reported in this section. We firstdiscuss the basic parameter settings for our experiments,then we describe our experiments on two different networkscenarios. Finally, we briefly examine the convergence ofFAVOR algorithm.

4.1 Experiment SettingsWe apply MicaZ Motes and TinyOS 2.1 as the hardware

and software platforms. As explained in Sec. 1, the availablefrequency spectrum we adopt is 2474–2481MHz, to avoid the“contaminated”spectrum by WiFi devices. According to theZigBee standard [2], each channel has a 2MHz bandwidthand the center frequencies of two neighboring channels haveto be separated by 5MHz. Therefore, only two orthogonalchannels (with center frequencies 2475 and 2480) can fit intothis spectrum (hence we term this scheme two-channel).However, we modify the codes for FAVOR to choose sixpossible center frequencies: 2475, 2476, 2477, 2478, 2479,and 2480MHz.7 We will also test the proposal made in [29],where a center frequency interval of 3 or 2MHz has been sug-gested. This means that, given our available spectrum, three

7The CC2420 radio used by MicaZ Motes can adjust thefrequency with only a granularity of 1MHz, which somewhatlimits the potential of FAVOR. FAVOR can perform betterif frequencies can be tuned continuously.

1s

2r

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Two−channelw/ CSMA

Three−channelw/o CSMA

Three−channelw/ CSMA

FAVORw/o CSMA

(a) Network deployment (b) Statistics on TRPs for all links

Figure 8: A five-link scenario and the corresponding experimental results.

channels are available: 2475, 2477 (or 2478), and 2480MHz(hence we term this scheme three-channel). We apply agreedy graph coloring approach to allocate channels for bothtwo- and three-channel schemes, while FAVOR uses its ownalgorithm for frequency allocation. In the following, we useonly the center frequency to indicate a channel.

If we can avoid assigning the same channel to more thanone link, we disable CSMA for all links. This allows packetsto be pushed into a channel faster: one packet every 2msaccording to Sec. 2.1.2. For cases where the same channelhas to be assigned to different links, we test both with andwithout CSMA: we can only send one packet every 9ms inthe former situation (see Sec. 2.1.2 again), whereas colli-sions may totally ruin some links in the latter situation, asalready shown in Figure 5(a). We deploy our WSNs on theceiling of our laboratory (see Figure 9), in order to emulatean indoor monitoring application scenario. We perform eachexperiment for 5 minutes, and use the total received packets(TRPs) at each destination node as the performance mea-sure; it is actually an indicator of the throughput. For eachreported data point, we perform 10 experiments, and plottheir statistical quantities such as means and/or interquar-tile ranges.

Figure 9: A MicaZ-based WSN testbed on the ceil-ing of our research center.

4.2 A Five-Link ScenarioWe first test a scenario containing five links {li = (si, ri), ∀i =

1, ..., 5}, as shown in Figure 8(a). We deliberately put the

five links in a relatively small area (about 20m2), in order tomimic a small section of a densely deployed WSNs (whichwe do not have at our disposal). The optimal frequency al-locations based on different schemes are shown in Table 1.Obviously, for schemes other than FAVOR, the number ofavailable frequencies (channels) is smaller than the numberof links, so some frequency has to be allocated to more thanone link; the optimal allocation can simply try to space theseco-channel links as far as possible.

Table 1: Frequency allocations for the five-link sce-nario based on different schemes.

Links l1 l2 l3 l4 l5Single-channel 2480 2480 2480 2480 2480Two-channel 2480 2475 2480 2475 2480

Three-channel 2475 2477 2480 2475 2477FAVOR 2476 2477 2480 2475 2478

We test all the four schemes: single-channel, two-channel,three-channel, and FAVOR; each with CSMA enabled anddisabled (except FAVOR, as it does not need CSMA at all).The results in terms of TRPs per link are shown in Fig-ure 8(b), where both interquartile ranges (boxes) and means(circles) are shown. It is obvious that FAVOR operatesthree out of five links (l2, l3, and l4) much better than otherschemes: mean TRPs can be up to three times higher thanthe one second to it. For another two links, FAVOR also doesa relatively good job (better than any CSMA-enabled cases).Consequently, the total throughput of FAVOR is five timesof the commonly used single channel with CSMA. Althoughthree-channel without CSMA appears to achieve rather highmean TRPs in some links (l3 and l5), the huge interquartileranges indicate a very unstable performance, rendering thisscheme useless in practice.

The tradeoff between using CSMA or not (for other schemes)is very evident: CSMA delivers a rather stable performanceby sacrificing throughput: the nature of a random accessscheme. However, FAVOR achieves both stable and highthroughput without the need for CSMA. In fact, FAVOR

n_2 n_3 n_4 n_5 n_6 n_7 n_8 n_9 n_10 n_11 n_12 n_13 n_14 n_15 n_16 n_170

1000

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of

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Ps

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FAVOR w/o CSMA

Figure 10: Performance of six different media access schemes in an unbalanced data collection tree.

could perform better if the radio allowed a finer granular-ity in tuning frequencies: we have to round the frequencyallocation done by FAVOR to integer values of MHz, whichleads to the relatively bad performance of l1 and l2.

4.3 Unbalanced Tree-based Data CollectionIn order to demonstrate the benefit of applying FAVOR

in a practical situation, we test the performance of differentschemes in an arbitrary (unbalanced) data collection tree.The deployment area is roughly 600m2, and the node loca-tions, as well as the network topology, are shown in Fig-ure 11(a). The frequencies (or channels) are allocated tonon-leaf nodes, and we apply the labeling method in [23] forlink schedules. Note that the disjoint-tree based schedul-ing [24] does not apply to this small network.

According to what is shown in Sec. 4.2, the schedule needsalso to avoid links with the same frequency transmittingsimultaneously. This leads to the obvious consequence thatthe more frequencies we can allocate, the less time slots weneed in one round (during which every node gets a chanceto transmit). As a result, two-channel scheme needs at least29 slots, three-channel scheme needs at least 24 slots, whileFAVOR needs only 22 slots. For single channel, we enableCSMA and apply CTP [9] to perform data collection. Wealso enable CSMA for two- and three-channel schemes, butwith a different schedule: it needs only to guarantee a senderand a receiver staying at the same frequency when the linkbetween them is active. Consequently, only 9 time slots areneeded. Given limited space, we show only the frequencyallocation and schedule for FAVOR in Figure 11.

As expected, the results in Figure 10 show that FAVORsurpasses all other schemes, and it achieves a throughputthat is 3.36 times of that achieved by CTP. Apparently, FA-VOR beats two- and three-channel schemes due to the lesstime slots in a round, and it prevails against all CSMA-enabled cases thanks to the elimination of the overheadbrought by CSMA. Moreover, FAVOR allows for a more fairsharing of the bandwidth (every node gets roughly the samethroughput), which cannot be guaranteed by any CSMA-based schemes.

4.4 Balanced Tree-based Data CollectionOne may argue that FAVOR’s continuous (hence poten-

tially irregular) frequency allocation cannot offer significantnetwork performance in a regular network topology, e.g.,a balanced data collection tree. Therefore, we re-deploy

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(a) Data collection tree (frequency allocation marked on links).

1 2 3 4 5 6 7 8 9 10 11 12 𝑛2 → 𝑛1 𝑛3 → 𝑛1

𝑛14→ 𝑛7

𝑛15→ 𝑛8

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13 14 15 16 17 18 19 20 21 22 𝑛4 → 𝑛1 𝑛5 → 𝑛2 𝑛6 → 𝑛2

𝑛11→ 𝑛5

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𝑛7 → 𝑛3 𝑛9→ 𝑛4

𝑛8 → 𝑛3

𝑛10 → 𝑛4

(b) Minimum delay schedule on the tree.

Figure 11: Unbalanced data collection tree, withFAVOR frequency allocation (a) and min-delaytransmission schedule (b). The node locations in(a) are plotted roughly proportional to their actuallocations in our ceiling testbed.

our testbed to form a balanced data collection tree withnodes regularly spaced, as shown in Figure 12. All settingsare maintained as those in Sec. 4.3, except that differentFAVOR frequency allocation and transmission schedule arecomputed to suit this tree.

The results in term of TRPs are reported in Figure 13.Obviously, the observations made for Figure 10 still holdhere, except that the advantage of FAVOR over others hasbeen slightly reduced. This stems from the reduced numberof links involved in this tree: as FAVOR surpasses others byoffering higher frequency utilization, its advantage becomesmore conspicuous if a higher utilization is actually needed.

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Figure 13: Performance of six different media access schemes in a balanced data collection tree.

2n 4n

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1n

24772477 2477

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Figure 12: Balanced data collection tree with FA-VOR frequency allocations marked on links. Thenode locations are plotted roughly proportional totheir actual locations in our ceiling testbed.

4.5 Convergence of FAVORWe briefly verify the complexity (in terms of communica-

tion rounds) of FAVOR in a distributed computing scenario:a 30-node WSN. As we unify both frequency and distanceinto a scale of [0, 1], the A-CVT objective value is alwayssmaller than 1. As shown in Figure 14, the convergence un-der different step size α’s often takes 20–30 rounds. As suchmessage exchanges can piggyback with other transmissionactivities and frequency (re)allocation does not happen veryoften, the overhead of FAVOR (in terms of the entailed com-munication and computation costs) is affordable, given thesubstantial throughput improvement it can bring.

0 5 10 15 200.0305

0.031

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# of rounds

A-C

VT

ob

jective

= 10

= 15

= 20

= 25

Figure 14: The convergence of FAVOR in 30-nodeWSN.

5. RELATED WORK AND DISCUSSIONSWhile exploiting multi-channel access to improve the per-

formance of general multi-hop wireless network has been in-tensively studied in the last decade (e.g., [20]), dedicatedinvestigations for WSNs started rather late [13, 24]. Mostproposals make use of graph-coloring heuristics to allocatechannels in the whole network, but the work of [24] inno-vated in allocating channels to disjoint trees in WSNs. Asthe allocated channels are assumed to be orthogonal, theinter-channel interference is often neglected. However, theinter-channel interference does exist and its impact on linkcapacity and the performance of multi-channel protocols aresystematically explored in [24,27].

Given the limited number of non-overlapping (or orthog-onal) channels, partially overlapped channels were later in-troduced to improve the spectrum utilization in WiFi net-works [19]. However, it is only recently that the specialinter-channel interference feature of ZigBee radio was identi-fied [29]. In particular, whereas the center frequencies of twopartially overlapped channels have to be sufficiently apartfrom each other for WiFi radios to properly operate [19],the ZigBee radios used by WSNs are far more robust due totheir simple design: as we have also shown in Sec. 2.1.2, onlya difference of 1MHz is enough for two channels to delivera reasonable throughput. However, the work in [29] did notdiscover the advantage of continuous frequency allocation; itfocuses only on adjusting CSMA. As demonstrated by ourFAVOR, CSMA may not be needed anymore if frequencyallocation is applied.

The multi-channel feature of ZigBee radios has also beenapplied to improve the quality of individual links [7] andto avoid the interference from WiFi devices [28]. However,the scalability of these proposals are still confined by thelimited channels. We believe that the flexible spectrum uti-lization offered by FAVOR can also contribute to tacklingthese problems, as well as problems under a joint routingand link scheduling framework (e.g., [16]) or for duty-cycledWSNs (e.g., [10]).

Currently, FAVOR cannot be directly applied to WiFinetworks due to the significant inter-channel interference be-tween two partially overlapped channels [25]. This may stemfrom the particular filter design for a WiFi radio receiver,but we may be able to redesign the filter to reduce the inter-channel interference (hence to apply FAVOR for achievinga higher spectrum utilization), at a cost of slightly reduceddata rate.

6. CONCLUSIONIn this paper, we present FAVOR, a novel framework for

efficient spectrum utilization in WSNs. We exploit a con-tinuous frequency allocation to replace the conventional dis-crete multi-channel allocation. We then combine frequencyand location into one space and thus transform the optimalfrequency allocation problem into a spatial tessellation prob-lem. Our FAVOR algorithm innovates on the CentroidalVoronoi Tessellation method to search for the nearly optimalfrequency allocations. Finally, we perform extensive experi-ments to demonstrate the feasibility and superiority of FA-VOR. For future work, we plan to apply FAVOR to broaderscenarios including data aggregation WSNs (e.g., [26]) andWSNs with mobile elements (e.g., [15]).

AcknowledgmentsWe would like to thank the anonymous reviewers for their in-sightful comments and constructive suggestions. This workwas supported in part by AcRF Tier 2 Grant ARC15/11and Tianjin Research Program of Application Foundationand Advanced Technology (China) No. 12JCQNJC00200.

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