opportunistic channel sharingin cognitive radio networks

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Opportunistic Channel Sharing in CognitiveRadio Networks

Tarun Bansal, Dong Li, and Prasun Sinha

Abstract—Licensed white space channels can now be used opportunistically by unlicensed users, provided the channels arerelinquished when needed by the primary users. In order to maximize their potential, these channels need to be assigned to thesecondary users in an efficient manner. The protocols to enable such an assignment need to simultaneously aim for fairness, highthroughput, low overhead, and low rate of channel reconfigurations. One way of channel assignment is to allow neighboring AccessPoints (APs) to operate on the same channel. However, if not done properly, this may increase the number of collisions resulting inlower throughput. In this paper, we present a new channel assignment algorithm that performs controlled channel sharing amongneighboring APs that increases not only the fairness but also the total throughput of the APs. Controlled sharing and assignment ofchannels leads to a new problem that we call as the Shared Coloring Problem. We design a protocol based on a centralized algorithm,called Share, and its localized version, lShare that work together to meet the objectives. The algorithm has tight bounds on fairness andit provides high system throughput. We also show how the 802.22 MAC layer protocol for Wireless Regional Area Networks (WRANs)can be modified considering the typical case of low degree of interference resulting from the operations of Share and lShare. Resultsfrom extensive ns-3 simulations based on data traces show that our protocol increases the minimum throughput among all APs by atleast 58% when compared to the baseline algorithms.

Index Terms—Cognitive radio networks, spectrum allocation, opportunistic channel sharing.

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1 INTRODUCTION

Cognitive Radio (CR) technology has gained increasedattention due to an FCC mandate that now allowsunlicensed radios to operate in the unused portionsof the UHF band. Such channels, however, need to berelinquished when primary (or incumbent) users beginusing them. Solutions that can opportunistically use suchchannels can help alleviate the congestion in the ISMbands. In one of the first such efforts, the nation’s first TVwhite space network was deployed in Claudville, VA inlate 2009 [1]. We envision a proliferation of such wirelesssolutions that take advantage of the white space chan-nels. If used judiciously, these can revolutionize highspeed wireless data services using both infrastructure(access-point based) [2] and peer-to-peer architectures.Our focus in this paper is on the former.

Advances in hardware technologies have made itpossible to simultaneously use the capacity of a largenumber of channels that may or may not be contiguousby the use of Non-Contiguous OFDMA (See Section6 for details). Even if a collision happens on one ofthe channels used by the node, the packets transmittedon other channels are still delivered successfully. But,even with multiple channels assigned to Access Points(APs), it has been shown [3] that if neighboring APsare assigned different channels, then for 50% of USpopulation, white space will provide bandwidth of less

• Authors are with the Department of Computer Science, Ohio StateUniversity, Columbus, OH, 43210.E-mail: {bansal, lido, prasun}@cse.ohio-state.edu

A B C D E

AP 1 AP 2

Fig. 1. Channel allocation using 2M channels. Solid anddotted lines represent the transmission and interferenceranges of APs, respectively. With channel sharing, eachAP increases its throughput by a factor of 1.6.

than 720 Kbps per user1. This is particularly limiting forapplications that have high bandwidth requirements ofthe order of 5-6 Mbps such as HD video streaming [4],HD video conferencing [5]. One way to further increasethe available bandwidth is to allow neighboring APs toopportunistically share channels. This may increase thenumber of collisions, but at the same time it can increasethroughput of APs under several scenarios as explainedbelow:

• Scenario 1: Low interference between neighboringAPs: Consider Figure 1 that shows a network of2 APs with a total of 2M channels in the system.The two APs are said to be neighbors of each othersince clients associated with one of the APs may liein the interference range of the other AP. If we donot allow the neighboring APs to share a channel,then maximum throughput achieved by each APunder fair channel assignment is M units, where 1

1. Assuming every user spends only 20 mins per day on white spacechannels

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IEEE TRANSACTIONS ON MOBILE COMPUTINGThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

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exclusive channel is considered equivalent to 1 unitof throughput. If we assign all the 2M channels toboth the APs, then a collision can happen when thefollowing two conditions hold simultaneously: (i)An AP is communicating with its client in the regionB, C or D; and, (ii) The other AP is simultaneouslycommunicating on the same channel. However, ifthe size of the overlapped region (B, C and D) issmall, then the chances of such an event is low.Suppose that due to such collisions each AP onlyobtains 80% of the exclusive throughput, then intotal each AP obtains a throughput of 1.6M , whichis an improvement of 60%. However, channel shar-ing must be performed only when the overlap islow, otherwise the increased collision probabilitycan lower the throughput.Using the data trace collected previously [6], westudied the deployment of cellular Base Stations(BS) and computed the interference caused at mobilephones if neighboring BSs operate on the samechannel. [6] provides the values of signal strengthsat the mobile phones from the associated base sta-tion as well as all the neighboring BSs. Combiningthe readings of multiple users over a long periodof time, we had a total of approximately 260,000readings. We studied the variation in the SINR ofthe signals transmitted from the associated BS to thephone. We call the set of readings (or scenarios) thatlie between 12.5th and 87.5th percentile as median75% readings. We found that on an average if eachBS shares a channel with 2 of its neighboring BSs,then the median 75% of SINR readings would bebetween 18 dB and 31 dB. On the other hand, ifBSs do not share channels, then the median 75%readings were between 21 dB and 33 dB. Thus,sharing channels among multiple BSs would lead tovery little interference in the median 75% scenarios.

• Scenario 2: Large number of available channelsand high density of APs: In a simple experimentin a typical student apartment building near ourcampus, we observed up to 65 interfering APs. Insuch a scenario, without sharing it may be impos-sible to assign unique channels to neighboring APs.However, with sharing, each AP can be assignedat least one channel and thus will have non-zerothroughput.

The problem of channel assignment under this newparadigm of opportunistic channel sharing, that wecall as Shared Coloring, is distinct from other coloringproblems previously studied like list coloring, partialcoloring, fractional coloring, defective coloring (see Sec-tion 6 for details). It is also in contrast to traditionalchannel assignment problems in cellular networks whereneighboring APs are disallowed from operating in thesame channel in order to provide guaranteed packet de-livery to the real-time voice traffic. Although, LTE basedsolutions allow neighbors to share the same channel,

however edge users are still assigned different channelsregardless of the amount of the overlap among neigh-boring SBSs [7].

We define a channel assignment of white space chan-nels to a set of Access-Points (APs) to be feasible if achannel assigned to an AP does not interfere with anyprimary user. We seek to design a comprehensive andpractical protocol to enable the computation of a feasiblechannel assignment while ensuring the following: (1)Fairness in the number of channels assigned to APs;(2) High throughput of the system; (3) Low computationdelay; (4) Low message overhead; and, (5) Fewer channelreassignments.

Designing a system where neighboring APs share thesame channel while ensuring fairness and high through-put is particularly challenging due to the followingreasons: (1) Channel sharing may lead to throughput lossif it is not done in a controlled way; (2) Transmission andinterference ranges of APs may not follow a disk model;(3) Throughput of each AP needs to be computed con-sidering channel sharing across multiple neighbors; (4)Ability of APs to transmit on multiple channels furtheradds to the complexity as APs may have different trans-mission and interference ranges on different channels;and, (5) Frequent arrivals and departures of licensedusers as well as changes in throughput requirements(e.g. in case of Internet usage by smartphone users) maynecessitate high overhead reconfigurations.

Our protocol is comprised of a centralized algorithm,Share and its localized version, lShare, both of whichseek to find a fair channel assignment for the APs. Tominimize the number of channel reassignments, lShareoperates in between periodic executions of the Sharealgorithm. This paper makes the following key contri-butions:

• We propose a new system model that allows neigh-boring APs to opportunistically share channelsamong themselves depending on the overlap amongneighboring SBSs. We call the problem of fair allo-cation under this system model as Shared Coloringand prove that it is NP-Hard.

• We show how the 802.22 MAC protocol for WRANscan be modified to enable controlled channel sharingamong APs. Using ns-3 simulations, we show thatfor a system with opportunistic channel sharing, themodified MAC protocol provides higher throughputthan the sensing based MAC protocols.

• An approximation algorithm, Share with provableperformance bounds is proposed. The bound on theminimum throughput achieved by Share is provento be tight.

• Through extensive realistic ns-3 simulations thatalso consider sensing uncertainties, we demonstratethe performance improvement of our protocol withrespect to other algorithms. Our protocol increasesthe max-min throughput to at least 58% when com-pared to the baseline algorithms.

Our design and analysis assumes that radios may


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have non-circular transmission and interference ranges,our algorithm performs well even in scenarios withobstacles (shown using real data in Section 5). In the nextsection, we present the system model. In Section 3, wepresent the problem statement and our solution. Section4 discusses some aspects of our algorithm that makesit more practical. In Section 5, we present extensivesimulation results. The next section, contrasts our workwith prior work in related areas. Finally, we concludethe paper in Section 7.

2 SYSTEM MODEL

We consider a Wireless Regional Area Network (WRAN)with M Secondary Base Stations (SBSs) (or nodes/APs)r1, r2, . . . , rM , which are located in a 3D space. MultipleSecondary Users (SUs) may be associated with the sameSBS. The set of SUs associated with SBS ri is denoted byset Qi. Two SBSs are neighbors of each other if some clientassociated with one SBS can be interfered by the otherSBS on some channel. The set of SBSs that can interferewith the reception of signal at SU sj on channel ck isdenoted by the set N(sj , ck). The universal channel setU consists of channels c1, c2, . . . , c|U|. SBSs (or nodes)refrain from communicating on channels occupied byPrimary Users (PUs). Each SBS is capable of operatingon multiple channels that has been made possible byNon Contiguous OFDMA technology (See Section 6 fordetails). The set of channels on which an SBS ri cancommunicate without interfering with PUs is termedas its availability set and is denoted by W (ri). The setof channels that are assigned to SBS ri is denoted byA(ri). We denote the assignment of channels over thewhole network by A. For simplicity of explanation,we assume that all channels provide the same amountof throughput, although, it is possible to extend thealgorithm to take into account the variation in channelconditions.

The nodes communicate with a central entity, knownas Channel Assignment Server (CAS) over a backbonenetwork, such as the wired Internet. The CAS is responsi-ble for making decisions regarding channel assignmentand then informing the SBSs. This centralized compu-tation increases the throughput of the SBSs. Further,the SBSs do not need to communicate with each othersince all communications are done with CAS over thebackbone network. This requires the SBSs to cooperatewith each other and to follow the channel assignmentas given by CAS2. We also assume that SBSs provideequal throughput to all SUs associated with them asexplained in Section 3.2. The throughput available to allSUs associated with SBS ri is denoted by T (A, ri). Thisis also termed as the throughput of SBS ri. We calculate

2. We assume that the different SBSs cooperate with each other andfollow the channel assignment as specified by the CAS. However, ifthe SBSs are selfish or belong to different administrative domains, theymay not follow the specified channel assignment. For such a scenario,our algorithm would need to be extended to take the presence of non-cooperating SBSs into account.

TABLE 1Symbols used

Symbol DescriptionU Universal channel setM Number of SBSs in the networkΔ Maximum neighbors of any SBS among all SBSsri (Radio) Node or SBS isj SU sj associated with some SBSck kth channel in the universal channel set UW (ri) Availability set of ri : W (ri) ⊆ UN(ri) Set of neighboring SBSs of SBS riN(sj , ck) Set of SBSs that interfere the reception at sj on ckA(ri) Set of channels assigned to ri: A(ri) ⊆ W (ri)A Assignment of channels over all the nodesT (A, ri) Throughput available to SUs associated with ripij Probability that SBS ri will transmit on channel cjQi Set of SUs associated with SBS ri

the throughput under saturation conditions which meansthat the transmission queues of all SBSs are backlogged.In this paper, we focus only on downstream traffic, asmost of the traffic is downstream [8]. Since the upstreamtraffic is generally quite low, a no-interference assign-ment of channels may provide enough throughput forupstream.

Objective: As discussed in Section 1, sharing of chan-nels among neighboring SBSs can result in higherthroughput for the end-users. In this paper, our primaryobjective is to compute a shared channel assignmentfor SBSs that maximizes the lexicographic sequence ofthroughput of the end-users while maintaining fairnessamong them. We will describe our formal objective inSection 3.4.

3 SHARED CHANNEL ASSIGNMENT PROTO-COL

In this section, we present our channel assignment proto-col that allows opportunistic sharing of channels. In Sec-tion 3.1, we first present the MAC layer algorithm chosenfor WRANs that is suitable when neighboring SBSs sharechannels. In that section, we also discuss why sensingbased algorithms are not appropriate when neighboringSBSs opportunistically share channels. The next sub-section explains how to estimate the throughput thatthe SBSs would receive under channel sharing model.This estimation technique is later used by the channelassignment algorithm. Then, we explain the setup ofour algorithm and the problem formulation, specificallythe objective is to assign channels to SBSs such thatthe lexicographic sequence of the throughput of theSUs is maximized. Subsection 3.6 describes the Sharealgorithm in detail. Our algorithm works by convertingthe channel assignment problem to a vertex coloringproblem where vertices represent the SBSs in the channelassignment problem. However, unlike traditional graphcoloring, here it is possible to assign the same channelto the neighboring vertices if the overlap between thecorresponding SBSs is small. Finally, Subsection 3.7.2describes the performance of our algorithm.


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3.1 Selecting Appropriate MAC Layer Algorithm

For an infrastructure based network with associatedclients, most of the work in the literature has assumedthat neighboring Access Points (or APs) are assigneddifferent channels (see Section 6). In a Wireless Re-gional Area Network (WRAN) with channel sharing, theneighboring SBSs should typically be assigned the samechannel only if the overlap between the transmissionrange of one and the interference range of the other issmall. Under such a constraint, three observations can bemade:

• A small overlap between neighboring SBSs impliesthat these SBSs may be far away from each othersuch that they do not lie in mutual interferencerange, thus making the sensing component of MACalgorithms redundant. For example, in Figure 1, SBS1 and SBS 2 cannot sense transmissions of eachother. This may result in higher packet collisionsas well as capture effect such that one of the SBS isunable to get channel access.

• A small overlap between neighboring SBSs furtherimplies that the CTS from only a few clients asso-ciated with an SBS is able to inhibit transmissionfrom the neighboring SBS. For example, in Figure1, only the CTS from clients in region C is ableto prevent the other SBS from interfering. Further,usage of RTS/CTS along with carrier sensing leadsto loss in throughput [9] due to increased overheads.

• Even if a collision happens at some SU due totransmission from a neighboring SBS, in the nextslot, it is still possible for the two neighboring SBSsto transmit simultaneously provided the receivers ofthe transmissions are far away (e.g., in region A forSBS 1 and in region E for SBS 2 in Figure 1).

Thus, sensing based algorithms are not appropriatefor WRANs where neighboring SBSs may share chan-nels and may even result in throughput loss due tounnecessary backoffs and sensing overheads. For theWRANs, IEEE 802.22 working group has also proposeda MAC layer algorithm [10], [11] that requires eachSBS and its associated clients to be synchronized. Timeis divided into superframes that are further dividedinto 16 frames of 10ms duration each. Each frame isaccompanied by a “Frame Preamble” at the beginningand a “Time Buffer” at the end. In each frame, theSBS assigns multiple channels for both upstream anddownstream data corresponding to each of its clients.Within each frame, SBS can communicate with multipleSUs or communicate with the same SU multiple times.Further, as described before, it is possible for the SBSto communicate with multiple SUs at the same time bymaking use of different channels.

For the scenario with channel sharing, it is imperativeto modify the MAC layer algorithm so that the prob-ability of collisions when neighboring SBSs are trans-mitting on the same channel is reduced even further.To that end, we propose a slight modification to IEEE

802.22 MAC that enables controlled channel sharing amongSBSs and reduces the probability of collisions at theSUs. At the beginning of each frame, SBS ri makes adecision whether to use channel cj for transmission ornot. However, it needs to ensure that the fraction offrames in which ri transmitted on cj (over the last Lframes) is maintained below pij (called the channel usageprobability). Thus, by keeping the long-term usage ofchannel cj below pij , ri can utilize cj only when otherchannels do not provide sufficient bandwidth to handlesudden high bursts of data while allowing neighboringSBSs to use cj at the same time. The SBSs and the SUsdisable carrier sensing. By avoiding sensing, the chancesof collision may increase in certain cases where theoverlap between neighboring SBSs is high. However, bysetting pij carefully, it is possible to reduce the collisionprobability, thereby increasing the throughput. For eachSBS, ri and channel cj , pij is computed by the CAS on thebasis of the channel usage probability of neighbors of ri,the total throughput that ri obtains on all channels otherthan cj (described in Section 3.6) and the interferenceexperienced by clients associated with ri from neighbor-ing SBSs. Note that the IEEE 802.22 MAC algorithm doesnot guarantee synchronization among neighboring SBSs.If the neighboring SBSs are sharing the same channel,it can lead to increase in collisions since it is possiblethat a frame from one SBS interferes with multipleframes from the neighboring SBS resulting in highercollisions. Weak synchronization among neighboring SBSsensures that they begin and end transmitting on a sharedchannel at approximately the same time, thus ensuringthat a frame in channel cj by SBS ri can collide withat most one frame in channel cj by some neighbor ofri. Section 4.3 describes how neighboring SBSs can beweakly synchronized with little overhead (see Section4.4).

We performed experiments in ns-3 to evaluate andcompare the performance (see Figure 2) of the modified802.22 MAC layer algorithm (with weak synchroniza-tion), modified 802.22 MAC (with no synchronization),CSMA-CA (without RTS-CTS) and CSMA-CA (withRTS-CTS). In both the flavors of IEEE 802.22 MAC proto-col, channel usage probability was computed (details inSection 3.6) for every SBS such that collision probabilityamong neighboring SBSs is reduced. The size of the fieldwas chosen as 200km × 200km in which SBSs and SUswere deployed using the data obtained [6]. Each SBShad 50-150 clients associated with it. Mobility patternof SUs and the resulting variation in signal strengthvalues (from the associated SBS as well as the neighbor-ing interfering SBSs) were simulated using traces from[6]. However, some of the packets reaching SUs maynot be successfully decodable due to interference fromneighboring SBSs operating on the same channel. Totake this into account in the simulations, Packet ErrorRate (PER) at SUs was formulated as a function ofSINR at SUs and the modulation used. Communicationwas only considered from SBS to SUs (see Section 2).


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0 25 50 75 100

Ave

rag

e T

hro

ug

hp

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SB

Ss (

in k

bp

s)

Number of SBSs in the system

Modified 802.22 with SyncModified 802.22 without Sync

CSMA / CACSMA / CA with RTS/CTS

Fig. 2. Plot of average throughput for various MACalgorithms using ns-3

The data requested by SUs followed the trace collectedin [12]. However, rate of data request by SBSs wasscaled so as to achieve saturation conditions at SBSs.With synchronization, the chances of collision amongneighboring SBSs is reduced and thus throughput isalso increased (see Figure 2). Also, by limiting the long-term usage probability of channel by SBSs, the collisionprobability is further reduced. When the number ofSBSs is small, the CSMA/CA algorithm performs betterthan RTS/CTS based algorithms as the throughput lossdue to fewer collisions is lower than that due to theoverhead of RTS/CTS packets. However, the sensingbased algorithms do not perform as well as modified802.22 protocols due to unnecessary higher overheadsof sensing and backoffs, as discussed before.

3.2 Estimating throughput under channel sharingmodelIn order to assign channels in a fair manner, a prereq-uisite is to estimate the throughput obtained by eachSU under the channel sharing model. This estimate ofthroughput that an SU sj associated with SBS ri obtainson channel ck should take into account the followingfactors: (i) Number of neighboring SBSs with whomri shares ck; (ii) Probability that ri transmits on ck;(iii) Probability that a neighboring SBS will transmit onchannel ck; and, (iv) Number of clients associated withri that are in the interference range of neighboring SBSs.

A transmission from SBS ri to an associated client sjon channel ck could be interfered by other transmissionsfrom neighboring SBSs that are operating on the samechannel. Specifically, a transmission from ri to sj on ckwill be successfully received only if none of the SBSsin N(sj , ck) that have ck assigned to them transmiton ck in the same frame. Therefore, the probabilitythat a transmission from ri to sj is successful will be∏

{rm:rm∈N(sj ,ck)∧ck∈A(rm)}(1− pmk).In order to compute the estimated throughout that

SUs would obtain, we assume that 802.22 frames aredivided into multiple equal-duration time slots such thatone time slot is enough for an SBS to send data to oneSU on every channel. This assumption is not required inthe working of the network but is only used to simplifythe computation for throughput estimation. Further, weassume that in order to maintain fairness among asso-ciated SUs, the SBS provides equal throughput to all its

associated SUs. This may require the SBS to devote moretime-slots to those SUs that are in the interference rangeof neighboring SBSs. Therefore, to deliver a packet toan SU sj that lies in the interference region of multipleneighboring SBSs, ri may require multiple time-slots. Ineach time-slot, ri tries to send data to sj on a randomlyselected channel. Thus, we can compute the expectednumber of time-slots required to send 1 packet from rito sj as:

tj =|A(ri)|

|A(ri)|∑

k=1

(pik ×∏

{rm:rm∈N(sj ,ck)∧ck∈A(rm)}(1− pmk))

(1)Observe that a SBS can send at most |A(ri)| packets

in 1 slot. Therefore, if ri has to send 1 packet to all itsassociated SUs (denoted by set Qi), then the expectednumber of required time slots will be:

=1

|A(ri)|×

∑

{sj :sj∈Qi}tj (2)

So, given a channel assignment A, the throughput ofSUs associated with ri is given by reciprocal of (2):

T (A, ri) =|A(ri)|∑

{sj :sj∈Qi}tj

(3)

By estimating the throughput of each SU, it is nowpossible for CAS to assign channels to SBSs in a fairmanner. In Section 5, using ns-3 [13] simulations we willevaluate the correctness of this estimation.

3.3 Setup of the Channel Sharing Protocol

All SBSs send their sensing data (viz. Channels available,number of associated clients and the set of neighboringSBSs of each client on each channel) to the ChannelAssignment Server (CAS). Based on this information, CASuses the Share algorithm (discussed in Section 3.6) tojointly compute the channel assignment for each SBS aswell as the channel usage probability for each channelassigned to each SBS. SBSs can deduce channels availableto them by periodic sensing of the spectrum [10], [11],[14]. One way to compute the set of neighboring SBSsfor the associated SUs is to use a geometrical disk modelfor transmission and interference ranges and assume thatclients are uniformly distributed. However, due to thepresence of obstacles, such a model is not accurate inpractice. Therefore, in order to arrive at more realisticvalues, SUs report the set of their neighboring SBSs totheir associated SBS which in turn forwards it to CAS asdescribed later in Section 4.2. Once CAS has the neigh-borhood information, it can estimate the throughput thatan SBS (or associated SUs) will obtain under a givenassignment A using (3), and thus the CAS can assignchannels among SBS in a fair manner.


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3.4 Problem FormulationThe primary objective is to assign each SBS a subset ofchannels from its availability set and to determine thechannel usage probability for every channel assignedto each SBS such that the non-decreasing lexicographicsequence of the throughputs assigned to the SUs ismaximized. A non-decreasing lexicographic sequence L1of length n is said to be greater than the other sequenceL2 of the same length iff there exists i : L1[i] > L2[i]where 1 ≤ i ≤ n and L1[j] = L2[j] ∀j : 1 ≤ j < i. Then,the channel assignment problem (denoted by Problem 1)is formulated as:

maxA, pij

(Lexicographic sequence of throughputs, T (A, ri))

subject to:

A(ri) ⊆ W (ri) ⊆ U0 ≤ pij ≤ 1 ∀i ∈ [1,M ], j ∈ [1, |U|]

pij > 0 iff cj ∈ A(ri)

Here T (A, ri) depends on a variety of factors such asMAC layer algorithm used, transmission and interfer-ence range of ri and its neighbors, exact location of SUsassociated with ri and channel usage probability of riand its neighbors for different channels.

3.5 Reduction to Graph Shared ColoringWe convert our problem statement to an equivalent graphcoloring problem. We construct the conflict graph G(V , E)such that each node in V corresponds to an SBS in thenetwork. An edge is drawn between two vertices of Vif the SBSs corresponding to these vertices are neighborsof each other. Each channel in U corresponds to a colorin the equivalent shared coloring problem. A node canbe colored with only those colors that correspond to thechannels in its availability set. Allocation of a channelto an SBS is equivalent to coloring the correspondingvertex in the graph with the equivalent color. However,a color can be shared among neighboring SBSs and inthat case every SBS gets a certain amount of the colordepending on the interference between the clients of thisSBS and its neighbors. The total share that an SBS (ornode) gets over all the colors is called its effective colorcount that is equally divided among its associated clients.The equivalent objective of Problem 1 would be to “Max-imize the lexicographic sequence of effective color countassigned to SUs”. Opportunistic sharing of colors leads to anew class of problems that has not been discussed beforein either the graph theory or the networking literature.We call our particular problem (Problem 1) as the sharedcoloring problem. In the following discussion, we willuse the term “effective color count” and “throughput”interchangeably. The proof of the following theorem isincluded in the Appendix.

Theorem 3.1: Problem 1 (or Shared Coloring Problem)is NP-Hard.

3.6 Share Algorithm Overview & Description

Algorithm Overview: The Share algorithm works in 3phases. In each phase, the CAS computes the assign-ment of channels to the SBSs as well as the channelusage probability for every SBS for each of its assignedchannels. Sharing of channels increases throughput onlyif overlap between neighboring SBSs is low. Therefore,our algorithm starts by first doing a proper coloringof the graph in Phase 1. Then, colors are shared be-tween neighboring nodes in Phases 2 and 3 only if ithelps in increasing the throughput of the SBSs. By firstperforming a proper coloring, algorithm Share ensuresthat neighboring SBSs share channels only if it helpsin increasing the lexicographic sequence of throughputs.Further, by increasing the number of shared channelsgradually, Share is able to compute the pij for eachchannel assigned to each SBS in polynomial time. Next,we describe the Share algorithm in more detail.

Phase 1 of the algorithm involves proper coloringof the graph (Lines 4-10 of Algorithm 1). This phaseincreases fairness as well as the total throughput ofthe system. In the second phase that involves mutualsharing of colors, for each pair of neighboring SBSs acheck is performed to see (Lines 12-19) if simultaneouslysharing their channels would improve the lexicographicsequence. For example, it is possible that if SBS ri startssharing channel cl with neighbor rk and at the same timerk starts sharing channel cj with ri, then the throughputachieved by both of them increases (e.g. see Fig. 1). Thismay happen if the area of overlap between ri and rkis very small. Sharing of channels is done conservativelystarting with at most 1 conflicting assignment and goingup to 1 + Δ conflicting assignments (Line 12) where Δis the maximum degree of a node in G. This helps usin maximizing the throughput. This phase also increasesthe fairness as well as the total system throughput.

In Phase 3, to improve fairness, Share rearrangesthe colors by performing one-way sharing. Each node(say ri) sorts its neighbors in the increasing order ofthe throughputs available to them (Line 23). Then, foreach neighbor, ri checks if there exists any color thatcould be shared with its neighbor while improving thelexicographic sequence of throughputs (Line 26). Thisphase is particularly helpful for networks where the SBSshave only a few colors available to them or the sequenceof nodes chosen in Phase 1 was sub-optimum. Observethat the time complexity and message complexity ofall the three phases of the algorithm is polynomial.Specifically, the time complexity of three phases of thealgorithm is respectively O(ΔM |U|), O(Δ3M |U|2) andO(M |U|Δ3 logΔ). Therefore, overall complexity of Shareis linear in the number of SBSs in the network and isindependent of number of SUs in the network. In Section5, we will discuss how much time is taken in an actualexecution of Share.

Computing transmission probabilities (pij): Transmis-


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sion probabilities need to be computed in each of thethree phases. Initially, pij is set to be 0 for all i : 1 ≤i ≤ M and j : 1 ≤ j ≤ |U|. We now discuss how thetransmission probability is computed in each phase:

• Phase 1: In this phase, if a channel cj is assigned tori, then we set pij as 1 since no other neighbor of riis simultaneously assigned cj .

• Phase 2: In this phase, some node ri may share achannel cl with neighbor rk and at the same time rkmay share channel cj with ri. We solve the followingset of equations in order to compute pij , pil, pkl andpkj . A valid solution to this set of equations willimply that both ri and rk are able to increase theirthroughput while the throughput of their neighborsmay decrease slightly. However, the overall lexi-cographic sequence will increase (Line 18). Here,T old(A, ri) represents the original throughput of ribefore this mutual sharing is performed. The firsttwo equations ensure that throughput of both riand rk increase. The third equation ensures thatthroughput of all neighboring nodes of rk that havecl assigned stays above the original throughput ofrk. This ensures that the computed transmissionprobabilities increase the lexicographic sequence ofthroughputs. The fourth equation can be explainedin a similar way.

Max T (A, ri) + T (A, rk) such thatT (A, ri) ≥ T old(A, ri)

T (A, rk) ≥ T old(A, rk)

T (A, rx) ≥ T old(A, rk)∀rx ∈ N(rk) : cl ∈ A(rx)

T (A, ry) ≥ T old(A, ri)∀ry ∈ N(ri) : cj ∈ A(ry)

• Phase 3: In this phase, it is possible that some noderi shares channel cj with neighbor rk. We solve thefollowing set of equations to compute pij and pkj .This allows rk to increase its throughput withoutconsiderably decreasing the throughput of its neigh-bors. Here also, the overall lexicographic sequenceimproves (Line 26). The first equation ensures thatthe node (ri) that starts sharing a channel with itsneighbor rk, must finally have higher throughputthan its neighbor. The second equation is similar tothe third equation of Phase 2.

Max T (A, rk) such thatT (A, ri) ≥ T (A, rk)

T (A, rx) ≥ T old(A, rk)∀rx ∈ N(rk) : cj ∈ A(rx)

In both phases 2 and 3, the optimization problem is aQuadratically Constrained Quadratic Program (QCQP)that can be solved in polynomial time using interiorpoints method since the solution space is a convexpolytope [15]. Also, the number of variables and con-straints are O(Δ) in both phases. Note that in both thephases if the QCQP is infeasible, then Share does notperform sharing between those two corresponding SBSs.For example, this can happen in Phase 3 when ri that has

a lower throughput than its neighbor rk, tries to sharea color with rk. In the next subsection, we evaluate theperformance bounds provided by Share and compare itwith the optimal algorithm.

Algorithm 1: Algorithm Share

Input: Graph G(V, E) and the availability set1W (ri)∀i : 1 ≤ i ≤ NOutput: A fair channel assignment with high throughput2//Phase 1: Assign proper colors using a greedy approach3foreach color j = 1 to |U| do4

while true do5S1 ← {rm : cj ∈ W (rm) and cj /∈ A(rm) and cj is not6assigned to any neighbor of rm}if S1 = Φ then7

break8i ← argmin

m:rm∈S1

T (A, rm)9

A(ri) ← A(ri) ∪ {cj}10//Phase 2: Simultaneously share colors to improve fairness and11total throughputforeach max number of conflicts v = 1 to 1 + Δ do12

foreach ri do13foreach rk : rk ∈ N(ri) do14

foreach15cj : cj ∈ W (ri) and cj /∈ A(ri) and cj ∈ A(rk) do

foreach16cl ∈ W (rk) and cl /∈ A(rk) and cl ∈ A(ri) do

A(ri) ← A(ri)∪{cj},A(rk) ← A(rk)∪{cl}17if lexicographic sequence is worse or any SU is18sharing cj or ck with more than v neighborsthen

A(ri) ← A(ri)\{cj},A(rk) ←19A(rk)\{cl}

//Phase 3: Share colors to improve fairness20foreach max number of conflicts v = 1 to 1 + Δ do21

foreach ri do22foreach rk : rk ∈ sort(N(ri)) do23

foreach cj ∈ W (rk) and cj /∈ A(rk) and cj ∈ A(ri)24do

A(rk) ← A(rk) ∪ {cj}25if lexicographic sequence is worse or ri is sharing cj26with more than v neighbors then

A(rk) ← A(rk)\{cj}27

3.7 Discussion3.7.1 Picking appropriate channel for transmissionWhile transmitting data to the user, it is beneficial forthe SBS to transmit on the channels that reduce thechances of collision with neighboring transmissions. Forthis, when transmitting to SU sj , the SBS first attemptsto use the channel that the SBS is not sharing with anyof the SBSs that interfere with the reception at sj . Ifsuch a channel is unavailable, then the SBS uses a chan-nel over which it has highest transmission probability.Further, if the user is located close to the SBS, then tominimize the chances of collision, the SBSs reduce thepower level of transmission. This architecture helps usin further reducing the collisions among neighboringtransmissions. Further, it provides flexibility to the SBSssuch that they can dynamically choose the best channelfor transmission to SUs.

3.7.2 Performance AnalysisThough our algorithm maximizes all the terms ofthe non-decreasing lexicographic sequence of assigned


8

throughput, our following analysis is restricted to onlythe first term of the sequence (otherwise known as themax-min term). For that purpose, we next compare theperformance of Share with the exponential time optimalalgorithm, OPT . We assume that all SBSs have thesame number of SUs (say |Q|) associated with them.Here, OPT is defined as the algorithm that maximizesthe lexicographic sequence of problem 1. Let ΥShare =min

1≤i≤MT (AShare, ri); and ΥOPT = min

1≤i≤MT (AOPT , ri).

The proof for the following theorems can be found inthe Appendix.

Theorem 3.2: For a given network and a set of colors,

ΥShare ≥|Q|ΥOPT −Δ

|Q|(1 + Δ)

Theorem 3.3: Under the assumption that |Q| is 1, it canbe shown that Share provides tight approximate boundson the first term of the lexicographic non-decreasingsequence of assigned throughputs.

Another important measure of a channel allocationalgorithm is the total system throughput provided.The throughput of the system can be calculated as∑

1≤i≤M T (A, ri). In section 5, using ns-3 simulations,we will compare the total system throughput achievedby Share with other baseline algorithms.

4 DISCUSSION

4.1 Localized AlgorithmDue to continuous arrival and departure of primaryusers, it is possible that some SBS (or node) may havelow throughput as compared to its neighbors. Invok-ing Share frequently over the whole network to restorefairness to such an individual SBS may require a lotof channel reconfigurations at all SBSs. To avoid that,the CAS can execute a localized version of Share, calledlShare, in the neighborhood of the node that has lowthroughput. lShare helps in achieving local fairness in areactive fashion while Share is invoked proactively atregular intervals to ensure fairness across the whole net-work. If the number of hops chosen initially for lShareare not sufficient (i.e., throughput of some nodes is stillconsiderably lower than that of their neighbors), thenthe number of hops are doubled until all SBSs in thathop-restricted network have throughput comparable totheir neighbors. This helps us in reducing the numberof SBSs that need to be reconfigured. Another option isthat CAS invokes Share when it observes that variationin throughput among SBSs over the whole network issignificantly high. In this paper, we simply assume thatShare is invoked at regular intervals.

4.2 Acquiring Neighborhood InformationIn order to compute the expected throughput achievedby each SBS, CAS needs to know how the transmissionsfrom SBS to SUs are interfered by the neighboring SBSsoperating on the same channel. For this, we require that

SBSs send beacons at regular intervals on each channelthat the SBS has been assigned for communication.These beacons are scanned by SUs to determine theirinterfering neighbors. An SU can also compute the setof its neighboring SBSs by listening for neighboring SBStransmissions during those time-slots when the SU isnot scheduled to send/receive data from its associatedSBS. This measurement is performed at regular intervalsby SUs and any change in the neighborhood set isreported by SUs to the SBS. Such information can bepiggybacked on data or acknowledgment packets. Byperforming this measurement at regular intervals, we arealso able to take into account the effects of mobility ofSUs since mobility may change the set of neighboringSBSs. Further, since the measurement and reporting isperformed independently on each channel, it takes intoaccount the differences in interference ranges on differ-ent frequencies. The next theorem states that for any SBS,the maximum size of neighborhood update informationthat SBS will need to forward to CAS is polynomial inthe degree of the SBS. The proof of the theorem is givenin the Appendix.

Theorem 4.1: Assume that the intersection of transmis-sion range of an SBS and interference range of any neigh-boring SBS is a convex region. Then the maximum sizeof neighborhood update information that SBS forwardsto CAS is O(Δ3

i |U|) where Δi is the degree of ri.

4.3 Achieving weak synchronizationAs discussed in Section 3.1, weak synchronization amongSBSs would reduce the chances of collision at SUs. Weaksynchronization among SBSs can be achieved by usingReference-Broadcast Synchronization (RBS) [16] duringthe time buffer window at the end of every IEEE 802.22MAC frame. RBS has been used to achieve synchroniza-tion among sensors in Wireless Sensor Networks andcan be extended to any network that supports wire-less broadcasts. Since the neighboring SBSs are locatedgeographically close to each other, therefore RBS canprovide synchronization accuracy within 7 μs with 95%guarantee [16] among them3. Also, since the time bufferprovided by 802.22 at the end of every frame is longerthan 7 μs, synchronization ensures that every transmis-sion of ri can collide with at most one transmission of aneighboring SBS. This helps in reducing the chances ofcollisions, thereby increasing the throughput.

4.4 OverheadsThe overheads of using Share for channel sharing are asfollows:

• Synchronization: Share requires neighboring SBSsto be weakly synchronized. Achieving weak syn-chronization among SBSs requires cooperation

3. With the split-functionality architecture [17], it is possible toachieve a synchronization of as low as 125ns. on commodity softwareradios.


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among neighboring SBSs. However, such cooper-ation among neighboring SBSs is nevertheless re-quired in the IEEE 802.22 MAC protocol to ensurequiet periods and for SUs to perform accurate channelsensing [11].

• Acquiring Neighborhood Information: Forthroughput estimation, knowledge about theneighboring set of all SBSs is required. In Share,such information is acquired through beaconsfrom SBS and listening to SBSs when SUs arenot scheduled to send/receive. When SUs aremobile, the overhead associated with acquiringneighborhood information is expected to increase.However, observe that typically in AP basednetworks (for example, cellular networks or IEEE802.11) the access points send beacons at regularintervals for the purpose of advertisement and inhelping clients in associating with the closest SBS.Such beacons are expected to be used in WRANsas well, and thus can be utilized by Share tocompute neighborhood information as discussedin Section 4.2. Further, the SUs report change inneighborhood by piggybacking the information ondata or acknowledgment packets. If the SU is notinvolved in an active communication, then it caninform the SBS later when it has some useful datato send to the SBS. All these actions considerablyreduce the overhead in acquiring neighborhoodinformation.

• Communication: In Share, the SUs need to informtheir neighborhood set to the SBS. Such informationcan be piggybacked on data or acknowledgmentpackets. Further, the SBSs need to communicate thisinformation over to the CAS. However, as proved inTheorem 4.1, the size of this message is polynomial.

5 SIMULATIONS

In this section, using ns-3 simulations, we will comparethe performance of Share and lShare with other algo-rithms. Section 5.1 describes our simulation setup. Thenext subsection describes the results from our simula-tions.

5.1 Simulation SetupWe simulated a network of size 500km × 500km in ns-3 [13]. Each SBS had 50-150 clients associated with it(see Table 2). One of the uses of white space channels isexpected to be to provide higher capacity to the mobileusers [18]. Thus, in the simulations the mobility of SUsand the resulting variation in signal strength values(from the associated SBS as well as the neighboringinterfering SBSs) was simulated using data trace from[6] which contains the log of signal strength of differentGSM towers as recorded by mobile users.

To study the performance of our algorithm undervarying density of SBSs, we scaled the trace data asfollows: If the number of SBSs in the simulation were

fewer than those in the trace, then a random subset ofSBSs from the trace were used. However, if the numberof SBSs in the simulation were higher, than the SBSs inthe trace were randomly duplicated until their countwas same as the number of SBSs in the simulation.Since, the signal strength values at SUs was generateddirectly from the real trace, therefore it implicitly takesinto account the effect of channel variations such as fastfading and slow fading. As described before (see Section3.1), the successful decoding of the packets at SUs wassimulated by taking into account the SINR at SUs. Thebursty traffic generation at SUs was done using the tracefrom [19]. However, we scaled the traffic by a factor of10 so as to attain a saturated network.

Finally, 25 PUs were deployed in the network usingFCC’s location database [20] and temporal on/off pat-tern [21]. Each simulation was repeated 20 times and themean along with its 95% confidence interval is plottedfor every measurement. In order to better analyze theperformance of our algorithm, we also designed andsimulated 4 other channel assignment algorithms:

1) Proper: This algorithm only does a proper coloring ofthe graph such that no two neighboring SBSs areassigned the same channel.

2) FFR-A [7]: Here, we use the FFR-A algorithm from[7] that uses graph coloring to assign channels tousers such that no two neighboring users (or SUs)have the same channels assigned. FFR-A allowseach AP to use two different power levels suchthat the users closer to the AP are served at lowerpower level while the users far away from AP areserved at higher power. This results in frequencyreuse of 1 among users in the AP core comparedto frequency reuse factor of 3 for the edge users.However, since [7] assigns channels to users (insteadof AP), it is not suitable for cognitive radios wherethe transmissions involve bursty data traffic (insteadof voice). Therefore, under such an architecture, per-packet channel reconfigurations may be required toadjust with changing bandwidth requirements forevery user. This may not only result in delay indata transmission but also increase traffic betweenthe SBSs and CAS. To handle this, we modify [7]such that channels are assigned to groups of users(instead of individual users). For this, the usersassociated with each SBS are categorized into twogroups: (i) Core users; and, (ii) Edge users. Thus, anetwork with N SBSs would have 2N number ofgroups. Further, we modify [7] such that it assignsmultiple channels to each group of users if the samechannels are not assigned to any of the conflictingnodes. Observe that FFR-A will still assign differentchannels to neighboring SBSs even if the overlapbetween them is small. Observe that these modifica-tions still preserve frequency reuse factor of 1 amongcore users and factor of 3 among edge users.

3) Soft FFR-B [22]: Soft FFR-B [22] increases channel


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TABLE 2Default simulation parameters

Variable ValueNumber of SBSs 300Interference range of primary users 50km - 75kmNumber of channels 50

sharing by allowing two SBSs to operate on the samechannel. Specifically, an SBS can transmit to its edgeusers on a channel if all its neighboring SBSs areusing that channel only for transmitting data to coreusers. To evaluate the performance of Soft FFR-B,we implement the algorithm proposed in [22]. Asdiscussed later in Section 6, their algorithm implic-itly assumes that SBSs are located in a hexagonalpattern and thus leads to high interference if theneighboring SBSs are placed close to each other.

4) Genetic algorithm for cognitive radio networks [23]:Here, we use a genetic algorithm similar to [23] thatassigns at most one channel to each access point. Wemodify the algorithm such that it assigns multiplechannels to each AP as long as the assignment doesnot conflict with channels already assigned to neigh-boring APs or the primary users. For consistency, wealso modified [23] such that the channels adjacentto the channels assigned to PUs can also be used bySBSs for transmissions.

All the 4 algorithms and Share used the modified802.22 MAC algorithm. The probability of transmissionin Share was computed using Algorithm 1. Since Proper,FFR-A and [23] do not assign the same channel to neigh-boring SBSs, therefore, the probability of transmissionwas set to 1 for the channels assigned to the SBS.Metrics: We studied different metrics under diverseconditions: (1) Minimum throughput assigned over allSBSs; (2) Total throughput of the system; (3) Executiontime; (4) Number of reconfigurations; (5) Fairness; and,(6) In-conflict time.

5.2 Comparison with Baseline Algorithms

5.2.1 Increasing density of SBSsIn the first scenario, we increased the number of SBSs inthe field (See Figure 3). When the number of APs is 300,we observe that Share increases the minimum through-put by 58%, 67%, 300% and 220% when compared toFFR-A, Soft-FFR, Proper and Genetic, respectively. Thisdemonstrates that sharing of channels can improve bothfairness and the total system throughput. At low den-sities, all the algorithms perform almost equally wellsince at low densities transmissions from SBSs do notinterfere at SUs and thus channel sharing is not required.However, as the density increases, throughput obtainedby the baseline algorithms decrease due to increasedinterference, however Share performs well as it allowscontrolled sharing of channels. [22] assumes that APs areplaced far away from each other. Thus, with higher

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density, the throughput of Soft-FFR decreases as thenumber of collisions increases. Further, it was observedduring the simulations that all the algorithms terminatewithin 0.5 second.

5.2.2 Fairness

A detailed analysis of lexicographic ordering (Fig. 4(a))of nodes with respect to their color-count verified thatthe other algorithms assign colors to only a few nodeswithout giving much preference to other nodes withlower color-count. Since, Share explicitly accounts forfairness, the minimum throughput among all nodes ishigher for Share compared to the other algorithms.

To analyze the fairness at SU level, we also studied thelexicographic ordering of the variation of latency amongSUs4. The latency was computed by taking the differenceof the time when the SBS has data for the SU to the timewhen the SU received the data correctly (See Figure 4(b)).Since, Share explicitly takes into account the fairness ofSBSs and the SUs, it is able to achieve high fairness interms of latency. Other algorithms have higher latencybecause of lower throughput as well as because

5.2.3 Increasing number of channels

Here, we varied the number of channels in the sys-tem. As expected (Figure 6), the minimum throughputincreases with an increase in number of channels forall the algorithms. Share performs better than otheralgorithms in terms of both fairness and the total systemthroughput.

4. Throughput was not analyzed since the throughput is highlydependent on traffic demand of SUs which may not be fair by itself.


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5.2.4 Behavior with timeNext, we studied the behavior of different algorithmswith variation in time. With change in time, PUs mayturn on or off and the traffic requirement at SUs mayvary, resulting in variation in network performance. Inthis simulation, we invoked Share at every 300 secondswhile lShare ran proactively as discussed in Section 4.1.On the other hand, other algorithms were invoked every100 seconds. As we can see from Figure 7, the minimumthroughput assigned by decreases with time after theexecution of lShare (e.g. between the intervals 1800-2100, 2100-2400 etc.). The invocation of Share globallyevery 300 seconds (starting from time = 1800) restoresthe system to a network-wide fair state. The advantageof the localized algorithm is that it requires far lessreconfigurations of channels at SBSs. We define thetotal number of reconfigurations for a new assignmentas

∑1≤i≤M (|Aold(ri) \ Anew(ri)| + |Anew(ri) \ Aold(ri)|)

where Aold(ri) and Anew(ri) are respectively the assign-ment sets of the node ri before and after the execution ofthe channel assignment algorithm. The figure shows thatthe number of reconfigurations made by our combinedalgorithm were far less than the number of reconfigura-tions required by other baseline algorithms. The numberof reconfigurations done by Share were around 4000,while all the baseline algorithms typically exceeded 8000.

5.2.5 Sensing InaccuraciesIn practical systems, the spectrum sensing may notbe accurate and instantaneous. In order to measure theeffect of real-life inaccuracies in sensing, we induceda uniformly distributed random delay between the in-sertion/removal of a primary user and its sensing bythe SBSs for all the algorithms. The delay introducedwas randomly chosen between [0, MaxDelay]. Figure 5shows the variation in percent in-conflict time computedover all PUs during their on period. A PU operating onchannel ck is said to be in-conflict at some time t if at t,

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either of the following conditions is true: (i) Some SBSin the transmission range of PU is transmitting on ck; or(ii) Some SU in the transmission range of PU is receivingdata from its associated SBS on ck. Assignments for allthe algorithms were observed to have a similar averagepercentage of time for which some SBS is in conflict withthe primary user.

5.2.6 Comparison of multiple phasesShare achieves improvement in system performancefrom multiple phases. Figure 8 shows the variation in theminimum throughput and the total system throughputat the end of different phases for varying number ofSBSs. It can be observed that the improvement providedby the second phase of the algorithm is more than thatprovided by the third phase. This may happen becausethe second phase of the algorithm improves throughputof two nodes at the same time, compared to the thirdphase that improves throughput of only one node.

6 RELATED WORK

The problem of channel assignment has been extensivelystudied before in various domains viz. cognitive radios,cellular networks, multi-radio multi-channel networks,wireless networks and graph theory.Cognitive Radio: Various protocols have been proposedin the literature for channel assignment for cognitiveradio networks. In [24], authors have studied channel as-signment in multi-radio wireless mesh networks whereeach node calculates the rank of channels available to iton the basis of interference and channel utilization. Theserankings are then forwarded to the Channel AssignmentServer that assigns channels to nodes in a breadth-firstfashion. The distributed algorithm proposed by Gandhiet al. [25] involved APs bidding for channels in anauction. However, no two neighbors are assigned thesame channel. None of these algorithms allow controlled


12

sharing of channels. Further, these algorithms do notprovide any worst case bounds on performance. Otheralgorithms [2], [23], [26] only assign at most one channelper AP or assume that the network has only one AP.Cellular Networks and LTE: The problem of multicol-oring a graph with fixed number of colors has beenextensively studied in cellular networks [27]. Unlikecognitive radio networks, in cellular networks the sameset of channels are available at all nodes. Tradition-ally, in cellular networks, neighbors are not allowedto share the same channel as resulting collisions mayaffect the QoS of the real-time voice traffic. However,the recently proposed LTE architecture [7], [22] allowssharing of channels among neighboring APs at the cellcore. The FFR-A architecture [7] assigns the same set ofchannels to all the BSs at the cell core. However, edgeusers are still assigned different channels regardless ofthe amount of overlap among neighboring SBSs. Thisprevents maximum use of the edge channels when theoverlap between the neighboring BSs is small. Soft FFR-B [22] further increases the throughput per channel byallowing neighboring SBSs to use the same channel aslong as one SBS uses the channel for edge transmissionswhile the other SBS uses for core-transmissions. How-ever, a fixed core radius [7], [22] or a fixed frequencyreuse factor may not be appropriate for networks wherethe density of the users is non-uniform or when SBSsare located non-uniformly as shown in [28]. Authorsin [22] compute the transmission power level for SBSs,however, their channel assignment may assign samechannel to neighboring SBSs even if they are located veryclose to each other, thereby leading to high interference.Authors in [29] assign the same channel to all the SBSswhich can lead to high interference if the SBSs are notarranged in a hexagonal fashion. Further, [7] assignschannels to users (and not APs). It is not clear howtheir algorithm will perform for data networks wherethe channel requirement at SUs is bursty.Multi-radio multi-channel networks: Kodialam et al.[30] proposed a greedy algorithm for Multi-Radio Multi-Channel Multi-hop wireless networks that satisfies agiven traffic demand for different source-destinationpairs. Similarly, [31], [32] aim at assigning the channelsin a way that maximizes the throughput of the networkor satisfies given flow constraints. Clearly, all theseapproaches would not work in our problem scenariowhere the requirement is to assign channels to theneighboring nodes while ensuring fairness. Chandra etal. [33]–[35] proposed using variable channel width forfair channel allocation. However, their algorithm doesnot allow channel sharing which can be very useful invariety of scenarios as discussed in Section 1. Further,cognitive radio networks can communicate on multiplenon-contiguous channels using OFDMA [14], [36]–[39].Platforms like USRP GNU radio [40], KUAR , WARP andSORA [41] already support non-contiguous OFDM trans-missions. However, it is not clear how their algorithmscan be extended to assign non-contiguous channels to

the nodes. Similarly, [42] also does not allow sharing ofchannels among neighbors.Wireless Networks: In wireless networks, [43], [44] havepresented algorithms for overlapping 802.11 channelassignments for an AP-like setting that minimizes in-terference. However, the existing work in overlappingchannel assignment for wireless LANs is distinct fromour work in several ways. First, in wireless LANs, onlyone contiguous channel is assigned to one access point.Also, it is not trivial to extend the algorithms in theseworks to multi-channel assignment scenario. Second,assigning the same channel to the neighboring APs ina fair manner requires a different way to estimate thethroughput that the APs will obtain. Third, most ofthe previous works do not present any bounds on theproposed algorithms [43]–[45]. Lastly, none of the pre-vious algorithms perform controlled sharing of channels.Without controlled sharing, the number of collisions maybecome high. Mishra et. al. [46] have proposed a client-driven approach where they allocate channels to the APssuch that the number of clients that are in the rangeof multiple APs with the same channel are minimized.Akl et al. [47] have proposed a similar scheme wherethe overlap between neighboring APs is quantified onthe basis of overlap between the channels assigned toneighboring APs. In the survey paper, Chieochan et al.[48] describe multiple algorithms that have been usedfor channel allocation in WiFi networks. However, allsuch algorithms try to avoid assigning the same channelto the neighboring APs. On the contrary, our algorithmproactively assigns the same channel to neighboring APsif it leads to an increase in throughput for both the APs.

Kim et al. [49] have proposed an algorithm that im-proves fairness and throughput in infrastructure wirelessnetworks by carefully associating the clients with theAPs. In this paper, we assumed that the clients arealready associated with a single AP. It is possible thatoptimal association of the clients reduces the throughputgain provided by channel sharing. Conversely, by jointlydetermining the optimal channel assignment and clientassociation, the fairness and throughput of clients maybe larger compared to if association and channel assign-ment is done independently. We leave this extension forfuture work.Graph theory: In the domain of graph theory, theproblem of multiple channel allocation has been termedas multi-coloring, [50] where the objective is to assignmultiple colors to all the nodes while ensuring thatno two neighbors get the same color. Partial coloringrequires assigning colors to only a subset of nodes in thegraph. Fractional coloring [51] allows assignment of onlya fraction of a color to a node. However, two neighborscan still not be assigned the same color. In the problemof List coloring [51], a node can be colored only froma list of colors applicable to that node. List coloringalso does not allow the same color to be assigned toneighbors. Defective Coloring [52] allows the same colorto be assigned to a maximum of d neighboring nodes


13

all of which get a color count of 1 from that color. Onthe other hand, upon sharing, shared coloring assignsfractional color count to each neighbor. Thus, defectivecoloring does not exhibit the concept of channel sharingamong neighbors.Link Scheduling in Wireless Networks: The linkscheduling problem involves finding the schedule ofminimum duration while assigning a fixed number oftime-slots to each link. On the other hand, the channelallocation problem involves maximizing the number ofchannels assigned to each node from a fixed set ofchannels [53].MAC Protocols for Cognitive Radio Networks (CRNs):Various MAC protocols have been proposed for CRNs[54]. However, none of them specifically apply to thenetworks where neighboring APs may be assigned thesame channel. Lien et al. [55] have assumed that PUsfollow a classical CSMA protocol which may not betrue in all cases. Zou et al. [56] propose a game theorybased approach for channel contention. However, aspointed out [54], their algorithm does not work well ifthe number of players is high. Also, it is not clear howmany iterations are needed before the players convergeto a Nash equilibrium. Other MAC algorithms [57], [58]have been proposed for Ad-hoc CRNs that propose RTS-CTS based schemes. However, these are not suited forchannel sharing among APs as argued in Section 3.1.

7 CONCLUSION AND FUTURE DIRECTIONS

In this paper, we proposed a new paradigm for channelsharing in which neighboring APs can be assigned thesame channel. We showed that if performed carefully,sharing can lead to an increase in both fairness andtotal system throughput. We showed that the problemof fair channel assignment to WRAN APs under thisshared channel paradigm is NP-Hard. We modified theIEEE 802.22 MAC layer protocol to make it suitablefor channel sharing and showed that the resulting con-trolled channel sharing performs better than the tradi-tional sensing based MAC algorithms. We then proposedalgorithm Share for channel assignment. The proposedalgorithm for solving this problem has provably tightbounds in terms of the max-min throughput. In order toreduce the number of reconfigurations in the network,we also proposed its localized version. Combining thecentralized algorithm and its localized version, our com-plete protocol is able to achieve high fairness, and highnetwork throughput with few channel reconfigurations.Using ns-3 based simulations, we showed that controlledchannel sharing increases max-min throughput by by atleast 58%. Our algorithm for channel assignment can beextended to be used for WiFi APs as well. However,there we also need to take into account the possibilityof using overlapping channels for additional throughputgains. In this paper we only considered sharing channelsfor downstream data. It would be interesting to explorehow channel sharing performs for both downstream andupstream transmissions.

8 ACKNOWLEDGEMENTSWe thank the anonymous reviewers for comments thatimproved this paper. This material is based upon worksupported by the National Science Foundation underGrants CNS-1254525 and CNS-1161490.

REFERENCES[1] S. Bridge, “High Speed Broadband to Rural Areas,”

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Tarun Bansal received the BS degree in Com-puter Science and Engineering from Indian Insti-tute of Technology, Roorkee, India, in 2006 andthe MS degree in Computer Science from UTDallas, Richardson, in 2009. He is currently aPhD student at Ohio State University, Columbus.His research interests include Cognitive RadioNetworks and Dynamic Spectrum Access.

Dong Li received his BS degree in InformationSecurity from University of Science and Tech-nology of China, Hefei, China in 2009. He iscurrently a PhD student at Ohio State University,Columbus. His research interests include wire-less networks.

Prasun Sinha is an Associate Professor in theDepartment of Computer Science and Engineer-ing at Ohio State University. His interests are inthe area of wireless networking. Prior to joiningOSU he worked at Bell Labs, New Jersey. Heholds a PhD from UIUC (2001), MS from Michi-gan State University (1997) and BTech from IITDelhi (1995), all in Computer Science and En-gineering. He won the Lumley Research Awardat OSU in 2009 and the NSF CAREER awardin 2006. During his graduate studies he won the

Ray Ozzie Fellowship (UIUC, 2000), the Mavis Memorial Scholarship(UIUC, 1999), and the Distinguished Academic Achievement Award(MSU, 1997). More information about his research can be found athttp://www.cse.ohio-state.edu/ prasun.


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