distributed scheduling in mimo empowered cognitive radio ad hoc networks

1456 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 7, JULY 2014

Distributed Scheduling in MIMO EmpoweredCognitive Radio Ad Hoc Networks

Cunhao Gao, Shan Chu, and Xin Wang, Member, IEEE

Abstract—Two fast growing technologies, MIMO and cognitive radio (CR), can both effectively combat the transmission interferenceamong links and thus increase the network throughput. MIMO exploits spatial degree of freedom (DoF) through spatial multiplexingand interference cancelation within the same frequency channel, while CR exploits all available frequency channels for transmissions.We consider an ad hoc network where each node is equipped with an array of cognitive radios. A radio can tune to a different channeland transmit independently, or transmit together with other radios on the same channel using MIMO mode. Additionally, differentfrequency and spatial channels could have different conditions. There is a big challenge for nodes to distributively coordinate inselecting a transmission channel and/or a spatial DoF taking advantage of this unprecedented flexibility and diversity of channels for ahigher network performance. In this work, we mathematically model the opportunities and constraints for such a network with theobjective of maximizing the weighted network throughput. We propose a centralized algorithm as our comparison benchmark, and adistributed algorithm to flexibly assign spectrum channel or spatial DoF exploiting the multiuser diversity, channel diversity and spatialdiversity for a higher performance in a practical network. The algorithm further supports different transmission priorities, reducestransmission delay and ensures fair transmissions among nodes by providing all nodes with certain transmission probability. Theperformance of our algorithms are studied through extensive simulations and the results demonstrate that our algorithm is veryeffective and can significantly increase the network throughput while reducing the delay.

Index Terms—Cognitive radio, MIMO, scheduling, MAC, ad hoc network

1 INTRODUCTION

COGNITIVE radio (CR) techniques have received grow-ing research interests in recent years. CR promises

unprecedented flexibility in radio functionalities via theprogrammability at the lowest layer, which was once donein the hardware. Due to its spectrum sensing, learning, andadaptation capabilities, CR is able to address the heart ofthe problem associated with spectrum scarcity (via dynamicspectrum access (DSA)) and inter-operability (via chan-nel switching). CR has been accepted as one enablingradio technology for the next-generation wireless commu-nications [1], [2], and has been implemented for cellularcommunications [3], military applications [4], and pub-lic safety communications [5]. It is envisioned that CRwill be employed as a general radio platform upon whichnumerous wireless applications can be implemented.

Instead of exploiting the spectrum opportunities,multiple-input multiple-out MIMO [6] techniques target toharvest the spatial channel gain through intelligent antennaand signal processing techniques. With multiple antennasat the transmitter and/or receiver, a MIMO system takes

• C. Gao is with Amazon.com, Seattle, WA 98109 USA.E-mail: [email protected].

• S. Chu is with Motorola Solutions, Holtsville, NY 11742 USA.E-mail: [email protected].

• X. Wang is with the Department of Electrical and Computer Engineering,Stony Brook University, Stony Brook, NY 11794 USA.E-mail: [email protected].

Manuscript received 29 Sep. 2012; revised 16 Mar. 2013; accepted 11 July2013. Date of publication 14 Aug. 2013; date of current version 2 July 2014.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier 10.1109/TMC.2013.105

advantage of multiplexing to simultaneously transmit mul-tiple data streams on the same channel to increase thewireless data rate and diversity to optimally combine sig-nals from different transmission streams to increase thetransmission reliability and range. The benefits of MIMOlead many to believe it is the most promising techniqueof emerging wireless technologies. MIMO is prominentlyregarded as a technology of choice for next generation wire-less systems such as IEEE 802.16, IEEE 802.11n, and thethird and fourth generation cellular systems.

Currently, the advances of CR (see [2], [7]–[9]) andMIMO (see [10]–[15]) are largely independent and in paral-lel. Due to the challenge of each research direction, there isvery limited work studying the two together to exploit bothspectrum opportunities and spatial opportunities. Somerecent studies [16]–[18] investigate the information gainby exploiting MIMO beamforming to constrain the inter-ference towards the primary users instead of the jointexploration of spectrum and spatial resources. Withoutknowledge of primary user signatures, it is also hard tomeasure the channels and constrain the interference inreality. A recent work in [19] intends to understand thepotential capacity gain with joint use of MIMO and CR. Theimplicit assumption that an antenna can simultaneouslyaccess multiple frequency bands makes it similar to conven-tional work on OFDM plus MIMO and fundamentally dif-ferent from our framework. The paper focuses on formingan optimization framework, rather than provides an actualtransmission algorithm. The ordering of transmissions maybe difficult to realize distributively, and the OFDM kind oftransmissions may apply to sub-carriers but not to wide

1536-1233 c© 2013 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.

GAO ET AL.: DISTRIBUTED SCHEDULING IN MIMO EMPOWERED COGNITIVE RADIO AD HOC NETWORKS 1457

spectrum channels. Different from work on multi-channelallocations [20]–[26] which normally assume all nodesaccess the same group of channels and mainly considerchannel coordination, our design takes into account thedifference in channel availability at different nodes as aninherent nature of cognitive radio transmissions, the dif-ferent channel conditions and multi-user diversity, andparticularly the opportunities and constraints of antennasin supporting concurrent MIMO and CR transmissions. Wefocus on addressing the challenge of exploiting concurrentMIMO and CR opportunities, while assuming the spectrumavailability can be detected via various spectrum sensingtechniques [27]–[32] proposed in the literature.

The goal of this work is to develop a distributed algo-rithm that can concurrently exploit the agility of CR andMIMO to benefit from both the opportunities of spare spec-trum channels and spatial degree of freedom (DoF) for anoverall higher throughput and lower delay in a multi-hopwireless network. Different antennas can transmit over dif-ferent idle frequency channels to harvest the spectrum gain,while all or a subset of antennas of a node can also form aMIMO array to exploit the spatial gain. There is a tradeoffbetween the two options and how to assign transmissionchannels and antennas depend on many factors, includ-ing the network topology, the physical channel conditions,the node density, and the traffic patterns. Generally, weexpect MIMO plays more roles when the available numberof channels is small or the node density is high in a neigh-borhood. MIMO also could work better in a more severechannel condition. In addition, we consider the heterogene-ity in transmission conditions of both spectrum channelsand spatial channels. We coherently model all the optionsand develop scheduling algorithms to enable concurrentexploration of the two cutting-edge technologies to addressthe challenge of spectrum scarcity.

To our best knowledge, this is the first work that pro-vides the cognitive distributed scheduling algorithm thattakes into account the network and channel conditions andexploits benefits of both CR and MIMO for their seamlessoperations over an ad hoc network. Our contributions canbe summarized as follows:

• We form a mathematical model to capture the oppor-tunities and constraints of concurrent exploration ofMIMO and CR techniques, taking into account thediversity of different frequency and spatial channels.

• We provide a centralized algorithm to solve the prob-lem for performance reference, considering variousdiversities.

• We propose an adaptive and distributed schedulingalgorithm to jointly allocate the spectrum channeland spatial DoF taking advantage of both CR andMIMO for an overall higher network performance.In addition, our algorithm exploits the potentialof antenna selection and stream allocation takingadvantage of the multiuser diversity, channel diver-sity and spatial diversity to further improve thenetwork performance.

The remainder of this paper is organized as follows. InSection 2, we introduce the tradeoffs of different configu-rations of CR and MIMO, thus laying the foundation for

mathematical modeling in Section 3 for joint optimizationof CR and MIMO. Sections 4 and 5 propose a centralizedalgorithm as a performance benchmark and a flexible dis-tributed algorithm for application in a practical network,respectively. In Section 6, we present simulation results,evaluate the algorithms performance, and validate the effi-ciency of our algorithms in comparison to other referencealgorithms. Section 7 concludes the paper.

2 PRELIMINARY AND MOTIVATION

We consider a multi-hop CR ad hoc network with anantenna array at each node, and we call this network aMIMO-CRN. With its CR, a node is able to sense its envi-ronment and identify a set of available frequency channelsfor wireless communications. The set of available frequencychannels at one node may be different from those atanother node in the network. Two nodes can communi-cate only if they have at least one available channel incommon, and a link can interfere with another link onlyif these two links operate on the same channel at thesame time. Therefore, a CRN can exploit available spec-trum and avoid the transmission interference via the use ofdifferent channels.

Complementary to a CR’s ability to handle the inter-ference at the channel level, within a frequency channel,MIMO technique can mitigate co-channel interference byexploiting spatial degree of freedom (DoF). At the trans-mitter side, the number of data streams is limited by thenumber of antenna elements. Due to the broadcast natureof wireless communication, at the receiver side, a node willreceive not only the data streams targeting to it, but alsointerference streams targeting to other nodes nearby. To suc-cessfully decode data streams at a receiving node, the totalnumber of data streams and interference streams should befewer than the number of antenna elements at the receiver.

Before formally formulating the problem, we provide afew case studies to illustrate the issues and opportunitieswith the concurrent use of these two advanced technologiestogether.

1. Transmissions over frequency channels versus spa-tial channels. The DoF of nodes can be flexibly used fortransmission over frequency channels or spatial channels,and an antenna can only access one frequency channel ata time. In Fig. 1(a), node 1 transmits 3 data streams overchannel b towards node 2 and 1 data stream towards node4 over channel c, taking up its 4 DoF. Node 4, which uses1 DoF to receive from node 1 over channel c, could spareits remaining 3 DoF to receive from node 3 over channel a.An optimum assignment of DoF over both frequency andspatial domain could allow more concurrent stream trans-missions. For example, in Fig. 1(b), 8 data streams can betransmitted concurrently, 4 from node 1 to node 2 using thechannel b and another 4 from node 3 to node 4 on channelsa and c respectively.

2. Tradeoff between multiplexing and interference can-celation. In Fig. 2, six nodes each with two antennas runon the same channel and form three links, 1 → 2, 3 → 4,and 5 → 6. In the MIMO multiplexing mode [6] shown inFig. 2(a), if any link X activates two data streams, then theother two links must keep idle to avoid colliding with or


Fig. 1. Frequency channels vs. spatial channels. (a) Via spatial multiplexing. (b) Via interference cancellation.

Fig. 2. MIMO spatial multiplexing vs. interference cancellation A. (a) Via spatial multiplexing. (b) Via interference cancellation.

Fig. 3. MIMO spatial multiplexing vs. interference cancellation B. (a) Via spatial multiplexing. (b) Via interference cancellation.

being collided by transmissions on the link X. For exam-ple, when node 1 transmits two data streams using bothof its antennas through spatial multiplexing, it will createtwo interference streams at node 6. Therefore, node 5 canno longer transmit any data stream to node 6. Similarly,if node 3 transmits any data stream, it will create addi-tional interference to node 2, while node 2 has appliedboth of its antennas to receive data from node 1 and cannotspare any antenna to cancel the interference. Totally onlytwo streams can be transmitted in this case. However, ifeach link only transmits one data stream, each receiver canuse one antenna to receive data and the other to combatthe interference from the interfering transmitter by decod-ing the interfering stream and removing it from the totalreceived signal. As shown in Fig. 2(b), the network allowsthree simultaneous data steams, thus interference cancella-tion is exploited here to transmit more streams than simplyusing MIMO multiplexing.

A counter example is shown in Fig. 3. Each node hastwo antennas and all nodes transmit on the same fre-quency channel. With MIMO multiplexing, as shown in

Fig. 3(a), both link 1 → 2 and link 3 → 4 can transmit twodata streams, so there are totally four data streams in thenetwork. However, when exploiting the benefit of MIMOinterference cancellation, both link 5 → 6 and link 1 → 2have one active data stream, while link 3 → 4 must keepidle to avoid colliding at node 6. In this case, the maximumtotal number of data streams is only two.

We can see from the above two examples that there is atradeoff between MIMO multiplexing and interference can-cellation. Given different network topologies, and differentinterference relationship among nodes, it is important tofind the optimal strategy for maximizing the total numberof data streams.

3. The impact of channel condition and diversity. Theabove examples only try to maximize the total numberof concurrent number of data streams without consider-ing the difference in channel conditions thus rate, which isover-simplified and easily fails in achieving a high networkthroughput in reality. In Fig. 2(a), when node 1 transmits 2data streams to node 2, the two data streams have differ-ent channel gains. While in Fig. 2(b), node 1/3/5 each can


select the better spatial channel among two possible onesto transmit to node 2/4/6, which takes advantage of thespatial diversity to further increase the capacity.

4. The Impact of decoding scheme. The other thing thatimpacts the link capacity is the decoding scheme at thereceiver side. For example, the commonly used “SequentialInterference Cancelation” (SIC) decoding scheme normallydecodes the strongest signal first. In Fig. 2(a), when twodata streams are transmitted from node 1 to 2, the firststream decoded will be impacted by the interference fromthe second one, thus the capacity of the link is com-promised. In Fig. 2(b), however, each link has one datastream and one interference stream. If we vary the origi-nal SIC to decode the interferer first, the data stream canachieve a higher rate once the interference is cancelled. Asa result, Fig. 2(b) can achieve a higher rate per streamin addition to transmitting a larger number of streams.Therefore, in a distributed cooperative transmission envi-ronment where interference and data transmissions are notfrom the same transmitter, it is beneficial to decode theinterference streams first.

3 MATHEMATICAL MODELING

3.1 Modeling of MIMO-CRNIn a CR network, as different nodes may have differentchannel accessibility due to spectrum policy and interfer-ence, a common control channel (CCC) accessible to allnodes is used in the network to coordinate transmissions.For each neighboring node j, a node i ∈ N in a MIMO-CRN can access one available frequency channel in a setBi not occupied by primary users, and has a packet queueQij. The set Bi may be different at different geographic loca-tions and time, and the set of commonly available channelsbetween nodes i and j can be denoted as Bij = Bi

⋂Bj.Two nodes can communicate if and only if they have atleast one common data channel and within the transmis-sion range. Denote Ai as the set of antennas at node i.Each antenna can only access one channel at a time. Inour work, we assume that all the nodes have the samenumber of antennas, A, for the convenience of presenta-tion. Our scheme, however, can be easily extended to thecase where each node has different number of antennas.With the use of multiple antennas at both the transmit-ter and the receiver, it is possible to apply different MIMOtransmission strategies, e.g., exploiting all antennas to per-form spatial multiplexed transmissions or using some ofthe antennas to cancel the interference, as introduced above.As we focus on concurrent exploration of CR and MIMO’sability to handle interference, we do not consider spatialdiversity technology for range extension and leave this asour future work.

Before presenting algorithms for scheduling, we firstmathematically model the problem and our objective is tomaximize the weighted system throughput.

3.1.1 Transmission/Reception ConstraintsWe first present the constraints at the transmitters andreceivers. To model the half-duplex nature of each node,we use two binary variables gi and hi to indicate nodei’s transmission/reception status, i.e., gi/hi = 1 if node i

is transmitting/receiving and 0 otherwise. Then the half-duplex constraint can be represented as

gi + hi ≤ 1 (i ∈ N ). (1)

To represent a node i’s behavior on a channel b, wedefine a new set of binary variables gb

i and hbi , where

gbi /hb

i = 1 if node i is transmitting/receiving on channelb and 0 otherwise.

Clearly, when node i is a transmitter, it must be trans-mitting on some channels; and if it is not transmitting onany of the available channels, it must not be a transmitter.Thus, we have

gbi ≤ gi ≤

∑

b∈Bi

gbi (i ∈ N , b ∈ Bi). (2)

For the receiver case, similarly we have,

hbi ≤ hi ≤

∑

b∈Bi

hbi (i ∈ N , b ∈ Bi). (3)

For a target receiver and a given channel b, the chan-nel condition thus data rate is different when a differentantenna is used. For the same antenna, the achievabledata rate is different over different frequency channels.Therefore, when performing the scheduling algorithm atthe transmitter side, we need to identify which antenna isactually selected for the transmission on a specific chan-nel. We define gb

i,k = 1 if node i is using its kth antenna fortransmission on channel b, and 0 otherwise.

An antenna can only work on one channel at a time, thus∑

b∈Bi

gbi,k ≤ 1 (i ∈ N , k ∈ Ai). (4)

Also when gbi,k = 1 for some antenna k, it means node

i is transmitting on channel b, then gbi must be 1. On the

other hand, if gbi = 0, it means node i is not transmitting on

channel b, then all its antennas will not use channel b, thusgb

i,k = 0. This relationship can be represented as follows.

gbi,k ≤ gb

i ≤∑

k∈Ai

gbi,k (i ∈ N , b ∈ Bi, k ∈ Ai). (5)

Let N bi represent the set of neighbors of i that share the

same channel b. To identify the packet transmitted out, wedefine the variable gb,p

i,k = 1 if node i is using its kth antenna

to transmit packet p on channel b, and gb,pi,k = 0 otherwise.

Similar to the analysis with constraints in equation (5),we have the following constraints on variables gb,p

i,k .

gb,pi,k ≤ gb

i,k ≤∑

p∈Qi

gb,pi,k , (6)

where i ∈ N , b ∈ Bi, j ∈ N bi , k ∈ Ai, p ∈ Qij.

If a node is chosen to be a transmitter for its packet p, saygb,p

i,k = 1, then the corresponding destination node of packetp, i.e., node j should be a receiver on the same channel viasome antenna. That is, denoting a binary variable hb

i to be 1if node i is receiving packets on channel b, and 0 otherwise.Then gb,p

i,k = 1 leads to hbj = 1. This can be represented as

follows.

gb,pi,k ≤ hb

j (i ∈ N , b ∈ Bi, j ∈ N bi , k ∈ Ai, p ∈ Qij). (7)


To facilitate concurrent transmissions from multiplenodes and antennas, our scheduling solution is slot-based,with which the time domain is divided into transmissiondurations (TD). A TD consists of control signal exchangeand several time slots. The channel assignment and antennaallocation is fixed for a TD. Note that an antenna can sendout multiple packets targeting to the same receiver with-out exceeding the data rate over the channel, we have thefollowing capacity constraint.

∑

p∈Qij

gb,pi,k · sp ≤ TD · rb,j

i,k, (8)

where sp denotes the size of packet p, rb,ji,k denotes the data

rate on channel b between the antenna k ∈ Ai of the trans-mitter i and the receiver j, and i ∈ N , b ∈ Bi, j ∈ N b

i , k ∈ Ai,and p ∈ Qij. The data rate is impacted by the channelcondition, signal strength, noise and interference levels.

We know that the total number of data streams for trans-mission or reception at a node is limited by its numberof antennas. First we have the following constraints for atransmitter.

gi ≤∑

k∈Ai

gbi,k ≤ gi|Ai| (i ∈ N ). (9)

For a receiver, it needs to use its antennas for both datareception and interference cancellation. Denote the set ofneighbor nodes of the receiver i on channel b as N b

i , thenthe antenna constraints at a receiver node is as follows.

∑

b∈Bi

⎛

⎜⎝hb

i

∑

j∈N bi

∑

k∈Aj

gbj,k

⎞

⎟⎠ ≤ |Ai| (i ∈ N ). (10)

3.1.2 ObjectiveOur objective is to maximize the total weighted throughputduring the transmission. Here the weight is represented asthe priority of the packets. The objective can be mathemat-ically formulated as follows:

∑

i∈N

∑

k∈Ai

∑

b∈Bi

∑

p∈Qij

gb,pi,k · pr(p) · sp (j ∈ N b

i ), (11)

where pr(p) denotes the priority of the packet p. The packetpriority depends on the service type and queuing delay,thus the consideration of priority helps to reduce the trans-mission delay. The value of pr(p) is initially set to the servicepriority of the packet and increases as the queuing durationincreases.

Then the optimization problem can be formulated asfollows.

max∑

i∈N∑

k∈Ai

∑b∈Bi

∑p∈Qij


i ),

s.t. Constraints (1) − (10).

In this formulation, gi, gbi , gb

i,k, gb,pi,k , hi, hb

i are optimizationvariables and sp, rb

k,i, Ai, pr(p) are given constants. Becauseof the nonlinear term hb

i∑

j∈N bi

∑k∈Aj

gbj,k in (10) and integer

variables, the problem is in the form of Mixed Integer Non-Linear Programming (MINLP).

3.2 A Linearization ReformulationDue to the nonlinear term in the above formulation, itrequires much more efforts to solve such an optimizationproblem. Mature commercial packages, e.g., CPLEX, can-not easily handle an MINLP. A closer examination of theabove formulation shows that we can actually reformulatethe original problem and make it simpler. Now define anew variable θb

i as follows.

θbi = hb

i

∑

j∈N bi

∑

k∈Aj

gbj,k (i ∈ N , b ∈ Bi). (12)

The physical meaning of θbi is the number of DoFs that

costs node i for data reception and interference cancelationon channel b. With θb

i , (10) can be rewritten as:∑

b∈Bi

θbi ≤ |Ai| (i ∈ N ). (13)

Let Ai = |Ai|. Now, a set of new constraints for θbi

are required. For the binary variable hbi , we have the fol-

lowing two constraints: hbi ≥ 0, 1 − hb

i ≥ 0. Similarly,for

∑j∈N b

i

∑k∈Aj

gbj,k, we have:

∑j∈N b

i

∑k∈Aj

gbj,k ≥ 0, Ai −

∑j∈N b

i

∑k∈Aj

gbj,k ≥ 0. Multiplying each constraint involving

hbi by one of the two constraints involving

∑j∈N b

i

∑k∈Aj

gbj,k,

and replacing the product term with the new variable θbi ,

we have the following new constraints.

θbi ≥ 0 (14)

θbi ≤

∑

j∈N bi

∑

k∈Aj

gbj,k (15)

θbi ≤ Ai · hb

i (16)

θbi ≥ Ai · hb

i +∑

j∈N bi

∑

k∈Aj

gbj,k − Ai (17)

It can be verified that for the case when hbi is a binary

variable, (12) is equivalent to the constraints in (14) to (17).Therefore, we have a new formulation as follows.

max∑

i∈N∑

k∈Ai

∑b∈Bi

∑p∈Qij


i ),

s.t. Constraints (1) − (9), (13) − (17).

In this new problem formulation, gi, gbi , gb

i,k, gb,pi,k , hi,

hbi , θb

i are optimization variables and sp, rbk,i, Ai, pr(ip) are

given constants. This new formulation is in the form ofInteger Linear Programming (ILP) which can be handledby commercial package, e.g., CPLEX, to obtain the optimalobjective value.

4 CENTRALIZED ALGORITHM

An ILP problem is NP-hard in general, and needs expo-nential time complexity to find a solution. Although theabove formulation can be solved by a commercial pack-age, it is not suitable for the practical implementation. Inthis section, we develop an efficient centralized algorithm tosolve the problem where all the queue and stream informa-tion is assumed to know at a central controller. The designand performance of the centralized algorithm provide abenchmark for the distributed algorithm.


4.1 InitializationAt the beginning of the algorithm, the central controller col-lects all the information from nodes. The information of anode i includes its channel availability, the set of neighbor-ing nodes, the condition of each frequency channel betweenan antenna and a neighboring node, the packets in queueand their priority. Based on the neighboring information,the central controller creates a directed graph G0 to indi-cate the connection and interfering relationship betweennodes without specifying the antenna and frequency chan-nel assignment. Each node in the network is represented bya vertex. For any node pair (i, j), if i has packets targetedfor j, there is a data edge from i to j; if the transmission ofi interferes with the receiving of j, there is an interferenceedge from i to j. The information and the connected graphare updated in each transmission duration.

4.2 Greedy SchedulingFor a transmission duration t where t = 1, 2, . . . , the centralcontroller iteratively performs the following steps based ona weighted directed graph Gt−1.

1) Pre-Scheduling UpdateThis step is performed at the beginning of a trans-mission duration. As modeled in Section 3, eachnode i in the network keeps a queue Qij with pack-ets targeted for each neighboring node j, and thequeues are updated in each interval. The priorityof packet p, denoted as pr(p), depends on the ser-vice type and queueing time. The queue priorityis the cumulative priority of packets in queue withQprio

ij = ∑p∈Qij

pr(p), and is a weight associated withthe data stream edge from node i to j in the updatedconnected graph Gt.The optimal solution, formed by selected datastream edges, is a subgraph of Gt and denoted asGopt. We also create another subgraph called blockgraph Gb to save the edges that cannot be sched-uled in the current duration. At the beginning ofeach transmission duration, both Gopt and Gb areset to ∅, and each node is allowed to be either atransmitter or a receiver.

2) Stream and Channel AllocationThe central controller selects the edge with the high-est weight from Gt, denoted as eh = (sh, dh) wheresh and dh are the source and destination nodes of ehrespectively.

• Construct a set to include the stream qual-ity of the selected edge with all the avail-able antenna and channel combinations: Sh ={Q(k, b)|eh = (sh, dh), k ∈ Ash , b ∈ Bsh,dh} whereAsh is the set of unused antennas at sh, andBsh,dh is the set of available channels betweensh and dh. Q(k, b) is the stream quality fac-tor for the stream between the antenna k andthe node dh via the channel b. The streamquality depends on the transmission power ofthe stream and the channel condition betweenthe transmitter antenna and the receiver node

of this stream. For a given total transmissionpower at a node, if more streams are selectedfrom the node to be transmitted, the transmis-sion power for each stream will reduce. Thiswill reduce the signal to interference and noiseradio of the stream at the receiver thus thecorresponding rate the stream can support.

• Find the largest element in Sh, denote itas Qmax, and the corresponding transmitternode, receiver node, antenna, channel as smax,dmax, kmax and bmax respectively. Note thatsmax = sh and dmax = dh. For the conve-nience of presentation, we also denote theedge formed by smax and dmax as emax.

• Tentatively add emax with the antenna assign-ment kmax and channel assignment bmax to Gopt.Check whether (10) is still satisfied for Gopt.

– If not, remove emax from Gopt, and removethe elements in Q(k, b) corresponding tok = kmax and b = bmax from Sh, as theassignment kmax and bmax for emax is infea-sible to be scheduled. If Sh = ∅, removethe edge emax from Gt and add it to Gb,as emax is infeasible to be scheduled withany assignment of antenna and channel.

– Else, mark smax as a transmitter node anddmax as a receiver node if they are notcurrently marked yet. Assign emax to theantenna kmax and channel bmax, add emaxalong with the channel allocation infor-mation to Gopt, and update Asmax . Removethe set of edges with smax as the receivernode or dmax as the transmitter node fromGt and add them to Gb. Meanwhile, ifany node associated with emax becomesfully loaded (i.e., (9) or (10) now becomesequation), delete all edges that may over-load the node from Gt and add them toGb. Delete elements associated with kmaxfrom Sh.

3) End CheckCheck whether there is still any edge in Gt. If yes,go to (2); else go to (4);

4) Post-scheduling UpdateSchedule the transmissions according to the graphGopt generated. Add the edges in Gb back to Gt,which will be used for the scheduling in the nexttransmission duration.

4.3 Algorithm PropertiesThe proposed centralized scheduling algorithm has thefollowing property.

Property 1. For any edge (together with antenna and chan-nel information) that is not scheduled, and the correspondingqueue has a higher priority than the scheduled queue with thelowest priority, the scheduling will not be feasible if this edgeis added, i.e. (9) or (10) cannot be satisfied.

With this property, we can prove that the centralizedalgorithm achieves a fixed approximation ratio compared


with the optimum solution that obtains the highest aggre-gate data rate.

Theorem 1. The proposed centralized algorithm can achieve anapproximation ratio of1/(((2+maxi∈N |Ai|)maxi∈N |Ni|+2) · |⋃i∈N Bi|), where Niis the set of neighboring nodes of node i.

Proof. The worst case of the algorithm is that all datastreams are scheduled on the same channel. In suchcase, the performance degenerates to one channel case,where the approximate ratio of the algorithm to the opti-mal is proved to be 1/((2 + maxi∈N |Ai|)maxi∈N |Ni| +2) [14]. Therefore, in MIMO-CRN, the improvementfactor of the optimal is upper bounded by thenumber of channels |⋃i∈N Bi|). To conclude, the pro-posed centralized algorithm can achieve an approx-imation ratio of 1/(((2 + maxi∈N |Ai|)maxi∈N |Ni| + 2)·| ⋃i∈N Bi|).

5 DISTRIBUTED ALGORITHM

A centralized scheduling algorithm involves a high com-munication overhead and computation complexity, andis not suitable for a network with dynamic topology. Inthis section, we develop a distributed algorithm whichtakes advantage of multiuser diversity, channel diversity,and spatial diversity, to maximize the weighted through-put. As the centralized case, our distributed schedul-ing is also slot-based. Note that slot synchronization iscurrently achievable in the IEEE802.11 family of proto-cols [11], and the channel negotiations between nodes alsofacilitate synchronization. In each transmission duration(TD), our distributed algorithm contains several phases,namely, transmitter selection, channel measurement, chan-nel assignment, data stream allocation, and data transmis-sion. During each phase, nodes compete in transmitting outthe control messages using Carrier Sense Multiple Access(CSMA)-based scheme over the common control channel.

The common channel and different data channels mayhave different transmission ranges. The neighbor relationamong nodes on a channel is based on the received signalstrength measured, and does not change frequently. To facil-itate transmission negotiation, a transmitter will send thesignaling message at a large enough power so it can reachall its neighbors on data channels. As our focus is on theefficient MAC scheduling of channel and antenna resourcesin a MIMO-CRN, the detailed procedure of finding networktopology is beyond our scope.

There is a significant challenge for nodes to coordinatein selecting both the channel and antenna to use in a dis-tributed manner. The scheduling algorithm in each phasetries to consider the transmission priority and the channelconditions while reducing the transmission collision andinterference.

5.1 Transmitter SelectionAs a result of the half-duplex nature of wireless commu-nications, there is a need of selecting a set of nodes tobe the transmitters in a TD. Instead of randomly select-ing several nodes as transmitters, our algorithm adaptivelychooses transmitters such that a queue with the higher pri-ority would be transmitted with a higher probability to

reduce the transmission delay, while also introducing somerandomness for transmission fairness.

In a meshed network enabled with MIMO and CR,a transmitter can transmit simultaneously to multiplereceivers with one-to-many transmission, while multipletransmitters can also transmit simultaneously to a receiverwith many-to-one transmission. Both types of transmissioncan be carried over multiple frequency channels or multiplespatial channels. Specifically, in many-to-one transmission,multiple transmitters can transmit concurrently over thesame frequency channel forming cooperative-MIMO trans-mission with the receiver, which takes advantage of thespatial DoF to reduce the number of frequency channelsoccupied. Although one-to-many transmission can be alsosupported over the same frequency channel, it costs DoFsof each receiver to cancel the interference from transmis-sions towards other receivers. In addition, the maximumpower of the transmitter needs to be divided among sev-eral streams, leading to a lower per-steam capacity. It isalso hard to make a decision at the transmitter when dif-ferent receivers take conflicting stream allocation choices.Therefore our selection is more favorable to a multiusercooperative transmission in a many-to-one format.

We consider a node with packets to transmit as an activenode. To facilitate the selection of a subset of nodes to betransmitters in the neighborhood, we introduce a thresholdparameter PTX, which is estimated by each node based onthe priority values of all nodes in its neighborhood. In ordernot to exceed the decoding capacity of any node duringthe data transmission phase, the number of streams thatcan be simultaneously transmitted in the neighborhood isconstrained. To avoid unnecessary channel measurementand reduce processing complexity at a receiver, the numberof transmitters in a neighborhood is also constrained to TX,which can be calculated by a node i as:

TX ={ |Ni − Bi| if 2|Bi| < |Ni|,

|�Ni/2| otherwise.

This is because the number of concurrent transmissionsin the neighborhood of a node i is limited by two majorfactors: the number of available channels if the numberof neighboring nodes is relatively high, i.e. 2|Bi| < |Ni|;or the number of transmitting nodes thus the total traffic.In the first case, the number of receivers is set to be equal tothe number of channels Bi, and many-to-one transmission isexploited over the same frequency channel to improve thethroughput. If there are sufficient number of channels, halfof the nodes can serve as active transmitters to maximallysupport the concurrent number of transmissions using theavailable channels.

An active node i can calculate PTX as:

PTX =TX ∗ ∑

j∈NiQprio

ij∑

j∈Ni

∑k∈Nj

Qpriojk + ∑

j∈NiQprio

ij

. (18)

It then generates a random number γi with the value uni-formly distributed in the range [0, 1]. If γi < PTX, nodei self-decides to be a transmitter; otherwise, it has no rightto transmit. The use of a random number gives each nodea chance to serve as a transmitter, and also facilitates each


node to independently determine if it can serve as a trans-mitter in a time slot. On the other hand, as an active nodewith a higher priority has a higher PTX value, a node witha higher service level and/or larger load and hence longerdelay has a higher chance of being selected as the trans-mitter node. Our selection algorithm thus supports QoSand load balancing while ensuring certain fairness. Thisself-selection scheme avoids extra signaling overhead fortransmitter selection.

5.2 Channel AssignmentAfter a node self-decides to be a transmitter, it will select aset of receiver nodes for its data transmission. To supportQoS and different service levels, a transmitter node i firstsorts Qij for all j ∈ Ni in the descending order of queue’spriority. It then iteratively selects j as its receiver based onthe sorted queue priority. For each transmitter node i, up to|Ai| receivers will be selected. The set of receivers selectedby the transmitter node i is denoted as iRC.

With different channel availability, it is necessary for atransmitter and a receiver to negotiate channel usage overthe common channel before transmissions. To better exploitthe channel diversity while reducing the communicationand channel measurement overhead, we propose a weight-based channel assignment algorithm which contains twophases, one at the transmitter nodes and the other at thereceiver nodes, as described below.

Distributed Channel Assignment Algorithm

1) Step 1: channel selection at the transmitter nodesAt this step, a transmitter node selects a set of chan-nels to cover its intended receivers. To better utilizethe node and queue information, each transmitternode i assigns each channel b a weight wb

i as follows.

wbi =

∑j:j∈iRC,b∈Bij

Qprioij

|{u:u ∈ N bi , u is a receiver}| .

The weight for a channel b is higher under two con-ditions: 1) It is available for transmission betweennodes i and j which are associated with a higherpriority queue Qprio

ij , and 2) The channel is sharedamong more intended receivers, which reduces thenumber of channels to measure thus measurementoverhead and also allows the transmitter to flexiblyselect a receiver with a better channel condition tosend packets later. On the other hand, the weightis reduced when many unintended receivers sharethe same channel, so a transmitter tries to use adifferent channel exploiting the spectrum flexibilityto reduce the interference. Note that the channelsthat can be accessed by a node does not changevery quickly, so a node is aware of the channelsaccessible by its neighbors. The transmitter willsort and then select the set of channels based ontheir weights. On the one hand, as explained inSection 5.1, many-to-one transmission has severaladvantages over one-to-many transmission on thesame channel. The transmitter node is encouragedto select an individual channel for each intendedreceiver. On the other hand, the more channels

are selected, the more channel measurement over-head. To trade off between the two, we select thesubset bi from Bi with |bi| = min (|Bi|, |iRC|). Thetransmitter will select |bi| channels from the highweight to the low weight, and then pass the selec-tion result along with each channel’s weight to thereceivers.

2) Step 2: channel selection at the receiver nodesIt is easy to see that a receiver node may receiveseveral different channel selection results if multi-ple transmitters intend to send the packets to thereceiver, with the total candidate channels being thesuperset of these selected channels. Since a receiverj can work on at most |Aj| channels, symmetrically,it will further reduce the number of channels to |Aj|based on the refined weight wb

j for each channel bas follows:

wbj =

∑i:i∈jTX,b∈Bij

Qprioij

|{u:u ∈ N bj , u is a transmitter}| ,

where jTX represents the neighboring transmittersof j. From the numerator of the weight, we can seethe receiver prefers to select the channel that canbe shared by more transmitters to enable many-to-one cooperative MIMO transmission on the samechannel to reduce the number of channels occu-pied. From the denominator, the receiver tries toselect channels different from interfered transmitters(i.e., the channel with fewer sharing transmitters) toreduce the interference.This channel selection result, along with a chan-nel measurement sequence will be sent back tothe transmitters for their final channel assignment.Transmitters will base on this sequence to send theirtraining signals. Measurement of the same channelcan be carried at the same time with orthogonaltraining signals to reduce the overhead.

3) Step 3: channel assignment finalization at trans-mittersThe transmitter node now finalizes the channels tobe the ones selected by both itself and the corre-sponding receivers, and announces the channel tomeasure as well as the IDs of the selected targetreceiver nodes. The transmitter will avoid using thechannels that have been selected by not-intendedneighboring receivers which send back the channelselection results earlier.

5.3 Channel Measurement and Stream AllocationIn the distributed scheduling, the stream allocation deci-sion can be made either at the transmitter nodes or at thereceiver nodes, and there is a tradeoff for taking eitherof the options. We propose a distributed stream allocationalgorithm which makes decision first at the receiver nodesbased on the measured channel conditions and finalizes thedecision at the transmitter nodes to concurrently considerthe priority and quality of the streams and constrain thenumber of data and interference streams to be within thedecoding capability of the receivers.


Distributed Stream Allocation Algorithm

1) Step 1: actions at the transmitter nodesThe transmitter node broadcasts a training signalover the selected data channels through all antennassimultaneously using orthogonal waveforms, whilethe corresponding receivers tune their antennas tothe channels to measure.

2) Step 2: actions at the receiver nodesAfter a receiver node j decodes the informationsent from all the selected transmitter nodes in itsneighborhood, it learns the channel condition fromeach transmitter on all possible channels. For eachincoming stream, the receiver node records thefollowing parameters: transmitter node id, transmit-ter antenna id, channel id. The stream allocationscheme of a selected receiver node is then as fol-lows.

3) Step 3: pre-allocation at the receiver sideFor each incoming stream, the objective fromSection 3 is estimated by multiplying the queue’spriority with the channel gain which can beobtained from the channel measurement result.Then the streams can be sorted in the descendingorder of this objective values. Therefore, among thestreams with the same priority, the ones with thebetter channel conditions will be selected, whichexploits the multi-user diversity and spatial diver-sity to improve the capacity. Denote the sortedstreams for the receiver node j as Sj, and the set ofstreams selected by the receiver node j as Xj, thenthe receiver selects the streams as follows.

Initial Xj = ∅counter1 = 1for counter2 = 1 to |Sj| do

if Sjcounter2 does not share any specific antenna of atransmitter node with the previous selected streamsin Xj then

put Sjcounter2 into the set Xj++counter1if counter1 = |Aj| then

breakend if

end if++counter2

end for

After the stream allocation, the receiver node broad-casts this result and tune their antennas to thechannels associated with its stream allocation result.

4) Step 4: final stream allocation at the transmittersideAs a transmitter would receive several differ-ent stream allocation results from all its intendedreceivers and other receivers it interferes with, atransmitter needs a further decision on the streamallocation based on its own knowledge such that:(1) The weighted throughput is as high as possible,which again considers the stream priority as wellas exploits multi-user diversity and spatial diversityfor a higher throughput; (2) The stream allocationwill not create conflicting use of its antennas; (3)Reduce the chance of assigning multiple streams on

the same channel thus interference. To achieve thesegoals, a transmitter node i performs the followingstream allocation algorithm where Xi denotes theset of streams that i selects, and Si denotes theset of stream allocation result i receives from itsneighboring receiver nodes.

Sort Si in the descending order based on their objectivevaluesInitial Xi = ∅counter1 = 1for counter2 = 1 to |Si| do

if Sicounter2 does not share any channel with differ-ent receiver nodes or share any antenna with theprevious selected streams in Xi then

Add Sicounter2 into the set Xi++counter1if counter1 = |Ai| then

breakend if

end if++counter2

end for

After the stream allocation, the transmitters will startdata transmission. The intended receivers will decode thedata using the modified SIC which decodes the interfer-ing signals first, then the data streams sorted by the signalstrength until all are decoded.

Note the unscheduled data packets will be kept in thequeue and scheduled in the next duration. Their prioritygets higher as their queueing time increases, and will havea higher chance of being scheduled in future slots.

5.4 Analysis of Signaling OverheadIn this section, we briefly analyze the signaling overhead ofthe proposed distributed algorithm, specifically, distributedchannel assignment in Section 5.2 and distributed streamallocation in Section 5.3 which both involve signalingexchanges.

In step 1 of the channel assignment algorithm, afterdetermining a set of candidate channels, the transmitterbroadcasts a message to announce the selection resultsalong with the weight of each pre-selected channel overthe common control channel. The length of the messageis O(|bi|). In step 2, the receiver broadcasts its preferredchannels on the common channel. The length of the mes-sage is O(|Aj|). In step 3, the finalized channel selectionresult for training purpose is broadcast over the commoncontrol channel so receives can tune to the correspondingchannels. As the selected number of channels will not bemore than |ki| = min(|Ai|, |bi|), the length of the message isO(|ki|).

For the stream allocation algorithm, the signaling forstep 1 is for sending the training sequence. The totalnumber of signaling message is lower than the numberof antennas multiplying the number of selected channels,which is |Ai||ki|. With use of orthogonal codes, the mes-sages can be sent over all all antennas concurrently overeach channel. In step 3, there is only one signaling at thecommon control channel. The length of the message fornode j is O(|Aj|). No signaling message is required forsteps 2 and 4.


Fig. 4. MIMO-CRN performance with varying number of nodes. (a) Data rate vs. number of nodes. (b) Delay vs. number of nodes.

Note that the number of transmitters in a neighborhoodaround a node Ni is constrained by TX, which dependson the number of neighbors of the node Ni and the num-ber of available channels around. The number of candidatereceivers is constrained by Ni−TX. The number of a specifictype of messages broadcast in a neighborhood depends onthe number of transmitters and receivers, and thus Ni andthe number of available channels.

6 PERFORMANCE EVALUATION

In this section, we evaluate the performance of our proposedalgorithms through simulations. We consider an ad hoc net-workwithrandomtopology.Nodesaredistributeduniformlyover a 1200m × 1200m area. Each node has a transmissionrange of 250m. The MIMO channel between node pair ismodeled based on the node distance with path attenuationloss factor set as 3.5, and the small-scale fading coefficientsfollowing the Rayleigh model. White Gaussian noise withSNR = 10dB is added to include environment noise andinterference that cannot be canceled. If not otherwise speci-fied, the number of nodes in the network is 80, the numberof antenna elements at each node is 4 for all the algorithmsimulations, and the number of available frequency channelsin the network is 5. The set of available frequency channelsat each node is randomly selected from this 5-channel pool.

As we are not aware of any distributed scheme existingfor concurrent exploration of CR and MIMO, to demon-strate the effectiveness of our scheduling algorithms andthe benefit of using many-to-many cooperative transmis-sion by taking advantage of MIMO over CR, the perfor-mance of our algorithms is compared with: (1) a randomalgorithm; (2) a CR-only model where MIMO transmissionis disabled but each node has multiple antennas to exploitmultiple frequency channels. In the random algorithm, thenodes randomly make decisions on the transmitter selec-tion, channel assignment, and stream allocation. In a CRonly model, many-to-one and one-to-many transmissionsvia the same channel through MIMO are not allowed. Inaddition, any interference at a receiver on the same channelwill fail the reception. For the convenience of presenta-tion, we use CENT_ALG and DIST_ALG to represent theproposed centralized and distributed algorithms respec-tively, RAND_ALG and CR_ALG to represent the referencerandom algorithm and the algorithm for CR mode only.

The metrics we use for comparison are the aggregatedata rate and normalized delay, with the unit of data rate

for the results being Bit/s/Hz. We have added a sentenceto specify in the third paragraph of Section 6. Aggregatedata rate is the total data rates of the network averagedover the number of transmission durations. Delay time isdefined as the number of transmission durations a packetwaits in the queue before it is successfully transmitted. Weevaluate the impact on performance due to the variation ofnode density, total available channels, and number of DoFs.

Impact of node density: We vary the number of nodes inthe area from 40 to 100. The CENT_ALG has the global infor-mation on all available channels, spatial DoFs, and channelconditions. The more flexibility to explore in transmissions,the more difficult for a distributed algorithm to compete witha centralized algorithm. Even so, in Fig. 4(a), the data rateof DIST_ALG still reaches about 70% that of CENT_ALG,which shows that our distributed scheduling is promis-ing. Compared with other reference algorithms, DIST_ALGachieves more than 1.5 times the data rate of CR_ALG, anddoubles and even triples the data rate of RAND_ALG. Thisdemonstrates that the data rate can be greatly increased in anad hoc network via many-to-many cooperative transmissionsby fully exploiting multiuser diversity, channel diversity, andspatial diversity for a higher channel gain. Moreover, as thenumber of nodes in the network increases, the data ratesof both the proposed CENT_ALG and DIST_ALG increaseby exploiting the spatial domain DoFs. However, the datarate of CR_ALG becomes saturated, while the data rate ofRAND_ALG even decreases at a high node density, as thetwo algorithms reach their capacity limits and a large numberof nodes lead to more collisions thus throughput reduction.On the other hand, in Fig. 4(b), the delay of our DIST_ALGis really close to our CENT_ALG, while RAND_ALG hasa significantly higher delay compared to other algorithms.This is because our DIST_ALG design takes into considera-tion of the system objective whenever possible to maximizethe weighted throughput, where the weight is calculatedbased on the delay in our simulation to trade-off betweendata rate and delay.

Impact of the available number of frequency channels:We vary the number of available frequency channels from 3to 10 in the network. In Fig. 5, our DIST_ALG still achieves60% − 70% data rate of CENT_ALG. Without the globalinformation and scheduling as CENT_ALG, our DIST_ALGis still the best among all. Again, it achieves more than 1.5times the data rate of CR_ALG, and doubles, even triples,the data rate of RAND_ALG. This is because DIST_ALGcan concurrently take advantage of multiuser diversity,


Fig. 5. MIMO-CRN performance with varying number of channels. (a) Data rate vs. number of channels. (b) Delay vs. number of channels.

Fig. 6. MIMO-CRN performance with varying number of DoFs. (a) Data rate vs. number of DoFs. (b) Delay vs. number of DoFs.

channel diversity, and spatial diversity. From Fig. 5(a),as expected, all algorithms achieve a higher data rate asthe number of available frequency channels increases inthe network. As for the absolute increase amount of datarate, DIST_ALG increases nearly 100 while CR_ALG andRAND_ALG increase barely more than 50. This resultis interesting. It indicates that as the number of chan-nels increases, it allows for more transmission flexibilityand hence the performance increase with the interplay offrequency domain and spatial domain transmission oppor-tunities. In the network simulated, the available channels ateach node is different and smaller than the total channels.Therefore, the increase in the data rate is not proportionalto the total number of system channels. In Fig. 5(b), againwe verify that our DIST_ALG has the delay very closeto CENT_ALG, while the other two reference distributedalgorithms suffer from a high delay.

Impact of spatial DoFs: To demonstrate the bene-fit of MIMO many-to-many cooperative transmission byexploiting spatial diversity, we vary the number of DoFsat each node. According to Fig. 6(a), again, we can seeDIST_ALG achieves more than 60% the data rate ofCENT_ALG. This, together with Fig. 4(a) and Fig. 5(a),demonstrates the robustness of DIST_ALG as it can achievemore than 60% data rate of CENT_ALG under differ-ent circumstances, even though the significant challengein coordination among nodes to explore various flexibil-ity. As the number of DoFs at each node increases, bothCENT_ALG and DIST_ALG can effectively exploit the newtransmission opportunity via either MIMO multiplexingor MIMO interference cancelation, therefore leading to anincrease in data rate. In contrast, the rates of CR_ALG andRAND_ALG have only a slight increase when the num-ber of DoFs increases from 1 to 2, beyond which the rates

of both algorithms become flat. With CR_ALG, the sys-tem bottleneck is the number of available channels, whilea practical device often has a limitation on the number offrequency bands to operate.

Given more DoFs at each node, RAND_ALG tries toexploit more transmission opportunities blindly. When anode transfers more data streams with a randomly pickedchannel, it has a higher chance to collide with other trans-missions. As explained in Section 2, both variations inchannel conditions and SIC decoding will have a significantimpact on the final network performance. As a result, withthe increase of DoFs at each node, the increase of through-put is not proportionally. From Fig. 6, again, we can seethat DIST_ALG and CENT_ALG have very close delay, andRAND_ALG suffers from a high delay.

7 CONCLUSION

In this work, we have studied the scheduling problemin a MIMO-empowered CR network. We show that theunique characteristics associated with MIMO and CRmake this problem much more complex and difficult thanthat for an ad hoc network based on the traditional radios.We formulate the scheduling problem as an MILP tomaximize the weighted data rate by considering the trafficdemand, service requirements, and network load. Wecarefully model various constraints due to the availabilityof frequency channels, the limited number of antennas,and the different channel conditions in order to increasethe data rate while reducing the interference. We proposea centralized and a distributed scheduling algorithms tofully exploit the agility of both CR and MIMO as well asmultiuser diversity, channel diversity, and spatial diver-sity for a a higher network performance. Our algorithm


opportunistically selects transmitter nodes, transmissionchannels and antennas while considering the QoS andfairness among nodes. Nodes in a neighborhood canoperate on different available channels or cooperativelyform a many-to-many virtual MIMO array on the samechannel. The performance results demonstrate that ourproposed algorithms are very efficient in coordinatingtransmissions in a MIMO-CRN. Our distributed algorithmachieves much higher data rate than reference algorithms.When the MIMO ability are turned off, the system suffersfrom severe performance degradation, which demonstratesthe benefit and necessity of incorporating CR with MIMOto achieve performance boost in future wireless networks.

ACKNOWLEDGMENTS

Xin Wang’s research was supported by the U.S. NationalScience Foundation under grant numbers CNS-0751121 andCNS-0628093. This work was done when Cunhao Gaoand Shan Chu were with the Department of Electrical andComputer Engineering, Stony Brook University.

REFERENCES

[1] S. Haykin, “Cognitive radio: Brain-empowered wireless commu-nications,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220,Feb. 2005.

[2] A. Wyglinski, M. Nekovee, and Y. T. Hou, Cognitive RadioCommunications and Networks: Principles and Practice. Elsevier,Dec. 2009.

[3] Vanu Inc. [Online]. Available: http://www.vanu.com/[4] Joint Tactical Radio System [Online]. Available: http://www.

globalsecurity.org/military/systems/ground/jtrs.htm/[5] SAFECOM [Online]. Available: http://www.safecomprogram.

gov/SAFECOM/[6] D. Tse and P. Viswanath, Fundamentals of Wireless Communication.

Cambridge, U.K.: Cambridge University Press, Jun. 2005.[7] Y. T. Hou, Y. Shi, and H. D. Sherali, “Spectrum sharing for multi-

hop networking with cognitive radio,” IEEE J. Sel. Areas Commun.,vol. 26, no. 1, pp. 146–155, Jan. 2008.

[8] N. B. Chang and M. Liu, “Optimal channel probing and transmis-sion scheduling for opportunistic spectrum access,” IEEE/ACMTrans. Netw., vol. 17, no. 6, pp. 1805–1818, Dec. 2009.

[9] X.-Y. Li et al., “Almost optimal accessing of nonstochastic channelsin cognitive radio networks,” in Proc. IEEE INFOCOM, Orlando,FL, USA, Mar. 2012.

[10] R. Bhatia and L. Li, “Throughput optimization of wirelessmesh networks with MIMO links,” in Proc. IEEE INFOCOM,Anchorage, AK, USA, May 2007, pp. 2326–2330.

[11] M. Levorato, S. Tomasin, P. Casari, and M. Zorzi, “Analysis ofspatial multiplexing for cross-layer design of MIMO ad hoc net-works,” in Proc. IEEE VTC, vol. 3. Melbourne, VIC, USA, 2006,pp. 1146–1150.

[12] B. Hamdaoui and K. G. Shin, “Characterization and analysis ofmulti-hop wireless MIMO network throughput,” in Proc. ACMMobihoc, Montréal, QC, Canada, Sept. 2007, pp. 120–129.

[13] S. Chu and X. Wang, “Adaptive and distributed scheduling in het-erogeneous MIMO-based ad hoc networks,” in Proc. IEEE MASS,Macau, China, Oct. 2009.

[14] S. Chu and X. Wang, “Opportunistic and cooperative spatial mul-tiplexing in MIMO ad hoc networks,” IEEE/ACM Trans. Netw., vol.18, no. 5, pp. 1610–1623, Oct. 2010.

[15] S. Chu, X. Wang, and Y. Y. Yang, “Exploiting cooperative relay forhigh performance communications in MIMO ad hoc networks,”IEEE Trans. Comput., vol. 62, no. 4, pp. 716–729, Apr. 2013.

[16] R. Zhang and Y.-C. Liang, “Exploiting multi-antennas for oppor-tunistic spectrum sharing in cognitive radio networks,” IEEE J.Sel. Topics Signal Process., vol. 2, no. 1, pp. 88–102, Feb. 2008.

[17] S.-J. Kim and G. B. Giannakis, “Optimal resource allocation forMIMO ad hoc cognitive radio networks,” IEEE Trans. Inf. Theory,vol. 57, no. 5, pp. 3117–3131, May 2011.

[18] Y. Zhang and A. Man-Cho So, “Optimal spectrum sharing inMIMO cognitive radio networks via semidefinite programming,”IEEE J. Sel. Areas Commun., vol. 29, no. 2, pp. 362–373, Feb. 2011.

[19] C. Gao, Y. Shi, Y. T. Hou, and S. Kompella, “On the throughputof MIMO-empowered multi-hop cognitive radio networks,” IEEETrans. Mobile Comput., vol. 10, no. 11, pp. 1505–1519, Nov. 2011.

[20] A. Nasipuri and S. R. Das, “Multichannel CSMA with signalpower-based channel selection for multihop wireless networks,”in Proc. IEEE VTC, Boston, MA, USA, Sept. 2000.

[21] N. Jain and S. R. Das, “Protocol with receiver-based channelselection for multihop wireless networks,” in Proc. IEEE IC3N,Oct. 2001.

[22] S.-L. Wu, C.-Y. Lin, Y.-C. Tseng, and J.-P. Sheu, “New multi-channel MAC protocol with on-demand channel assignment formobile ad hoc networks,” in Proc. I-SPAN, Dallas, TX, USA,Oct. 2000, pp. 232–237.

[23] J. So and N. H. Vaidya, “Multi-channel MAC for ad hoc net-works: Handling multi-channel hidden terminals using a singletransceiver,” in Proc. ACM Int. Symp. Mobile Ad Hoc Networkingand Computing, Roppongi, Japan, May 2004.

[24] P. Bahl, R. Chandra, and J. Dunagan, “SSCH: Slotted seeded chan-nel hopping for capacity improvement in IEEE 802.11 ad-hocwireless networks,” in Proc. ACM MobiCom, Philadelphia, PA,USA, Sept. 2004.

[25] A. Tzamaloukas and J. J. Garcia-Luna-Aceves, “A receiver-initiated collision-avoidance protocol for multi-channel net-works,” in Proc. IEEE INFOCOM, Anchorage, AK, USA,Apr. 2001.

[26] J. Zhu, X. Wang, and D. Xu, “A unified MAC and routing frame-work for multi-channel multi-interface ad hoc networks,” IEEETrans. Veh. Tech., vol. 59, no. 9, pp. 4589–4601, Nov. 2010.

[27] T. Yucek and H. Arslan, “A survey of spectrum sensing algo-rithms for cognitive radio applications,” Commun. Surveys Tuts,vol. 11, no. 1, pp. 116–130, Jan. 2009.

[28] H. Li, C. Li, and H. Dai, “Quickest spectrum sensing in cognitiveradio,” in Proc. 42nd Annu. Conf. Information Sciences and Systems,Princeton, NJ, USA, Mar. 2008, pp. 203–208.

[29] A. W. Min and K. G. Shin, “An optimal sensing framework basedon spatial rss-profile in cognitive radio networks,” in Proc. 6thAnnu. IEEE Conf. Sensor, Mesh and Ad Hoc Communications andNetworks, Rome, Italy, Jun. 2009, pp. 1–9.

[30] T. Zhang and D. H. K. Tsang, “Optimal cooperative sensingscheduling for energy-efficient cognitive radio networks,” in Proc.IEEE INFOCOM, Shanghai, China, Apr. 2011, pp. 2723–2731.

[31] J. Zhao and X. Wang, “Channel sensing order for multi-usercognitive radio networks,” in Proc. IEEE DySpan, Oct. 2012.

[32] Q. Liu, X. Wang, and Y. Cui, “Scheduling of sequential periodicsensing for cognitive radios,” in Proc. IEEE INFOCOM, Apr. 2013.

Cunhao Gao received the B.S. degree incomputer science from the Department ofSpecial Class for the Gifted Young, Universityof Science and Technology of China, Hefei,China, in 2004. He received the M.E. degreein computer science from the University ofScience and Technology of China, Hefei,China, in 2007. In 2009, he received theM.S. degree in computer engineering from theBradley Department of Electrical and ComputerEngineering, Virginia Polytechnic Institute and

State University (Virginia Tech), Blacksburg, VA, USA. After that, hewas in the department of Electrical and Computer Engineering at StonyBrook University, Stony Brook, NY, USA. Since 2011, he has been withAmazon.com.

Shan Chu received the B.S. and M.S. degrees intelecommunications engineering from ZhejiangUniversity, Hangzhou, China, and the Ph.D.degree in electrical engineering from StonyBrook University, Stony Brook, NY, USA. She isnow with Motorola Solutions, Holtsville, NY, USA.Her current research interests include MIMO andcooperative communications, ad hoc networks,and cross-layer design.


Xin Wang received the B.S. and M.S. degreesin telecommunications engineering andwireless communications engineering, respec-tively from Beijing University of Posts andTelecommunications, Beijing, China, and thePh.D. degree in electrical and computer engi-neering from Columbia University, New York, NY,USA. She is currently an Associate Professorin the Department of Electrical and ComputerEngineering of the State University of New Yorkat Stony Brook, Stony Brook, NY, USA. Before

joining Stony Brook, she was a member of Technical Staff in the areaof mobile and wireless networking at Bell Labs Research, LucentTechnologies, New Providence, NJ, USA and an Assistant Professorin the Department of Computer Science and Engineering of the StateUniversity of New York at Buffalo, Buffalo, NY, USA. Her currentresearch interests include algorithm and protocol design in wirelessnetworks and communications, mobile and distributed computing, aswell as networked sensing and detection. She has served in executivecommittee and technical committee of numerous conferences andfunding review panels, and is the referee for many technical journals.She achieved the US NSF career award in 2005, and ONR challengeaward in 2010. She is a member of the IEEE.

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distributed scheduling in mimo empowered cognitive radio ad hoc networks

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