congestion control, routing, and scheduling 2015

3108 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015

Congestion Control, Routing, and Scheduling inWireless Networks With Interference

Cancelation CapabilitiesLong Qu, Jiaming He, and Chadi Assi, Senior Member, IEEE

Abstract—Recently, there has been strong interest in exploitingadvanced physical-layer techniques to increase the capacity ofmultihop wireless networks. Several recent studies have emergedwith a particular focus on successive interference cancelation(SIC) as an effective approach to allow multiple adjacent concur-rent transmissions to coexist, enabling multipacket reception. Thispaper is in line with those efforts in that we attempt to understandthe benefits of SIC on the throughput performance of wirelessnetworks. We consider a cross-layer design for the joint congestioncontrol, routing, and scheduling problem in wireless networkswhere nodes are endowed with SIC capabilities and under thegeneral physical signal-to-interference-plus-noise ratio (SINR) in-terference model. We use duality theory to decompose the jointdesign problem into congestion control and routing/schedulingsubproblems, which interact through congestion prices. This de-composition enables us to solve the joint cross-layer design prob-lem in a completely distributed manner. Given that the problemof scheduling with SIC and under the SINR interference regime isNP-hard, this paper develops a decentralized approach that allowslinks to coordinate their transmissions and, therefore, efficientlysolve the link scheduling problem. Numerically, we show that ourdecentralized algorithm achieves similar results to those obtainedby other centralized methods (e.g., greedy maximal scheduling).We also study the performance gains SIC brings to wireless net-works, and we show that flows in the network achieve up to twicetheir rates in most instances, in comparison with networks withoutinterference cancelation capabilities. These gains are attributedto the capabilities of SIC to better manage the interference andpromote higher spatial reuse in the network.

Index Terms—Cross-layer design, distributed scheduling, net-work utility maximization (NUM), successive interference cance-lation (SIC).

Manuscript received November 24, 2013; revised April 3, 2014 and July 11,2014; accepted August 15, 2014. Date of publication August 27, 2014;date of current version July 14, 2015. This work was supported in partby the Scientific and Technological Innovation Teams of Zhejiang Provinceunder Grant 2010R50009, Grant 2012R10009-11, Grant 2012R10009-12,Grant 2012R10009-19, and Grant 2012R10009-20; by the Mobile NetworkApplication Technology Key Laboratory of Zhejiang Province under Grant2010E10005; and by the Open Funding of Zhejiang Province under Grantxkxl1305. The review of this paper was coordinated by Prof. J. Tang.

L. Qu and J. He are with the School of Information Science and Engineering,Ningbo University, Ningbo 315211, China (e-mail: [email protected]).

C. Assi is with the Concordia Institute for Information Systems Engineering(CIISE), Montreal, QC H3G 1M8, Canada (e-mail: [email protected]).

This first author is currently visiting Concordia University.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TVT.2014.2352551

I. INTRODUCTION

THE capacity of wireless networks is strongly dependenton the number of concurrent active transmissions that can

be accommodated by the network, which is commonly referredto as the level of spectrum spatial reuse [1]. Determining aset of concurrent active transmissions is the link schedulingproblem, and optimal scheduling has been widely studied andshown to be complex and combinatorially hard to solve [2]–[4].In a wireless network where the spectrum is shared among allcommunicating links, neighboring communications may causestrong interference on adjacent links causing transmissions onthese links to collide and, therefore, be corrupted. Thus, theproblem of scheduling asks for finding a subset of links that canbe simultaneously active without causing strong interference inthe network, and the optimal scheduling asks for a maximalsuch subset [6], [7]. The problem of optimal scheduling is dif-ficult to solve given the complex relationship governing trans-mission concurrence and interference. Most often, simplifiedinterference models are used to solve the scheduling problem,such as the graph based or protocol based; such models havebeen shown to underestimate the interference in the network,and thus, the obtained schedules may not be feasible in practice[8]. Alternatively, other models, such as the physical modelor the signal-to-interference-plus-noise ratio (SINR) [4], aremore realistic in capturing the cumulative interference at eachreceiver; however, they are more challenging to deal with,and link scheduling under such models is shown to be NP-complete [5], [6].

Now, although link scheduling is an effective method formanaging the activation of interfering links and, thus, achievingoptimal spatial reuse, there has recently been growing interestin increasing concurrence by exploiting interference ratherthan avoiding it through scheduling [18]. Here, the networkallows interfering adjacent transmissions to coexist and relieson advanced physical techniques to remove interference and,thus, decode intended signals at their receivers. For instance,successive interference cancelation (SIC) [9], [15] gives areceiver the ability to decode two or more concurrent signalssuccessively: first by decoding the strongest signal (if it can bedecoded) and subtracting it from the combined one and, then,in turn, decoding other stronger signals successively until thesignal of interest intended to this particular receiver is obtained.At each step of the decoding, the receiver must ensure that thesignal being currently recovered meets the SINR requirement;otherwise, no further decoding is possible.

0018-9545 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

QU et al.: WIRELESS NETWORKS WITH INTERFERENCE CANCELATION CAPABILITIES 3109

Clearly, efficient link scheduling together with SIC help inpromoting better spatial reuse as well as transmission con-currence, resulting in increased throughput performance. Inthis paper, we consider a wireless network where nodes areendowed with SIC capabilities, and we study the problem oflink scheduling, under the SINR interference model, in thecontext of a cross-layer network design.

We consider a network utility maximization (NUM) problem(similar to [25] and [26]) in a multihop wireless network anddecouple the cross-layer optimization into congestion controland routing/scheduling subproblems. The congestion controlsubproblem can easily be solved at the source node of each flowby only using local information, and following a back pressureframework, the routing/scheduling subproblem is convertedinto a weight scheduling problem where the weight informationcan be illustrated as some scale of the queue length at eachnode. However, as mentioned earlier, previous work has shownthat the link scheduling under a binary interference model isan NP-hard problem [2] and under the SINR model as NP-complete [5], both with and without SIC, and polynomial-timeapproximation algorithms are presented (e.g., [10] and [24]).Scheduling methods such as maximum weight scheduling [11]and greedy maximal scheduling (GMS) [12] have shown toachieve 100% throughput in most practical wireless networkswith the second method being more amenable to distributedimplementation. In this paper, we will consider the GMS ap-proach for solving the link scheduling problem under the SICconstraints and the physical interference model; now, given thecomplexity of the scheduling problem in centralized settings,we develop a decentralized method for solving it. Our maincontributions are as follows. First, we revise the interferencelocalization method in [19] and show that it can be used tomaintain the interference constraints in a network with SICcapabilities. Second, we present a search-based method fordetermining the minimum interference neighborhood of eachlink. Our design reveals that the network throughput perfor-mance is mainly dependent on how much local informationcan be coordinated at each communication link. We show thatour decentralized algorithm yields the same maximal scheduleobtained by the centralized GMS method.

The rest of this paper is organized as follows. In Section II,we briefly survey the work related to cross-layer optimizationwith and without SIC. Our system model, the interferencelocalization technique, and problem formulation are presentedin Section III. Section IV presents the dual decomposition fordecoupling the cross-layer design problem as well as the designof our decentralized scheduling method. Finally, numericalresults are presented in Section V, and conclusions are drawnin Section VI.

II. RELATED WORK

Recently, there have been growing interests to exploit inter-ference among adjacent concurrent transmissions to increasethe network throughput. Mitran et al. in [13] formulated across-layer design optimization to solve the joint problem ofrouting and scheduling in a multihop wireless network withadvanced physical-layer techniques for interference cancela-

tion, such as SIC, superposition coding, and dirty-paper coding.The authors formulated the problem of routing and schedulingunder the physical interference model as a max–min optimiza-tion problem and developed a column generation method forsolving it efficiently. The authors have shown that SIC signifi-cantly improves the network performance and, in particular, themax–min per node throughput. Jiang et al. in [18] noted thatSIC is a very promising interference exploitation technique forincreasing the network throughput due to its ability in enablingmultiple concurrent transmissions. Upon developing a cross-layer optimization framework for the routing and schedulingproblem, the authors studied the optimal interaction betweeninterference exploitation, through SIC, and interference avoid-ance, through link scheduling. The authors have shown thatsubstantial performance gains can be achieved when both tech-niques are combined.

Now, the asymptotic transmission capacity of ad hoc net-works with SIC is studied in [15] and [16]; the former con-sidered that all signals within one hop from transmitters can besuccessfully decoded, and the latter supposed a more realisticSIC model in their analysis. Sen et al. in [17] studied the extentof throughput gains that is possible under SIC from a MAC-layer perspective. They argued that only little gains could beachieved in restricted scenarios (mainly for upload traffic inwireless local area networks). Furthermore, when transmitterschoose their bit rates independently, not much gain can beachieved. However, the authors showed (in a two-transmitterscenario) that one way to maximize the gain is through transmitpower level selection such that the feasible bit rate is equal forboth transmissions. Lv et al. in [22] proposed a layered protocolmodel and a layered physical model (to model the interference)and studied the problem of link scheduling to characterize theadvantages of SIC. The authors analyzed the capacity of a net-work with SIC and demonstrated the importance of designingSIC-aware scheduling. It was shown that significant through-put gains (20%–100%) can be obtained in chain/cell networktopologies. The problem of link scheduling with interferencecancelation using the SINR interference model is studied in[23] where Yuan et al. assumed multiuser decoding receivers.The authors showed that the optimal scheduling problem with(successive or parallel) interference cancelation is NP-hardand developed compact linear programming (LP) methods forobtaining exact solutions. The authors showed that in the lowerSINR regime, interference cancelation yields significant im-provements. Similarly, in [24], Goussevskaia and Wattenhoferstudied the same problem but developed approximation algo-rithms for solving the scheduling problem in polynomial time.SIC has shown to achieve up to 20% performance gains overnetworks that do not have interference cancelation capabilities.

It should be noted that all of the aforementioned methodssolve the link scheduling problem in a centralized manner;given the complexity of the problem, decentralized methods aremore practical. In [25], a distributed method that jointly adaptsdecisions made by different layers is proposed. Chen et al.presented then a dual driven decomposition approach for theoriginal problem, which is further decomposed into two sub-problems (one for congestion control and another for routing/scheduling), and the three are correlated through Lagrangian


multipliers. A fully distributed algorithm following thedecomposition is then presented. In [31] and [32], Joo andShroff and Joo et al., respectively, revised the distributedscheduling methods in wireless networks and classified theminto different categories. For the graph-based interferencemodel, the authors mainly focused on the problem of schedul-ing and proposed a revision of the GMS algorithm to satisfy thedistributed design. For the more practical interference model,Le et al., in [19], investigated the link scheduling problem byconsidering GMS; to simplify the complex relationship govern-ing the interference, the authors presented a method to localizethe interference around each link, thereby each link coordinatesits scheduling within a local neighborhood while maintain-ing scheduling feasibility. The authors subsequently devel-oped a decentralized scheduling method, which was shown toyield maximal link scheduling similar to the centralized GMSmethod. These decentralized methods did not however considernetwork with interference cancelation capabilities.

Note that our work is similar to [25] and [26] in that wetry to design an efficient distributed cross-layer method toimprove the performance of wireless multihop networks. Ourwork, however, differs from previous work in that we considernetworks with SIC capabilities in our distributed cross-layerdesign with the SINR interference model. This makes thedesign of a decentralized method more complicated because ofthe particularity of the SIC constraints.

III. SYSTEM MODEL

A. Network Model

We consider a network of N nodes and L links; we assumestationary nodes, each equipped with SIC capability. Let dn,n′

be the Euclidean distance between two nodes n and n′, and letGnn′ be the channel gain from n to n′ such that Gnn′ = d−pl

n,n′ ,where pl is the path-loss index. The transmission power at eachnode is assumed to be fixed and equal to Pw. Let F be the set offlows in the network, where each flow f (f ∈ F ) is identified bya source s(f) and a destination d(f) and a transmission rate yf .

B. Interference Model With SIC

In the physical interference model (also known as the ad-ditive interference model), in the presence of concurrent trans-missions on neighboring links, one transmission (e.g., on link i)is successful if the SINR at the intended receiver is above acertain threshold β. Then, the physical interference model canbe formulated as

SINRt(i),r(i) =PwGt(i),r(i)

η +∑

∀n∈NA−t(i) PwGn,r(i)≥ β (1)

where η is the background noise power. NA is the set of allactive nodes in the network, and t(i) and r(i) are the transmitterand the receiver of link i. β is the minimum SINR thresholdthat must be maintained to support a successful transmissionon link i while guaranteeing a tolerable bit error rate. If theSINR requirement is not met, then the received packet cannotbe correctly extracted from the received signal. In this paper,we assume β ≥ 1.

Now, SIC allows a signal to be correctly decoded in thepresence of other concurrent transmissions. Here, the receiverstarts decoding the strongest signal from the combined receivedsignal; then, the decoded signal is subtracted, and the processis repeated on the residual signal until the signal of interest iseither decoded or no more decoding is possible. This techniquetherefore allows a signal to be correctly received given thatother stronger signals are decoded first. Next, we illustrate theSINR constraints in the presence of SIC. Consider two linksi and i′ adjacent to each other. Denote by P 1

r(i)(P2r(i)) the

strength of the signal received at destination r(i) from t(i)(respectively, from t(i′)) and suppose P 2

r(i) > P 1r(i). Here, r(i)

will attempt to decode the signal received from t(i′) first; thissignal can be decoded if

SINR2r(i) =

P 2r(i)

η + P 1r(i)

≥ β. (2)

If the signal of t(i′) is successfully decoded at r(i), then r(i)will subtract it from the combined signal and will attempt todecode the signal arriving from t(i), i.e.,

SINR1r(i) =

P 1r(i)

η≥ β. (3)

The given procedure can be generalized in a straightforwardmanner to any number of transmissions.

C. Link Scheduling With Interference Localization

We consider a time-division-multiple-access-based MAClayer where time is divided into slots of equal length, and eachtime slot has two parts: a schedule and a transmission. Theschedule part has several intervals, and each interval is furtherdivided into minislots. We define the set of links that can beconcurrently active in the same time slot (without violating theSINR requirements) as a (feasible) configuration (or conf forshort). Then, our objective is to generate a new configurationduring the “schedule” period under SIC constraints and trans-mits data during the “transmission” period (each active link willtransmit one packet during the “transmission” period). Notethat, in a wireless network without SIC capabilities, in [19],Le et al. noted that only those concurrent transmissions withina neighborhood of a particular link may create significantcumulative interference at the receiver of this link. Accordingly,they presented an “interference localization” technique thatallowed them to decentralize the link scheduling problem. Theauthors presented a method to determine for each link a neigh-borhood such that interference from active links outside thisneighborhood will have negligible impact on received signalat the receiver of this link. Namely, for link l, the maximuminterference that can be tolerated is

Imaxl =

PwGt(l),r(l)

β− η. (4)

Let IN l and nIN l denote the interference neighborhoodand noninterference neighborhood of link l. IN l is a circle


centered around the receiver of l and whose radius will bedetermined later. All links whose transmitters are inside IN l

will be able to exchange information (therefore coordinate)with the transmitter of link l for scheduling purposes. nIN l

(complement of IN l) contains the set of links whose cumula-tive interference is assumed to be negligible at rl. Le et al. in[19] have shown that given a constant ε (0 < ε < 1), for link lto be feasible, the upper bound on the interference coming fromactive links located in IN l should not exceed (1 − ε)Imax

l , andthe total interference coming from links located in nIN l cannotexceed εImax

l . Therefore, when all active links in some set arefeasible, we obtain a feasible configuration.

Now, to account for the SIC property of the nodes in thenetwork, we first revise the interference localization techniquepresented earlier as follows. For a particular link l, we divide thenetwork into three regions: the strongest signal area, the inter-ference area, and the noninterference area. The strongest signalarea (Al) refers to a circular area with radius dt(l),r(l) centeredaround the receiver of link l. The interference area refers to thering-like area (IN l −Al) with radius from dt(l),r(l) to a certainlength λ(l) (λ(l) ≥ dt(l),r(l)) centered around the receiver oflink l. The noninterference area denotes the region outside theinterference area (nIN l). Next, we introduce the definition ofvector

−→λ .

Definition 1: For any feasible link l, λ(l) denotes the lowerbound of the radius of the interference neighborhood (IN l)such that the total interference coming from links located inthe noninterference area does not exceed εImax under SICconstraints.

We assume that each link l (l ∈ L) is able to communicatewith any link whose transmitter is located in IN l, or any link l′

such that t(l) ∈ IN l′ , to exchange link weight information andcoordinate the link scheduling. Definition 1 implies that there isa relationship between ε and

−→λ (we will present a procedure to

compute−→λ based on ε in the following section). Furthermore,

ε can be used to control the potential scheduling overload, andwe will verify in Section V that ε will have a significant effecton the achievable network performance.

Note that, in any feasible configuration, we assume that all“active” links l′ (such that t(l′) ∈ Al) have stronger receivedsignals at r(l) than the signal arriving from t(l), and therefore,using SIC, r(l) is capable of successively decoding thosesignals prior to decoding the signal arriving from t(l).

Definition 2: Given a certain−→λ , Θ(

−→λ ) is a class of schedul-

ing algorithms such that a particular scheduling method willbelong to Θ(

−→λ ) if it yields an active schedule satisfying

the following constraints: 1) For any active link l ∈ L, thetotal interference coming from active transmitters located inIN l −Al does not exceed (1 − ε)Imax(l); and 2) let k de-note the link from any active transmitter located in Al tor(l); then, the cumulative interference at r(k) = r(l) comingfrom active transmitters located in IN k −Ak does not exceed(1 − ε)Imax(k).

The second constraint in the given definition implies that allactive transmitters within the neighborhood of r(l) (i.e., in Al)should have their signals decoded at r(l) prior to decoding thesignal arriving from t(l). Here, r(l) will attempt to success-fully decode each of these arriving signals (using SIC); this is

possible because for each signal, we assume that the cumulativeinterference from active transmitters located in IN k −Ak doesnot exceed (1 − ε)Imax(k), which is required for successfuldecoding of the signal of t(k) at r(l).

Combining Definitions 1 and 2, it can be shown that for anyε (0 < ε < 1), there exists a vector

−→λ and a class of scheduling

methods Θ(−→λ ) such that any scheduling algorithm belonging

to Θ(−→λ ) will result in a feasible schedule satisfying the SIC

constraints. This is summarized in the following theorem.Theorem 1: Given any 0 < ε < 1, there exists a vector λ

that satisfies Definition 1, and the result of schedule Θ(λ) thatsatisfies Definition 2 is feasible under SIC constraints.

D. Problem Formulation

Following the given discussion, we assume that all activelinks in one conf can simultaneously transmit. Denote by Ethe set of all possible configurations/schedules, where eachconf is indexed by e. Each conf (e) is represented by a|L|-dimensional rate vector −→r e, where for each link l, rel canbe defined as

rel =

{c, if l ∈ e0, otherwise

(5)

where c is a constant link transmission rate. We define thefeasible rate region Γ as the convex hull of these rate vectors.We assume through time sharing that all interior points of Γare attainable. We define a link-flow matrix v to describe therouting of flows in the network, where each element vlf ∈v(∀ l ∈ L, f ∈ F ) corresponds to the fraction of flow f deliv-ered over link l. We assume a utility function U(yf ) to be twicedifferentiable, increasing, and strictly concave [25]. Our designtarget can be summarized in the following utility maximizationproblem:

[OBJECTIVE]

maxyf≥0,∀ f∈F

∑f∈F

U(yf ). (6)

Similar to [26], a feasible routing must satisfy two constraints:the interference and link capacity constraints (7) and the flowbalance constraints (8).

[CONSTRAINTS]

∑f∈F

vlf ∈ Γ ∀ l ∈ L (7)

yif +Υ−if ≤ Υ+

if ∀ i ∈ N, f ∈ F (8)

where yif (i ∈ N, f ∈ F ) denotes the node-flow variable suchthat yif = yf when i = s(f), and otherwise yif = 0. Υ−

if =∑l∈L:r(l)=i vlf and denotes the fraction of flow f incoming

into node i, and Υ+if =

∑l′∈L:t(l′)=i vl′f denotes the fraction

of flow f outgoing of node i.


IV. DISTRIBUTED CROSS-LAYER DESIGN WITH

SUCESSIVE INTERFERENCE CANCELLATION

A. Dual Decomposition

Similar to [25] and [26], we resort to the dual drivenLagrangian decomposition approach to get a distributed so-lution. For completeness, we briefly describe the process ofdecomposition, and the detailed demonstration can be found in[25]. Consider the dual problem of primal problem (6), i.e.,

minuif≥0,∀ i∈N,f∈F

D(u) (9)

with partial dual function

D(u) = maxyf≥0,v∈Γ

×

⎧⎨⎩∑f∈F

U(yf )−∑f∈F

∑i∈N

uif

(yif +Υ−

if −Υ+if

)⎫⎬⎭ (10)

where uif is a Lagrangian multiplier, and u = [uif ]i∈N,f∈F .Then, (10) can be further decomposed into the following twosubproblems:

D1(u) = maxyif≥0

∑f∈F

∑i∈N

(U(yif )− yifuif ) (11)

D2(u) = maxv∈Γ

∑f∈F

∑i∈N

uif

(Υ−

if −Υ+if

). (12)

Here, D1(u) can be solved by (13), which is the standard ratecontrol problem at the source node of each flow, i.e.,

yf = U ′−1(uf ) (13)

where uf = uif if node i = s(f). For the routing/schedulingproblem D2(u), we have the following identity:

D2(u) = maxv∈Γ

{∑l∈L

vlf∗ maxf∈F

{ut(l)f − ur(l)f

}}(14)

where f ∗ = argmaxf∈F {ut(l)f − ur(l)f}, l ∈ L.Based on (14), the routing/scheduling problem can be solved

by the following two-step process.Step 1) For each link l, we can use local informa-

tion u to find a flow f ∗ that satisfies f ∗ =argmaxf∈F {ut(l)f − ur(l)f}. Let wl = ut(l)f∗ −ur(l)f∗ be the weight of link l. Here, wl can alsobe interpreted as the scaled queue length at link lwith flow f ∗. In each time slot, the links in oneconf can be active to send data to the receivers (weassume one packet transmission per active link pertime slot). The given algorithm can be interpreted asa back pressure process to solve the routing problem.

Step 2) We convert (14) into its reduced form as follows:

D2(u) = maxv∈Γ

∑l∈L

vlf∗wl. (15)

The formulation of (15) can be seen as an ordinary linkscheduling problem where each link is associated with its

weight wl. However, it is difficult to solve the scheduling prob-lem because the interference relationship under the physicalinterference model (SINR) is nonconvex and combinatorial. Inthe sequel, we present a simplified distributed link schedulingmethod taking into account the SIC constraints and using theinterference localization technique presented earlier. We firstpropose a method to calculate the vector

−→λ under a certain ε,

and then, a distributed scheduling method is proposed underSIC constraints.

B. Identifying the Interference Neighborhood

Here, we present a binary-search-based method to determinevector

−→λ under a certain value of ε. Recall that, according

to Definition 1, λ(l) is the lower bound of the radius of theinterference neighborhood IN l, which guarantees that, under afeasible scheduling method (see Definition 2), the total interfer-ence coming from links in the noninterference region (nIN l)does not exceed εImax. For a link l, denote dmax(l) as thedistance from the farthest node in the network to the receiver oflink l. The search procedure for link l starts from dmax(l), andwe use a bisection search method to reduce the gap betweenthe current search radius and the optimal λ(l). At every levelof current radius, we have to determine the maximum inter-ference coming from the active links whose transmitters arelocated outside the current radius. One simple way to decide themaximum interference is to sum up the received signals fromall transmitters outside the current radius; it should be notedthat since some of these transmitters may not be active in ourconfiguration, this calculated maximum interference representsan upper bound. An alternative approach is to solve a simpleSIC-based scheduling problem on the links whose transmittersare located outside the current radius. We repeat this procedure(of updating the radius of interference neighborhood) for linkl until a tolerable performance is attained. This procedure isillustrated in Algorithm 1. Note that Algorithm 1 is a central-ized procedure that needs to be performed only once for a staticwireless network.

All links in the area outside the current radius are initiallystored in a link set Ψ. For current link l, we associate weightattribute wal(l′) = PwGt(l′),r(l), ∀ l′ ∈ Ψ and 0 otherwise. Wealso define a binary variable pi(i ∈ L), which is equal to 1 whenlink i is active, and otherwise, it is zero. Then, we define ouroptimization objective as

Maximize :∑i∈L

wal(i)pi. (16)

Similarly, we define another binary variable qt(j)(j ∈ L),which is equal to 1 when node t(j) is an active transmitter,and otherwise, it is zero. Let L+

n be the set of links whosetransmitter is node n and L−

n be the set of links whose receiveris node n. Therefore, we have

qt(j) =∑

i∈L+t(j)

pi (17)

∑i∈L+

n

pi ≤ 1. (18)


In this paper, we only consider the half-duplex mode at eachnode. Then, our half-duplex constraints can be written as

pi + pj ≤ 1(∀n ∈ N : i ∈ L−

n , j ∈ L+n

). (19)

Similar to [18], we use the concept of residual-SINR or r-SINRfor short. Due to its interference cancelation capability, areceiver node can sequentially cancel all interfering signals,which are stronger than the one of interest; therefore, one onlyneeds to consider the interference from senders whose signalsare weaker than that of the intended one. The r-SINR can bedefined as

r_SINRt(i),t(i) =PwGt(i),r(i)∑Gt(k),r(i)≤Gt(i),r(i)

k =i,t(i) =t(k) PwGt(k),r(i)qk + η.

(20)

Indeed, when scheduling variable vpi = 1 (link i is active), thisimplies that all other stronger received signals from adjacentsenders at r(i) have been correctly decoded, and the decodingof the signal of interest at link i is also successful. Namely, ifvpi = 1, then the following two constraints should be satisfied:

r_SINRt(i),r(i) ≥β, (pi = 1, i ∈ L) (21)

r_SINRt(j),r(i) ≥β,(j = i, t(j) = t(i), Gt(j),t(i)≥Gt(i),r(i),

pj = 1, j, i ∈ L) . (22)

To convert the SIC constraints into an LP format, we define a bi-nary variable ρi,t(j) to describe the relationship of pi and qt(j).Let ρi,t(j) = 1 if and only if pi = 1 and qt(j) = 1; otherwise, itis zero. Then, the relationship can be written as follows:

pi ≥ ρi,t(j) (23)

qt(j) ≥ ρi,t(j) (24)

ρi,t(j) ≥ pi + qt(j) − 1. (25)

Now, we can use mathematical programming to describeconstraints (21) and (22) as

PwGt(j),r(i) −Gt(j),r(i)≥Gt(k),r(i)∑

t(k) =t(j)

βPwGt(k),r(i)qt(k) − βη

≥(1 − ρi,t(j)

)Mi,t(j)

Mi,t(j) = PwGt(j),r(i)

−Gt(j),r(i)≥Gt(k),r(i)∑

t(k) =t(j)

βPwGt(k),r(i) − βη (26)

PwGt(i),r(i) −Gt(i),r(i)≥Gt(k),r(i)∑

t(k) =t(i)

βPwGt(k),r(i)qk − βη

≥ (1 − pi)Hi

Hi=PwGt(i),r(i)−Gt(i),r(i)≥Gt(k),r(i)∑

t(k) =t(i)

βPwGt(k),r(i)−βη. (27)

Algorithm 1: Determination of Interference Neighbourhood

1 Initialize ε(0 < ε < 1);2 Initialize itrCut;3 for l : l ∈ L do4 Initialize curr.decision = 1;5 Initialize curr.radius = dmax(l);6 Initialize success.radius = dmax(l);7 Initialize curr.decision = 1;8 for i = 1 to itrCut do9 curr.interval = (dmax(l)− dt(l),r(l))/2i;10 curr.radius = curr.radius+ (1 − curr.

decision) ∗ curr.interval − curr.decision ∗curr.radius;

11 Generate wal based on curr.radius;12 Solve optimal objective (16) under constraints

(17)–(19), (23)–(27);13 if (16) > εImax then14 curr.decision = 0;15 else16 success.radius = curr.radius;17 curr.decision = 1;18 end19 λ(l) = success.radius;20 end21 end

C. Distributed Scheduling Algorithm With SIC

Based on Algorithm 1, we can calculate−→λ under a certain

value of ε. Let Δ1l be the set of all links k such that t(l) is

located in Ak, Δ2l be the set of all links k such that t(l) is

located in IN k −Ak, and Δl = Δ1l

⋃Δ2

l . At the beginningof each scheduling period, each link l broadcasts its weightinformation (wl) to links in Δl and ΔIN

l [the set of links whosetransmitters are located in the interference neighborhood of linkl (i.e., in IN l)]. We further divide ΔIN

l into two link sets:ΔIN 1

l and ΔIN 2

l . The former denotes the set of links k suchthat t(k) is located in Al, and the latter denotes the set of linksk′ such that t(k′) is located in IN l −Al. The weight of linkl is computed as illustrated in Section IV-A. We assume thateach link l(l ∈ L) maintains two local link sets, i.e., the currentactive link set (currsl for short) and a candidate link set (canslfor short). The former contains links that have been addedinto a feasible configuration conf in a particular schedulingperiod, and the latter contains links that are candidate linksto be added into conf . At the beginning of each schedulingperiod, we initialize currsl = ∅ and cansl = {l,Δl

⋃ΔIN

l }.Each scheduling period consists of several intervals, and in eachinterval, each link l makes a decision as to whether it shouldbe added into currsl or removed from cansl. Therefore, thepurpose of our scheduling method is to generate a new con-figuration that satisfies the SIC constraints under the physicalinterference model such that the sum of the weights of thelinks in this configuration is the largest possible. Our schedulingmethod follows the classical GMS method but is implementedin a distributed manner.


To make sure that the new configuration, which has beengenerated, satisfies the SIC constraints under the physical in-terference model, each link will execute two main proceduresas follows. At the beginning of each scheduling interval, eachlink l (l ∈ cansl) compares its weight to the weights of linksin cansl. If link l has the largest weight among all links incansl, it will run Algorithm 2 to try to add itself into currsl.The detailed process is illustrated next. Link l first broadcasts aREQ message to links in Δl. Any link in Δl will add link l intoa local auxiliary link set (auxs for short); now, any link l′ ∈{currsl

⋃auxsl} will determine whether it remains feasible

under SIC constraints upon adding link l to the current scheduleas follows. For each link l′ ∈ {currsl

⋃auxsl}, we define the

SIC link set (sicsl′ for short) as the set of links whose trans-mitters are in ΔIN 1

l′⋂{currsl′

⋃auxsl′} and receivers are

r(l′). According to Theorem 1, any link l′ ∈ {currsl⋃auxsl}

satisfies SIC constraints if 1) the total interference (I1) comingfrom ΔIN 2

l′ is ≤ (1 − ε)Imax(l′) and 2) all links k ∈ sicsl′

are feasible (i.e., total interference (I2) coming from ΔIN 2

k is≤ (1 − ε)Imax(k)).

According to the given procedure, if any link l′ ∈{currsl

⋃auxsl} does not satisfy the SIC constraints, then

link l′ will send an ERROR message to link l indicating that linkl cannot be added to the configuration (that is, link l is causingstrong interference making the current schedule not feasible).If link l ∈ auxsl does not receive any ERROR message fromits neighbors, it adds itself into currsl, removes itself fromcansl, auxsl, and broadcasts a SUCCESS message to all itsneighbors to update their local link sets (cans, currs, andauxs). Otherwise, it removes itself from cansl, auxsl andbroadcasts a REMOVE message to all its neighbors to updatetheir local link sets (cans, auxs). The given process enforcesthat when adding a new link to a feasible configuration, thecurrent schedule remains feasible under SIC constraints.

The main purpose of our second procedure is to remove linksin cans (e.g., link l ∈ cansl), which have no chance of beingadded into currs. After the new conf is generated at eachinterval, all links l (l ∈ cansl) need to make a decision as towhether they satisfy SIC constraints as follows. For each linkl ∈ cansl, we define another SIC link set (sics′l for short) asthe set of links whose transmitters are in ΔIN 1

l

⋂currsl and

receiver is r(l). Similar to the process in the first procedure,any link l ∈ cansl does not satisfy SIC constraints if 1) thetotal interference (I ′1) coming from ΔIN 2

l is > (1 − ε)Imax(l)or 2) for any link k′ ∈ sics′l is infeasible (i.e., total interference(I ′2) coming from ΔIN 2

k′ is > (1 − ε)Imax(k′)). After the givenprocess, if there is a link l in cansl that does not satisfySIC constraints, then link l will remove itself from cansl andbroadcast a REMOVE message to all its neighbors to updatetheir local link sets (cans, currs). The given process makessure that each link in cans satisfies SIC constraints with thecurrent schedule.

In our distributed implementation, we set the number of inter-vals per scheduling period to a fixed value. In each schedulinginterval, each link will run Algorithms 2 and 3 to generate newfeasible schedule/configuration during the scheduling period.Once a schedule is obtained, links that have been selected willtransmit in the transmission period one packet each.

Algorithm 2: Distributed Scheduling Method With SIC(Link l)

1 Link l broadcast REQ message to all links in Δl;2 for link l′ in Δl

⋂{currsl

⋃auxsl} do

3 if link l′ received REQ message from link l then4 Link l′ adds link l into auxsk;5 Link l′ calculates cumulative interference I1;6 if I1 > (1 − ε)Imax(l′)) then7 Link l′ broadcasts ERROR message to link l;8 else9 Generate sicsl′ ;10 for k : k ∈ sicsl′ do11 Link k temporarily calculates cumulative

interference I2;12 if I2 > (1 − ε)Imax(k) then13 Link l′ broadcasts ERROR message to link l;14 end15 end16 end17 end18 end19 if Link l receives no ERROR messages then20 currsl = currsl

⋃l;

21 cansl = cansl − l;22 auxsl = auxsl − l;23 link l broadcasts a SUCCESS message to all its neigh-

bors to update their local link sets(cans, currs, auxs);24 Goto Algorithm 3;25 else26 cansl = cansl − l;27 link l broadcasts a REMOVE message to all its neigh-

bors to update their local link sets(cans, auxs);28 end

Algorithm 3: Distributed Scheduling Method With SIC(Part II)

1 for link k in Δl

⋂cansl do

2 if link k received a SUCCESS message from link l then3 Link k calculates cumulative interference I ′1;4 if I ′1 > (1 − ε)Imax(k)) then5 Link k broadcasts a REMOVE message to its neigh-

bors to update their local link sets(cans);6 else7 Generate sics′k;8 for i : i ∈ sics′k do9 Link i calculates cumulative interference I ′2;10 if I ′2 > (1 − ε)Imax(i) then11 Link k broadcasts a REMOVE message to its

neighbors to update their local link sets(cans);12 end13 end14 end15 end16 end


D. Joint Transport, Routing, and Scheduling With SIC

Consider the dual problem (9) and suppose that the functionD(u) is not necessarily differentiable. Therefore, (9) can besolved using the subgradient method. Now, it is easy to verifythat

v+if (u)−(yif (u) + v−if (u)

)(28)

is a subgradient ofD(u) at point u. Thus, based on the subgradi-ent method, the update algorithm can be formulated as follows:

uif (t+1)=[uif (t)+α

(v+if (u(t))−

(yif (u(t))+v−if (u(t))

))]+(29)

where α is a positive step size. Equation (29) achieves optimal-ity when α is set to a sufficiently small value [25]. The givendual algorithm (presented in Section IV-A) solves the cross-layer problem through a distributed manner where at the trans-port layer, nodes in the network individually update their pricesaccording to (29) and the source of each flow f individuallyadjusts its rate (y) according to the local congestion price (u);for solving the routing/scheduling subproblem, we generate anew conf at each time slot by using Algorithms 2 and 3, whichwork in a distributed manner. We summarize our joint conges-tion control, routing, and scheduling with SIC in Algorithm 4.

Algorithm 4: Distributed Cross-Layer Design With SIC

1 Initialize max iteration count as itrmax;2 Initialize y, v, u;3 for i = 1 to itrmax do4 for n ∈ N do5 node n updates u by calculating (29);6 end7 for f ∈ F do8 Source node of flow f updates y by calculating (13);9 end10 for l ∈ L do11 link l updates wl;12 end13 Generate a feasible conf by Algorithms 2 and 3;14 Data Transmission based on currently obtained

schedule;15 end

E. Complexity Analysis

The whole procedure includes a centralized process foridentifying the interference neighborhood (see Algorithm 1)and a link scheduling process under SIC, which is done ina distributed manner at each iteration (see Algorithms 2 and3). To analyze the complexity of the first part, we convert theinverse LP (ILP) problem into a complete binary tree for theworst case of solving the optimal objective (16). A route thatstarts from the root of the tree to the leaf is a feasible solution(or schedule). Based on backtracking, it is clear that the time

Fig. 1. Eight-node network topology.

complexity of a tree traversal search is O(2n), where n is thenumber of links in wal. However, in most cases, there is no needfor a complete traversal search, owing to the SINR constraintsbetween links. In practice, we can prune some invalid branches(i.e., the branch-and-cut method [34]) to improve the efficiencyof the search.

For the run time complexity of the distributed schedulingwith SIC, we omit the communication overload during thescheduling interval and only focus on the worst case compu-tation analysis. As shown in Algorithms 2 and 3, it is easy toverify that the time complexity of links in cansl is O(n) +O(n2) = O(n2) (i.e., the weight comparison and the order ofSIC decoding), where n is the number of feasible neighbors(i.e., active links) for link l. Given that there is no need to com-pare the weight information in links in currsl

⋃auxsl

⋃sicsl,

their run time complexity is O(n2). For each link that is not incansl

⋃currsl

⋃auxsl

⋃sicsl, it keeps silent and therefore

no calculation. Hence, the worst-case run time at each link isO(n2), which is polynomial.

V. NUMERICAL RESULTS

Here, we present numerical results to study the performanceof the cross-layer design method for solving the problem ofjoint transport, routing, and scheduling (JTRS) in wirelessnetworks with interference cancelation. We are particularly in-terested in studying the efficiency of the distributed scheduling(JTRDS) method with SIC, and we present comparisons withcentralized scheduling methods [JTRCS; both Pick & Com-pare (P&C) and GMS]. We also present comparisons of ourcross-layer design method with and without SIC to assess thebenefits of interference cancelation (JTRDS-SIC and JTRDS,respectively). We use a CPLEX solver to solve the ILP problemin Algorithm 1 to determine the radius of the interferenceneighborhood for each link. For our evaluation, we consider tworandom networks (Network 1 and Network 2), with eight nodes(48 links) and 15 nodes (124 links), each randomly distributedin a square region of 100 m × 100 m. The topologies ofthe networks are shown in Figs. 1 and 2. Under the physicalinterference model, the transmission power of each node is setto Pw = 0.001 W. We assume the path-loss index pl = 4; thebackground noise η is set to 10−10 W; the SINR threshold fora successful transmission is β = 1, ε = 0.05 (unless otherwisespecified); and the transmission capacity of each link is c = 1(packet/time slot). We assume that there are two flows and fourflows in Network 1 and Network 2, respectively.


Fig. 2. Fifteen-node network topology.

Fig. 3. Utility achieved by JTRDS-SIC (ε = 0.05) and JTRCS-SIC (P&C).

We start by evaluating the performance benefits of JTRDS-SIC in Network 1. There are two flows in the network (Flow 1:node 1 → node 8; Flow 2: node 3 → node 7). We compare ourdistributed method with P&C, which is a centralized schedulingmethod and is shown to achieve 100% throughput [19], [20]. Inthe P&C scheduling method, we randomly generate a maximalschedule under SIC constraints at each time slot (by randomlyselecting links to be included in the schedule as long as theysatisfy the interference constraints) and compare the currentschedule with the schedule generated in the previous time slot;the schedule with larger weight (sum of the link weights) isalways selected for data transmission at each time slot. In ourdistributed method, we set ε = 0.05. Figs. 3 and 4 show theutility and the congestion price of both methods. Clearly, thefigures show that our distributed method quickly convergesto the optimal solution and oscillates around it; however, thecentralized P&C has slower convergence time, which is due tothe random selection of transmission links to be included in theschedule. To better understand the obtained results, we look athow these two methods route the two flows and the achievableindividual flow rate; the results are shown in Tables I and II. Weobserve that both methods select different routes for the flowsand that flow 1 achieves an optimal rate of 0.8519 (using thecentralized P&C scheduling method), whereas flow 1 achieves

Fig. 4. Congestion prices of JTRDS-SIC (ε = 0.05) and JTRCS-SIC (P&C).

TABLE IAVERAGE RATES OF FLOWS THROUGH DIFFERENT

LINKS WITH JTRCS-SIC (P&C)

TABLE IIAVERAGE RATES OF FLOWS THROUGH DIFFERENT

LINKS WITH JTRDS-SIC

TABLE IIISOURCE NODE, DESTINATION NODE OF EACH FLOW IN THE NETWORK

a flow rate of 0.8332 using the proposed distributed schedulingmethod and a gap of 2% between the two methods. Flow 2,however, achieves the same flow rate of 1 in both methods. Itis to be noted that GMS achieves exactly similar results to ourmethod (results are omitted in the figures).

Next, we consider the larger network (Network 2) with fourflows (Flow1–Flow4: Table III). We start by studying the effectof the ε parameter on the achievable flow rate. We numericallysolve our JTRDS-SIC in this 15-node network, and the obtainedresults are shown in Fig. 5. We observe that when ε is smaller,


Fig. 5. Flow rates (under JTRDS-SIC) versus ε.

Fig. 6. Average number of active links per schedule versus ε.

the achievable flow rates are higher, and as ε increases, the ratedecreases. Clearly, when ε is small, the interference neighbor-hood of a link gets larger (see Fig. 7); therefore, a link l will beable to coordinate its scheduling/transmission with more linksin its interference neighborhood, i.e., IN l. This implies that,ultimately, each selected schedule may contain, on average,more active links (see Fig. 6), which, in turn, implies betterspectrum spatial reuse in the network. However, it should benoted that a larger interference neighborhood may result inhigher scheduling overhead to coordinate the selection of theschedule. Now, conversely, a larger ε implies a smaller inter-ference neighborhood, and as a result, most of the links in thenetwork will be located outside the neighborhood of a particularlink, preventing any effective coordination in the selection ofthe schedule and resulting in lower attainable flow rates.

The flow rate continues to decrease until it reaches a mini-mum value (at ε = 0.7) beyond which it starts to increase. Thiscan be explained as follows. When ε = 0.7, as we mentionedearlier, the radius of the interference neighborhood is small (seeFig. 7), and thus, fewer links may exist within the (IN l −Al)area. Fig. 8 indicates that almost 0 links within that area maybe active. However, according to the protocol, the value ofthe tolerable interference assigned to links within that area

Fig. 7. Average radius of neighborhood versus ε.

Fig. 8. Average number of active links in different areas versus ε.

is set to (1 − ε)Imax; given that almost no links are activewithin that area (see Fig. 8), this tolerable interference valueis wasted and would have been better off allocated to linksoutside this interference neighborhood (i.e., nIN l), wherethe other transmission links are located. As ε increases, thevalue of (1 − ε)Imax decreases, and more tolerable interference(i.e., εImax) is allocated to those links outside the interferenceneighborhood of link l, and such links will attempt to scheduletheir transmissions concurrently with link l. Fig. 8 shows thatas ε increases, more links outside the neighborhood are activein the schedule and none of the links within the interferenceneighborhood are. This explains the behavior of the traffic flowrates shown in Fig. 5 where beyond ε = 0.7, the rates startto increase. Fig. 6 shows the average number of active linksper schedule, and as previously explained, smaller ε indicatesbetter coordination to construct the schedule and, therefore,more active links per schedule, hence better spatial reuse, andlarger ε yields lower spatial reuse.

Finally, we study the benefits of SIC by comparing theperformance of JTRDS-SIC with JTRDS, where in the latter,nodes do not have any SIC capabilities. The results (individualflow rates) are shown in Fig. 9, and we use a value of ε = 0.3.The selection of ε = 0.3 is motivated by Fig. 7 where we show


Fig. 9. Achievable flow rates (JTRDS-SIC versus JTRS (ε = 0.3)).

that both methods have close average radius for the interferenceneighborhood. Fig. 9 shows that flows achieve much higherrates in a network with SIC capabilities (almost twice the rateis achieved by most of the flows). To better understand, weobserve from Fig. 6 that the JTRDS-SIC method (when ε =0.3) has a much better schedule length than that of the JTRDSmethod; indeed, the schedule length (i.e., number of activelinks per selected schedule) of JTRDS-SIC is almost twice thatof JTRDS. This shows that SIC is effectively managing theinterference in the network and promoting transmission con-currence, leading to better achievable flow rates in the network.

VI. CONCLUSION

In this paper, we have studied the benefits of SIC in improv-ing the performance of wireless networks. We considered solv-ing an NUM problem in the context of cross-layer optimizationof the joint congestion control, routing, and scheduling problemunder the SINR interference model. Through dual decompo-sition, we divided our design problem into a congestion con-trol subproblem and a routing/scheduling subproblem. Giventhe complexity of the scheduling subproblem, we presenteda decentralized method for solving the link scheduling prob-lem. Our decentralized method benefits from the interferencelocalization concept to help neighboring links coordinate theirtransmissions, taking into account SIC constraints, and withoutcausing sufficient interference that may corrupt ongoing sched-uled transmissions. Our approach to solving the joint designproblem is completely decentralized. We have numericallysolved the cross-layer optimization, and we have shown thatour distributed resource allocation method achieves very closeresults to centralized methods (e.g., our achieved results arebelow 2% from the centralized P&C scheduling method, whichachieves 100% throughput performance, and we obtain similarresults to the centralized GMS). We also studied the benefitsof SIC, and we have shown that the flows in the network mayachieve up to twice the achievable rates in a network with-out SIC. We have shown that networks with SIC capabilitiespromote better transmission concurrence and, therefore, betterspectrum reuse.

REFERENCES

[1] T.-S. Kim, H. Lim, and J. C. Hou, “Understanding and improving the spa-tial reuse in multihop wireless networks,” IEEE Trans. Mobile Comput.,vol. 7, no. 10, pp. 1200–1212, Oct. 2008.

[2] G. Sharma, R. R. Mazumdar, and N. B. Shroff, “On the complexity ofscheduling in wireless networks,” in Proc. 12th Annu. Int. Conf. MobileComput. Netw., 2006, pp. 227–238.

[3] S. A. Borbash and A. Ephremides, “Wireless link scheduling with powercontrol and SINR constraints,” IEEE Trans. Inf. Theory, vol. 52, no. 11,pp. 5106–5111, Nov. 2006.

[4] P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEETrans. Inf. Theory, vol. 46, no. 2, pp. 388–404, Mar. 2000.

[5] O. Goussevskaia, Y. A. Oswald, and R. Wattenhofer, “Complexity ingeometric SINR,” in Proc. 8th ACM Int. Symp. Mobile Ad Hoc Netw.Comput. ACM, 2007, pp. 100–107.

[6] M. Andrews and M. Dinitz, “Maximizing capacity in arbitrary wirelessnetworks in the SINR model: Complexity and game theory,” in Proc.IEEE INFOCOM, 2009, pp. 1332–1340.

[7] A. Capone, C. Lei, S. Gualandi, and Y. Di, “A new computational ap-proach for maximum link activation in wireless networks under the SINRmodel,” IEEE Trans. Wireless Commun., vol. 10, no. 5, pp. 1368–1372,2011.

[8] Y. Shi, Y. T. Hou, J. Liu, and S. Kompella, “How to correctly use theprotocol interference model for multi-hop wireless networks,” in Proc.MobiHoc, 2009, pp. 239–248.

[9] J. G. Andrews, “Interference cancellation for cellular systems: A contem-porary overview,” IEEE Wireless Commun., vol. 12, no. 2, pp. 19–29,Apr. 2005.

[10] X. Xu and S. Tang, “A constant approximation algorithm for link schedul-ing in arbitrary networks under physical interference model,” in Proc. 2ndACM Int. Workshop Found. Wireless Ad Hoc Sensor Netw. Comput., 2009,pp. 13–20.

[11] L. Tassiulas and A. Ephremides, “Stability properties of constrainedqueueing systems and scheduling policies for maximum throughput inmultihop radio networks,” IEEE Trans. Autom. Control, vol. 37, no. 12,pp. 1936–1948, Dec. 1992.

[12] C. Joo, X. Lin, and N. B. Shroff, “Understanding the capacity region ofthe greedy maximal scheduling algorithm in multihop wireless networks,”IEEE/ACM Trans. Netw., vol. 17, no. 4, pp. 1132–1145, Aug. 2009.

[13] P. Mitran, C. Rosenberg, and S. Shabdanov, “Throughput optimization inwireless multihop networks with successive interference cancellation,” inProc. WTS, 2011, pp. 1–7.

[14] Y. Zhou et al., “Distributed link scheduling for throughput maximizationunder physical interference model,” in Proc. IEEE INFOCOM, 2012,pp. 2691–2695.

[15] S. Weber, J. G. Andrews, X. Yang, and G. de Veciana, “Transmis-sion capacity of wireless ad hoc networks with successive interferencecancellation,” IEEE Trans. Inf. Theory, vol. 53, no. 8, pp. 2799–2814,Aug. 2007.

[16] J. Blomer and N. Jindal, “Transmission capacity of wireless ad hocnetworks: Successive interference cancellation versus joint detection,” inProc. IEEE ICC, 2009, pp. 1–5.

[17] S. Sen, N. Santhapuri, R. R. Choudhury, and S. Nelakuditi, “Successiveinterference cancellation: Carving out MAC layer opportunities,” IEEETrans. Mobile Comput., vol. 12, no. 2, pp. 346–357, Feb. 2013.

[18] C. Jiang et al., “Squeezing the most out of interference: An optimizationframework for joint interference exploitation and avoidance,” in Proc.IEEE INFOCOM, 2012, pp. 424–432.

[19] L. Le, E. Modiano, C. Joo, and N. B. Shroff, “Longest-queue-firstscheduling under SINR interference model,” in Proc. MobiHoc, 2010,pp. 41–50.

[20] E. Modiano, D. Shah, and G. Zussman, “Maximizing throughput wirelessnetworks via gossiping,” in Proc. SIGMETRICS, 2006, pp. 27–38.

[21] S. Lv, W. Zhuang, X. Wang, and X. Zhou, “Scheduling in wireless adhoc networks with successive interference cancellation,” in Proc. IEEEINFOCOM, 2011, pp. 1287–1295.

[22] S. Lv, W. Zhuang, M. Xu, X. Wang, and X. Zhou, “Understanding thescheduling performance in wireless networks with successive interferencecancellation,” IEEE Trans. Mobile Comput., vol. 12, no. 8, pp. 1625–1639, Aug. 2013.

[23] D. Yuan, V. Angelakis, L. Chen, E. Karipidisi, and E. G. Larsson, “Onoptimal link activation with interference cancellation in wireless network-ing,” IEEE Trans. Veh. Technol., vol. 62, no. 2, pp. 939–945, Feb. 2013.

[24] O. Goussevskaia and R. Wattenhofer, “Scheduling wireless links withsuccessive interference cancellation,” in Proc. ICCCN, 2012, pp. 1–7.


[25] L. Chen, S. H. Low, M. Chiang, and J. C. Doyle, “Cross-layer congestioncontrol, routing and scheduling design in ad hoc wireless networks,” inProc. IEEE INFOCOM, 2006, pp. 1–13.

[26] Z. Feng and Y. Yang, “Joint transport, routing and spectrum sharingoptimization for wireless networks with frequency-agile radios,” in Proc.IEEE INFOCOM, 2009, pp. 1665–1673.

[27] Z. Shao, M. Chen, S. Avestimehr, and S. R. Li, “Cross-layer optimizationfor wireless networks with deterministic channel models,” IEEE Trans.Inf. Theory, vol. 57, no. 9, pp. 5840–5862, Sep. 2011.

[28] M. Chiang, S. H. Low, A. R. Calderbank, and J. C. Doyle, “Layering asoptimization decomposition: A mathematical theory of network architec-tures,” Proc. IEEE, vol. 95, no. 1, pp. 255–312, Jan. 2007.

[29] M. F. Uddin, H. M. K. AlAzemi, and C. Assi, “Optimal flexible spectrumaccess in wireless networks with software defined radios,” IEEE Trans.Wireless Commun., vol. 10, no. 1, pp. 314–324, Jan. 2011.

[30] M. F. Uddin and C. Assi, “Joint routing and scheduling in WMNswith variable-width spectrum allocation,” IEEE Trans. Mobile Comput.,vol. 12, no. 11, pp. 2178–2192, Nov. 2013.

[31] C. Joo and N. B. Shroff, “Local greedy approximation for scheduling inmultihop wireless networks,” IEEE Trans. Mobile Comput., vol. 11, no. 3,pp. 414–426, Mar. 2012.

[32] C. Joo, X. Lin, J. Ryu, and N. B. Shroff, “Distributed greedy approxi-mation to maximum weighted independent set for scheduling with fadingchannels,” in Proc. MobiHoc, 2013, pp. 89–98.

[33] M. Dinitz, “Distributed algorithms for approximating wireless networkcapacity,” in Proc. IEEE INFOCOM, 2010, pp. 1–9.

[34] J. E. Mitchell, “Branch-and-cut algorithms for combinatorial optimiza-tion problems,” in Handbook of Applied Operations Research. London,U.K.: Oxford Univ. Press, 2000.

Long Qu received the B.S. degree in communica-tion engineering from Zhengzhou University, Henan,China, in 2010. He is currently working towardthe Ph.D. degree in communication and informationsystems with Ningbo University, Zhejiang, China.

From December 2012 to December 2013, he wasa visiting Ph.D. student with Concordia University,Montreal, QC, Canada. His current research interestsinclude cross-layer design in wireless communica-tion systems and wireless network optimization.

Jiaming He received the M.S. and Ph.D. degreesfrom Zhejiang University, Hangzhou, China, in 1993and 1996, respectively.

He is currently a Professor with Ningbo Univer-sity, Zhejiang, China. His research interests includebroadband wireless communication systems.

Chadi Assi (SM’08) received the B.Eng. degreefrom the Lebanese University, Beirut, Lebanon, in1997 and the Ph.D. degree from the City Universityof New York (CUNY), New York, NY, USA, in2003.

He is currently a Full Professor with the Concor-dia Institute for Information Systems Engineering,Concordia University, Montreal, QC, Canada. Be-fore joining Concordia University, he was a VisitingResearcher with Nokia Research Center, Boston,MA, USA, where he worked on quality of service in

passive optical access networks. His main research interests include networksand network design and optimization. His current research interests includenetwork design and optimization, network modeling, and network reliability.

Dr. Assi is on the Editorial Board of the IEEE COMMUNICATIONS SUR-VEYS AND TUTORIALS, IEEE TRANSACTIONS ON COMMUNICATIONS, andIEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. He was a recipient ofthe prestigious Mina Rees Dissertation Award from CUNY in August 2002 forhis research on wavelength-division multiplexing optical networks.