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  3120 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 10, OCTOBER 2010 Cooperative and ConstrainedMIMO Communications inWireless Ad Hoc/Sensor Networks Qi Qu, Laurence B. Milstein,  Fellow, IEEE,  and Dhadesugoor R. Vaman,  Senior Member, IEEE   Abstract —In this paper, we investigate the issue of coop-erative node selection in MIMO communications for wirelessad hoc/sensor networks, where a source node is surroundedby multiple neighbors and all of them are equipped with asingle antenna. Given energy, delay and data rate constraints,a source node dynamically chooses its cooperating nodes fromits neighbors to form a virtual MIMO system with the destinationnode (which is assumed to have multiple antennas), as well asadaptively allocates the power level and adjusts the constellationsize for each of the selected cooperative nodes. In order tooptimize system performance, we jointly consider the optimiza-tion of all these parameters, given the aforementioned systemconstraints. We assume that the source node either has CSI,or has no CSI. Heuristic algorithms, such as maximal channelgain (MCG) and least channel correlation (LCC) algorithms areproposed in order to exploit available system information and tosolve the constrained optimization problem.  Index Terms —Cooperative/virtual MIMO, ad hoc, sensor, cor-relation, fading, QR decomposition, power, energy, constellationsize, delay, optimization, channel state information (CSI). I. I NTRODUCTION I N modern wireless communications, enhanced spectralef  fi ciency can be achieved by the use of multiple-input-multiple-output (MIMO) systems. Recently, MIMO has at-tracted extensive attention and various techniques have beenproposed for both cellular systems and ad hoc networks [1,2] to achieve improved system performance. However, inwireless ad hoc/sensor networks, direct employment of MIMOto each node might not be feasible, since MIMO might requirecomplex transceiver and signal processing modules, whichresult in high power consumption. Furthermore, nodes inwireless ad hoc networks/sensor networks are often poweredby batteries with limited energy. This makes direct application Manuscript received July 27, 2009; revised January 4, 2010 and May 23,2010; accepted August 3, 2010. The associate editor coordinating the reviewof this paper and approving it for publication was X. Ma.This work is supported by the U.S. Army Research Of  fi ce with ResearchCooperative Agreement grant No. W911NF-04-2-0054 to the ARO Centerfor Battle fi eld Communications (CeBCom) at Prairie View A&M University,the U.S. Army Research Of  fi ce under the Multi-University Research Initiative(MURI) grant No. W911NF-04-1-0224, and the UC Discovery Program.Q. Qu was with the Electrical and Computer Engineering Department,University of California at San Diego, La Jolla, CA 92093, USA ( B. Milstein is with the Electrical and Computer Engineering Department,University of California at San Diego, La Jolla, CA 92093, USA ( R. Vaman is with the Department of Electrical and Computer Engineer-ing, Prairie View A&M University, Prairie View, Texas 77446, USA ( Object Identi fi er 10.1109/TWC.2010.090210.091119 of MIMO to each node inef  fi cient from a power-ef  fi ciencypoint of view. Also, nodes in an ad hoc/sensor network mightbe of small physical size, which precludes the implementationof multiple antennas at each node.As alternatives, cooperative MIMO techniques [3, 4] havebeen proposed. By the cooperation of multiple nodes, eachof which has a single antenna, a virtual MIMO structure canbe constructed which supports space-time processing, and thusimproved system performance can be expected. In [3, 5], it hasbeen shown that by using this type of cooperation, cooperativeMIMO can achieve better energy and delay performancecompared to a Single Input Single Output (SISO) system, evenconsidering the required overhead in a MIMO system. In [6],space-time coded cooperative diversity protocols are proposedto combat multipath fading. More speci fi cally, the protocolsexploit the spatial diversity available among a collection of nodes that can relay messages for one another such that thedestination node can effectively average the fading. In [7],adaptive spatial multiplexing techniques for distributed MIMOsystems are proposed, together with link adaptation basedon available channel state information. Further performancegain can be achieved by appropriate power allocation amongnodes that join the cooperation [8, 9]. In [8], optimal energydistribution is proposed with an attempt to minimize the linkoutage probability, while in [9], with only mean channel gaininformation, a source node jointly selects the cooperativenodes from its neighbors and optimally allocates power to eachcooperative node in order to minimize outage probability.However, the focus of the previous work (with a noticeableexception in [3]) is just one part of the entire cooperationprocedure. More speci fi cally, in order to achieve cooperativeMIMO, a source node should  fi rst distribute data informationto other cooperative nodes; this is the  fi rst stage or the”local distribution” stage. After each cooperative node receivesinformation from the source node, the second stage is carriedout by using a particular cooperative protocol, where thesource node and the cooperative nodes collaborate together toform a virtual MIMO system and transmit to the destinationnode. The second stage is sometimes referred to as ”longhaul” transmission. Most previous work, such as [4-9], onlyfocused on the second stage, without considering the effectsin the  fi rst stage. In order to have a complete view of cooperative MIMO in wireless networks, both stages shouldbe jointly considered. For example, the number of cooperativenodes should be chosen very carefully by taking into accountthe energy consumption and the delay induced at the local 1536-1276/10$25.00 c ⃝ 2010 IEEE  QU  et al. : COOPERATIVE AND CONSTRAINED MIMO COMMUNICATIONS IN WIRELESS AD HOC/SENSOR NETWORKS 3121 distribution stage, and this might limit the number of nodesused for cooperation. Furthermore, in order to improve thesystem performance against channel impairments, such asdeep fades, joint power control and rate adaptation shouldalso be considered such that the power level and rate assignedto each cooperative node can be adaptively adjusted in orderto achieve robust system performance.Therefore, in this paper, for a cooperative MIMO systemwith uncoded spatial multiplexing, we jointly consider theselection of cooperative nodes and the power/rate allocationamong the selected nodes in order to minimize the bit-error-rate performance of the system. More speci fi cally, we quantifythe energy and delay induced during the local distributionstage; then, for the long haul transmission stage, given a subsetof cooperating nodes, we express the system performance asa function of that subset of nodes, and the power/data rateallocated to each node; after that, we form a multi-variableoptimization problem to maximize the performance at thedestination node, taking into account both stages and theenergy/delay/rate constraints. Finally, we investigate how toselect the cooperative nodes and how to solve the optimizationproblem where the source node either has perfect instanta-neous channel state information (CSI), or the source node onlyknows the channel correlation information. It is worth notingthat the problem of cooperative node selection is similar tothe problem of antenna selection in MIMO [18-20], but inthis paper, it is applied with distinct application scenarios anddifferent system constraints.In practice, the proposed cooperative MIMO solution canbe employed in applications that have a rate constraint, wherea single node cannot satisfy the rate requirement due tocertain limitations. For example, the limitations can be dueto hardware (i.e., the maximum supportable modulation size)and/or due to channel fading conditions. In such scenarios, acooperative MIMO scheme would be superior to traditionalsingle node transmission schemes since no meaningful trans-missions can be achieved with single node because of therate constraint. In this paper, we discuss how to achieve thecooperative MIMO communications in such environments.This paper is organized as follows: in Section II, we presentthe system description; in Section III, we describe the overalloptimization problem when both stages are jointly considered;in Section IV, we quantify the energy consumption and delayinduced during the local distribution stage; in Section V,we investigate the long haul transmission optimization andpresent the cooperative node selection algorithms employed tochoose the subset of cooperative nodes under different systemconditions; in Section VI, we brie fl y describe the procedurewhich is used to realize the cooperation;  fi nally, simulationresults and discussions are presented in Section VII, followedby a conclusion in Section VIII.II. S YSTEM  D ESCRIPTION  A. System and Channel Models We assume that the source node can form a virtual MIMOsystem by cooperating with its neighbors, where all suchnodes, including the source node, have a single antenna. How-ever, the destination node is assumed to be large enough so that Fig. 1. Illustration of the system model. multiple receiver antennas can be implemented. For example,this scenario might correspond to one where multiple soldierswith small carry-on communication units want to transmit to adestination node mounted on a vehicle. Here, we assume thatthe source node has    -1 neighbors, and we want to select  󽠵  out of the     nodes to form a virtual MIMO system, includingthe source node. The destination node is assumed to have  􍠵 receive antennas, where  􍠵  ≥    . The distance between thesource node and the destination node is  󝠵 1 , and the neighborsof the source node are randomly distributed within a radius of  󝠵 0  of the source node. Here, we assume  󝠵 1  ≫  󝠵 0 , so thatthe distance between each cooperativenode and the destinationnode can be approximated as  󝠵 1  [3].The wireless channels between the source node and itsneighbors are assumed to experience  .. . frequency- fl atRayleigh fading with parameter   20  plus path loss with pathloss exponent equal to 4. On the other hand, the channel be-tween the cooperative cluster with  󽠵   nodes (source node pluscooperative neighbors) and the destination node is assumed toexperience a combination of frequency- fl at Rayleigh fadingwith parameter   21 , shadowing, and path loss with loss expo-nent equal to 4. The wireless channel is assumed to be slowly-varying and is taken to be constant within the duration of its coherence time. In wireless transmission, high correlationcan be induced between propagation paths by shadowing if they are blocked by the same obstacle, such as a tree or abuilding [10]. In this paper, for simplicity, we only considerthe correlation effect caused by shadowing. Typically, channelcorrelation caused by shadowing exhibits distance dependence,and thus we model the channel correlation between any twogiven cooperative nodes using an exponential model as in [10]:   =     󽠵 ,  (1)where    is the correlation between the two nodes separatedby distance   , and     is the correlation between two nodesseparated by distance  󝠵 .     and  󝠵  can be measured by  fi eldtests and then can be used to calculate the correlation betweenany two nodes [10]. The system model is illustrated in Fig. 1,where a source node selects 2 out of its 3 neighbors to formthe virtual MIMO system with the destination.We assume that the system is time-slotted, where the timesynchronization among the nodes can be achieved throughsome kind of beaconing (as in IEEE 802.11). At the re-ceiver, the multiple cooperative nodes would typically inter-  3122 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 10, OCTOBER 2010 fere with one another, and in order to remove the multi-stream interference, successive interference cancellation (SIC)is used. Assume we have  󽠵   cooperative nodes, and let x = [  1 , 2 ,...,   ]  denote the transmitted vector, and  y =[  1 , 2 ,..., 󽠵 ]  denote the received vector at the destinationnode with  􍠵  receive antennas. The received signal vector  y ,after matched  fi ltering, can be shown to be given by y  =  Hx + n ,  (2)where  H  represents the channel matrix between the coopera-tive cluster and the destination node, and has dimension 􍠵 × 󽠵  ,and  n  = [  1 , 2 ,..., 󽠵 ] 􍠵  represents  ...  Gaussian noise withzero mean and variance   2 󝠵 . For simplicity, if we assume thatthe correlation only resides at the transmitter side, then thechannel matrix  H  can be expressed as [11] H  =  H  R 1 󰀯 2 􍠵   ,  (3)where  H   is an  􍠵  ×  󽠵   matrix whose elements are  ... complex Gaussian random variables with zero mean and unitvariance, and  R 􍠵   is an  󽠵   × 󽠵   correlation matrix among thecooperative nodes, i.e., among the transmit antennas. From(1),  R 􍠵   can be expressed as follows: R 􍠵   = ⎡⎢⎢⎢⎢⎣ 1     12 󽠵 ...    1 􍠵 󽠵    21 󽠵 1  ...    2 􍠵 󽠵 ............   􍠵  1 󽠵   􍠵  2 󽠵 ...  1 ⎤⎥⎥⎥⎥⎦ ,  (4)where     is the distance between node    and node   , and    =    .  B. Local Distribution and Long-Haul Transmission We assume that, in total, the source node has a bit streamof    0  bits to be sent to the destination. By using the proposednode selection algorithms described in Sec V,  󽠵   nodes areselected to perform cooperation. Then, during the local distri-bution stage, the source node forms  󽠵   different substreams,and distributes the  󽠵   substreams to the  󽠵   selected cooper-ative nodes such that each cooperative node has one distinctsubstream. During this step, under the assumption that thesystem is time-slotted with slot duration     , and that TDMAis employed to distribute the source information,delay is intro-duced. We let    (1)   denote the total delay introduced duringthe local distribution. Also, the local distribution requires aminimum energy in order to guarantee the transmissions fromthe source node to its neighbors are reliably received. Welet    (1)   denote the total energy consumed in this stage, andassume it contains both the transmission energy and the circuitenergy consumption, as detailed in Section IV. For simplicity,we assume that the source node knows the location of eachneighbor and the corresponding channel gain between them.In the second stage, i.e., the long haul transmission, all the 󽠵   selected cooperative nodes collaborate together and forma virtual MIMO system with the destination node. The totaltransmission power for all the cooperative nodes is constrainedto be less than or equal to    􍠵  , as in [24, 25]. Further,we let    (2)   be the total energy used in this stage by allthe cooperative nodes and the destination node, where    (2)  contains both the transmission energy consumption and circuitenergy consumption. Lastly, the total delay associated withthis stage is given by    (2)   . All the parameters associated withthese two stages will be discussed in more detail in a latersection. C. Spatial Multiplexing and ZF-SIC with QR Decomposition We assume that the receiver has perfect CSI, and in order toexploit the capacity of a MIMO system, we consider the useof spatial multiplexing, where the source node  fi rst divides theincoming bit stream into  󽠵   substreams, and then the sourcenode distributes each of these substreams to one of the  󽠵  cooperative node. Finally, each cooperative node sends anindependent bit stream to the destination node simultaneouslywith other cooperative nodes via the virtual MIMO structurebetween the cooperating nodes and the destination node.At the destination node, in order to detect the originalbit-stream in MIMO-like transmissions, many receiver designstrategies can be considered, such as linear receivers (zero-forcing or MMSE), V-BLAST (Ordered Successive Interfer-ence Cancellation) and Successive Interference Cancellation(SIC) [11]. In this paper, we employ successive interferencecancellation with  fi xed detection order in conjunction with ZFat each detection stage. For simplicity, we assume all previousdecisions in the ZF-SIC are correct as in [20]. Then, based ona matrix QR decomposition [12], the channel matrix  H  can bedecomposed as  H = QR , where  Q  is an  􍠵 × 󽠵   unitary matrixwith orthonormal columns, i.e.,  Q   Q  =  I   ,( (  )   denotes theHermitian transpose), and  R  is an  󽠵   × 󽠵   upper triangularmatrix. The QR decomposition is widely used in MIMOcommunications due to its simplicity and high computationalef  fi ciency [16, 17]. Multiplying the received signal vector, Eq(2), with  Q   , we obtain the following modi fi ed received signalvector: 󰋆y  =  Q   y  =  Rx + Q   n  =  Rx + u = ⎡⎢⎢⎢⎣ 􍠵 1 󰀬 1  􍠵 1 󰀬 2  ... 􍠵 1 󰀬  0  􍠵 2 󰀬 2  ... 􍠵 2 󰀬  ............ 0 0  ... 􍠵 󰀬  ⎤⎥⎥⎥⎦ × ⎡⎢⎢⎢⎣  1  2 ...    ⎤⎥⎥⎥⎦ + ⎡⎢⎢⎢⎣  1  2 ...    ⎤⎥⎥⎥⎦ , (5)where  u  has the same statistics as  n , since  Q  is a unitarymatrix. Since  R  is an upper triangular matrix, it is clear thatthe   -th element of   󰋆   is only a function of the   -th and higherstream symbols, and can be expressed as follows: 󰋆    =  􍠵 󰀬    +   ∑  =  +1 􍠵 󰀬    +   .  (6)On the assumption that the detection order is from symbolswith higher indexes to lower indexes, i.e.,      to   1 , with SIC,the estimated symbol     can be shown to be given by 󰋆    =  󝠵 (󰋆   − 󲈑   =  +1 􍠵 󰀬 󰋆   􍠵 󰀬 )=  󝠵 ( 􍠵 󰀬    +    + 󲈑   =  +1 􍠵 󰀬    − 󲈑   =  +1 􍠵 󰀬 󰋆   􍠵 󰀬 )  (7)  QU  et al. : COOPERATIVE AND CONSTRAINED MIMO COMMUNICATIONS IN WIRELESS AD HOC/SENSOR NETWORKS 3123 where  󰋆    is the estimated symbol of     , and  󝠵 (  )  is thedecision operation. As in [11], ZF-SIC with a  fi xed detectionorder naturally converts an  􍠵 × 󽠵   MIMO channel into a setof   󽠵   parallel subchannels. Under the assumption that all theprevious decisions are correct, the last two summations in (7)cancel each other, so the quantity  ∣ 􍠵 󰀬 ∣ 2 can be viewed asthe corresponding channel gain for the   -th subctream fromthe cooperative node   . Finally, the QR decomposition can beperformed with the modi fi ed Gram-Schmidt method [12].  D. Performance Metric As we discussed previously, we desire to jointly select theoptimal subset of cooperative nodes and the per-node powerlevel as well as per-node rate (constellation size) in orderto minimize the  􍠵  at the receiver. For simplicity, weuse the minimum Euclidean distance     as a performancemetric on the   -th subchannel. Suppose an    -ary QAMmodulation is employed, and we have  󽠵   cooperative nodesand  󽠵   corresponding subchannels, where the   -th subchannelhas power level     , constellation size     and correspondingchannel gain  ∣ 􍠵 󰀬 ∣ 2 . Then, the received minimum squaredEuclidean distance of the output constellation of the   -thsubchannel is given by [13] as  2   = 6    ∣ 􍠵 󰀬 ∣ 2   − 1  (8)In other works, such as [20], it was shown that in aMIMO spatial multiplexing system, the system performance islimited by the weakest link. In order to maximize the systemperformance, we want the output minimum Euclidean distancefor each subchannel to be the same, and then maximizethat minimum Euclidean distance, subject to given systemconstraints. By letting     =   0 ,    = 1 ,...,󽠵  , the objectivebecomes maximizing   20 .III. O PTIMIZATION  P ROBLEM  F ORMULATION In order to consider the local distribution and long haultransmission together, we need to include the energy con-sumptions and the delays of the two stages in the optimizationproblem. That is, given     possible candidates, the optimiza-tion should look for the optimal subset of cooperative nodes,labeled as  󽠵 ∗ , with  󽠵   nodes, as well as the correspondingpower/bit allocations for each of them,      and    ,    = 1 ,,󽠵  .We denote by      and      the total end-to-end energy and thetotal end-to-end delay, respectively, with maximum allowablevalues      and     , respectively. Then, the overall optimizationproblem is given by:max ( 󰀬󰀬  󝠵 󰀬 󝠵 )  20 s.t.  (1)   ∑  =1     =    􍠵  ; (2)     =    (2)   +   (1)   ≤   0 ;(3)     =    (2)   +   (1)   ≤   0 ; (4)0  < 󽠵   ≤   ;  (9)In order to  fi nd the optimal  󽠵 ∗ ,  󽠵  ,      and    ,    = 1 ,...,󽠵  ,an exhaustive search is necessary, but this type of problemusually has a large search space when     is large.In order to solve this complex problem, we de-couple thesolution into multiple steps: we  fi rst quantify the energy anddelay induced during the local distribution stage; then, for thelong-haul transmission, for a given subset of cooperative nodesat the source, we present the resource allocation that achievesthe optimal performance at the destination; after that, given thesource node and its neighbors, we proposedheuristic algorithmto select a subset of cooperative node combinations which maypossibly maximize the performance at the destination;  fi nally,we compute the resulting   20  and the associated energy/delayconsumptions for each of the combinations; and pick upthe best node combination that provides the largest   20  andat the same time, satis fi es the total end-to-end delay/energyconstraints. In what follows, we present the details of theabove solution.IV. L OCAL  D ISTRIBUTION  A NALYSIS During the local distribution stage, the source node sendsthe data information to the selected nodes. The energy forthe local distribution to each cooperative node consists of thetransmission energy which ensures reliable communicationsfrom the source node to that particular cooperative node, andthe circuit energy consumption, which is the sum of the energyconsumptions of all the circuit blocks [3, 14].Since the transmission from the source node to a givencooperative node is in the form of packets, we assume thatthe source node has     bits within a packet to be transmittedto cooperative node   , and in the local distribution stage, a fi xed    0 -ary QAM is used together with coherent modula-tion/demodulation.Since a given   0  =       rectangular QAMsignal can be treated as two independent pulse amplitudemodulation (PAM) signals on phase-quadrature carriers, i.e.,   -ary PAM and   -ary PAM, the two PAM signals can ideallybe perfectly separated at the demodulator, and the probabilityof error for the srcinal QAM signal can be shown to be 􍠵  = 1 − (1 − 􍠵   )(1 − 􍠵  ) ,  (10)where  􍠵    and  􍠵   are the probabilities of symbol errorfor the two PAM signals. Hence, at relatively high SNR, thesymbol error rate  􍠵 , can be tightly approximated as [13] 􍠵 ≈ 4  (√   3    0 − 1 ) ,  (11)where   (  )  is the Gaussian tail function, and     is the corre-sponding signal-to-noise-ratio for the transmission to node   ,given by    =      (1)  󽠵  0 ,  (12)in (12)     is the channel gain (path loss plus fading),    (1)  is the employed transmission power per symbol, and  󽠵  0  isthe noise power. From (11) and (12), for a packet of      bitswhich has    0  =    󰀯 0  symbols (  0  =   2 (   0 ) ), when asymbol error rate threshold  􍠵   is required for the localtransmission, the minimal transmission power    (1)   for thelocal transmission to node    is given by   (1)   = (   0 − 1)  󽠵  0 3   × 􀁛  − 1 󰀨 􍠵  4 󰀩􀁝 2 .  (13)On the other hand, the circuit power for each symbol can beassumed to be a constant     for all the nodes [3]. In this paper,
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