Asynchronous Cooperative MIMO CommunicationHsin-Yi Shen

Department of Electrical, Computer,and System Engineering

Rensselaer Polytechnic InstituteTroy, NY 12180

Abstract-We consider a cluster-based cooperative transmis-sion scheme where the source node and destination node formclusters for transmission. Instead of using perfect synchronizationtechnique, we assume the cooperative transmission is asynchro-nous. Each member in transmitting cluster relays signal to thereceiving cluster after obtaining information from source node. Ageneral decision feedback equalizer (DFE) is used in the receivingcluster members to equalize the received MISO signal and detectas soft symbols. The receiving cluster members send the soft-decision outputs to the destination node. Thus, the decisionnode combines the soft-decision outputs and makes hard-decisiondetection for the transmitted information.

The performance of proposed system is shown and comparedwith conventional MIMO system. Major factors for systemperformance is discussed. The over-sampling rate plays animportant role in system performance. We also present a simplecapacity analysis for proposed cooperative transmission system.The capacity ratio between cooperative MIMO system and directtransmission (SISO) system is also presented and compared tothe capacity ratio of conventional MIMO system and directtransmission (SISO) system. We also extend the analysis toheterogeneous network and show the capacity ratio.

I. INTRODUCTIONIn wireless environments the fading effects and channel

variation often degrade signal transmission and increasesbit error rate. Diversity techniques have been widely usedfor suppressing channel variation in wireless channels. Thediversity can be achieved in network layer, link layer, orphysical layer. In link layer and network layer, opportunisticrouting and other designs, such as network coding [1] andExOR [2] are proposed to achieve diversity. In physical layer,MIMO (multi-input multi-output) systems are proposed touse multiple transmitting and receiving antennas for signaltransmission. If fading effect degrades the performance in oneof the wireless links, MIMO system can use receiving signalsfrom other links to detect the transmitted signal. Thus the biterror rate decreases due to the diversity gain and the increase indegree of freedom for signal detection. The capacity ofMIMOsystem is discussed in [3]. However, MIMO systems requiremultiple antennas equipped in each device, which may not befeasible in some wireless communication device because ofthe cost and size limitations. To achieve diversity in physicallayer without multiple antennas, cooperative network has beenproposed to achieve virtual MIMO systems with single antennadevices. [4]-[14]

In cooperative networks, the transmitting nodes use idlenodes as relays to reduce the adverse effect of multi-path

Shivkumar KalyanaramanDepartment of Electrical, Computer,

and System EngineeringRensselaer Polytechnic Institute

Troy, NY 12180

fading in wireless channels. Different cooperative schemesand performance evaluation are discussed. An overview ofcooperative transmission systems is given in [10] and the per-formance of several cooperation methods such as amplify-and-forward cooperation, decode-and-froward cooperation, andcoded cooperation are evaluated. The conclusion is that therequired mean uplink signal-to-noise ratio (SNR) with cooper-ative methods is significantly less than that of non-cooperativetransmission. There have been efforts that go beyond thebasic methods and models. For example, Stefanov and Erkip[15] consider cooperation of two users with different channelqualities and under both symmetric and asymmetric channels.Sendonaris, Erkip and Aazhang [5], [8] discuss the systemmodel of a cooperation diversity system and give a theoreticview of cooperative communication systems. They also con-sider the practical implementation and performance issues forcode-division multiple-access (CDMA) systems.Laneman et al. [7] present several cooperative diversity

protocols, which includes fixed relaying, selection relaying,and incremental relaying schemes, and elucidate the outagebehaviors and the robustness to fading characteristics. A.Scaglione and Y. Hong [6] elaborate broadcasting in wirelessnetwork and provide the idea of opportunistic large array(OLA). The idea of using space-time coding in cooperativenetworks is also explored in [4]: all relay nodes transmitspace-time coded symbols to the destination node at thesame time, i.e. synchronously. Kojima et al. [13] also takesynchronous space-time coding into account, and present adistributed ARQ protocol for OFDM-based Ad-hoc networks.Cooperative space-time block coding (STBC) is used wheneach node relays to packet to the destination.

However, most of these cooperative communication propos-als require symbol-level synchronization between cooperativenodes, but it is hard to achieve even in an infrastructure meshinvolving managed base-stations. The lack of synchronizationmay result in inter-symbol interference and dispersive chan-nels.

To address asynchronous diversity, Li [17], [18] thinks ofcooperative transmission with delay and contributes joint esti-mation schemes for asynchronous receiving signals.However,there are several limitations among these approaches. In [18]they allow up to two asynchronous senders using the Alamoutispace-time code and assume that the single receiver nodehas multiple antennas. The multiple receiving antennas are

used to obtain copies of signals to facilitate joint decoding.However, only two transmitting antennas are allowed (dueto the limitations of the Alamouti scheme) and there is noreceive cluster (i.e. it is a multiple sender, single multi-antennareceiver setup).

In [17] the authors do not require multiple receive antennas,but instead choose an arbitrary number of relay nodes. Ateach time, only two nodes (one sender and one receiver)can communicate, assisted by the relays. The receiver waitsuntil the transmission ends and all signal copies are received(for a period depending upon the number of relays) anduses joint decoding/equalization for signal estimation. Thissetup (developed in the sensor network context) will not befavorable for a number of concurrent network transmissionsin infrastructure mesh networks, and will incur large delaypenalties.

Recently, Wei and Goeckel [19] regard the asynchronoustransmission as an equalization problem. The system modelis a multi-relay channel and they propose a novel minimummean-square error (MMSE) receiver to combine the multipleinputs in this channel. The joint decision feedback equalizer(DFE) includes a feed-forward filter (FFF) and fractional-spaced feedback filter (FBF). The coefficients are chosen toachieve MMSE decision at the receiver. But the multi-relaychannel model assumes that the communication system is aMISO system. For distributed MIMO systems, asynchronousMIMO cooperative communication needs to be further con-sidered.

In this paper we consider a general scenario with multiplesenders, multiple receivers and a single antenna per-receiver,allowing for the possibility of higher cooperative gain. There isno theoretical limit on the number of transmitting or receivingnodes. We present a new scheme for asynchronous cooperativewireless networks. The system model is shown in Figure1 and 2. Each node relays information to receiving clusterafter receiving signal from source node. The received MISOsignal is with delay discrepancy. For cluster-based cooperativenetwork, the propagation delay between each nodes fromtransmitting cluster and receiver cluster would be differentdue to discrepancy in geographical distance. However, thediscrepancy in propagation delay is upper bounded becausethe cluster recruiting algorithm recruits nodes within certaingeographical range [20]. The assumption of bounded delaydiscrepancy is reasonable.

To detect the sending information from the MISO signalwith delay discrepancy, decision feedback equalizer (DFE) isused in receiver node. The equalized signal is then quantizedand represented by soft symbol. Each node in receivingcluster sends soft-decision results to the destination node. Thedestination node then combines the soft-decision results anddetect the transmitted symbols.

This paper is organized as below: the new system is pro-posed in section II, followed by the simulation results, sectionIII. The performance of proposed scheme and comparison withdirect transmission, 2-by-2 MIMO, and 3-by-3 MIMO systemare also shown. The theoretical model of capacity ratio and

(a) Source node transmits tocluster member and destination

Source node

TransmittingAcluster

Destination node

X Recei'ving1 cluster

(b) Inter-cluster transmission betweentransmitting cluster and receivin cluster

Source node

Transmitting Receiving Destination nodeTransmittih cluster

cluster

Fig. 1. Proposed cooperative scheme: (a) neighbor nodes recruiting to formclusters. (b)Inter-cluster transmission.

(c) Intra-cluster transmission for soft symbolsSource node

Transmittingcluster

Destination node

2 Receiving

cluster

(d) soft symbol combing in destination nodeSource node

Transmittingcluster

AReceivingcluster

Destination node

Fig. 2. Proposed cooperative scheme: (c) Relaying copies to destinationnode. (d) soft symbol combining

the extended model for heterogeneous network are discussedin section IV. Finally, conclusions are presented in Section V.

II. SYSTEM MODEL

Our cooperative diversity design is illustrated in Figure 1and 2. When the source node wants to transmit information tothe destination node, both source node and destination noderecruit neighbor nodes and form the transmitting and receivingcluster respectively. The source node and destination node areautomatically the master nodes in their respective clusters. Thesource node then transmits information to its cluster membersand destination. Then the nodes in transmitting cluster relaytheir signals asynchronously to receiving cluster, as shown inFigure 1. Note that there is a limit to the degree of asynchronytolerated and the channels are assumed to be quasi-static andflat fading. When the receiving cluster nodes obtain the signals,they use the decision feedback equalizer (DFE) to equalize

P(y dklOP(y dkY1t) - (i)

Sampling rate=n*data rate

yA( I- h(t)

Sampling rate=n*Wdata rate

1)-1)

log P(yi, Y2,... ,yMdk = 1)P(yi, Y2, .., YM ldk = -1)

Yi, Y2, , YM is the MISO signal sequence from eachreceiving cluster member respectively. The links betweentransmitting cluster members and receiving cluster membersare assumed independent. Thus the log likelihood is

log P(y1, Y2,... ,yMdk = 1)P(1, Y2..,, YMMdk = -1)

YMU)-I h(t)

Sampling rate=n*Wdata rate

P(yi dklOP(y1 dk

Fig. 3. Signals in each destination cluster member are processed by matchfilter and DFE before soft symbol quantization. The quantized soft symbolsare sent to destination node.

the MISO signal and perform soft-decision decoding ratherthan the hard-decision decoding. Then, each member will sendtheir soft decisions to the destination node. The destinationnode then combines these soft decisions (along with its soft-symbol) using a MLE combiner to achieve the cooperativeMIMO diversity, as shown in Figure 2.

The receiver structure is shown in Figure 3. For each node inthe receiving cluster, it receives MISO signal from transmittingcluster. For node m in receiving cluster, the received signalYrm (t) is first filtered by match filter h(t). The output of matchfilter is then sampled to discrete-time signal. The samplingrate is set as n times of the original data rate so the equalizercan appropriately correct the delay discrepancy. The discretesignal is processed by decision feedback equalizer (DFE) andthen down-sampled by n. After down-sampling, the signal isquantized to soft symbols. The soft-symbol output is sent tothe master node in receiving cluster, which is the destinationnode. The destination node combines soft-symbol result withits own copy and detects the transmitted information.

The members of receiving cluster receive MISO signal fromnodes in transmitting cluster. The channel is assumed flatfading with additive white Gaussian noise and the transmittedsymbols are assumed equiprobable BPSK symbols. The des-tination node receives soft-symbol sequences Yi, Y2, , YMfrom its cluster members 1, 2,... , M. To detect the BPSKsymbol, the maximum aposterior (MAP) detection rule is

TnaxP(dkc IY) = maP(y dk)P(dk)TheBSKsmaoP( detmas 1 P(y)

The BPSK symbol is detect as 1 if

P(yldk = 1)P(dk = 1) P(yldk

P(Y)

-1)P(dk

P(Y)Assume the BPSK symbol is equiprobable and express

above equation as log likelihood. The equation becomes

log P(yi 'dkP(yi dk

= 1)P(y2cdk-1)P(y2 dk =

1) ... P(YMA =

-1) ... P(YMI dk

1) + + (logP(yMdk-1) P(YMAd

1)= -1)

1)-1)

which is the sum of the likelihood ratio for each MISOsignal sequence. But the log likelihood of each MISO sig-nal sequence,L1, L2,... , LM, are quantized to soft-symbolL1, L2,... , LM. Thus the estimated likelihood in destinationnode is

L(dk) = Li + L2 + + LM (1)

Llq ql+L2q*q2+** +LMq qM (2)

And ql, q2, , qm is the representation of correspondingquantization level.

For each receiving cluster member, it receives MISO signaland use decision feedback equalizer (DFE) to eliminate theeffect due to delay discrepancy. The equalized signal is usedto compute the likelihood ratio L1, L2,... , LM. Assume thereceived MISO signal is Xk and noise is AWGN noise. Thelog likelihood is

L,(Xk) = P(x9[P(( dk 1)P(kdk -1)

xp( (xkl-/tk)

=log ec 5espf_(Xk +ttk )2)

2wY tcxp( (xk±lk)

2xWk (3)-2

where o2 is Gaussian noise energy and ,u is the transmittingsignal energy multiplied by path-loss, which is the receivingsignal energy without fading. The transmission energy isknown and the path-loss can be estimated since the distancebetween transmitting nodes and receiving nodes are known.Thus ,u can be precisely estimated. The computation result inequation 3 is then quantized to soft symbols, L,. The soft sym-bols are transmitted to the destination node. The destinationnode combines soft symbols from all cluster members withits own copy by equation 2. If the combined log likelihoodL(dk) is larger than 0, the symbol is detected as 1.

AsySnohronous cooperative BER vvith avg cluster size-3.1 and 348S7 oversample 010

1 l:

10

w 10

m

10 11 12 13 14 15 16 17 18

signal to nbise ratio (3NR) in cB

10

IL 1 6. 3w

m

19 20

Fig. 4. BER performance comparison of proposed system with typical MIMOsystems and direct transmission (Note: over-sampling rate=20, average clustersize is 3.1 for transmitting cluster and 3.49 for receiving cluster respectively.)

III. SIMULATION RESULTS

A network with 64 random distributed users is employed.The users are distributed over the range in a 1000 meterby 1000 meter square. The data rate is 5.5 Mbits/sec. Thedata is BPSK modulated. The BPSK symbols are then filteredby square root raised cosine (SRRC) transmitting filter andtransmitted to the receiving cluster. The virtual wireless MIMOchannels are assumed quasi-static flat fading and independentof each other.

The cooperative cluster recruits nearby nodes, which can

response the cluster recruiting message within one symboltime. Thus the maximum distance between cluster head andcluster members is 27.27 meter, which is corresponding thetransmission distance in 1/2 symbol time.

In each receiving node, a corresponding SRRC match filteris used, which is corresponding to the h(t) block in Figure 3.A decision feedback equalizer (DFE) with least mean square

(LMS) adaptive algorithm is used. The forward filter has 3complex weight taps and the feedback filter has 2 complexweight taps.

The performance of proposed system and comparison withMIMO systems is illustrated in Figure 7. The signal trans-mission energy in each user is the same. The performanceof direct transmission from source node to destination nodeis worst due to large path loss and fading effect. The 2-by-2 MIMO system transmits signals by 1/2 signal energy

in each transmitting antenna and obtains better performancebecause the increase in diversity gain and degree of freedomsuppress performance degradation from fading. The degreeof freedom and diversity gain increase when the number oftransmitting and receiving antennas increases, which explainsthe performance improvement for 3-by-3 MIMO system.

The proposed system has average cluster size as 3.0429for transmitting cluster and 3.2671 for receiving cluster, re-

spectively. The performance of proposed system is close to

.Asymchronous nooperative BER with avg luster size=3 1 and 3 4857

10 11 12 13 14 15 16 17signal to nbise ratio (3NR) in cB

18 19 20

Fig. 5. BER performance with different oversampling rate

the performance of 3-by-3 MIMO system since the sizes ofcooperative clusters are near 3. But the proposed system hasbetter performance in low SNR scenario compared to 3-by-3 MIMO. In high SNR the performance of proposed systemand 3-by-3 MIMO system does not have large difference. Thisis because the decision feedback equalizer (DFE) corrects thedelay discrepancy in MISO signals received by receiving clus-ter member and improves performance close to correspondingconventional MIMO systems.

The performance of equalizer also depends on the over-

sampling factor. When the over-sampling factor is larger,the decision feedback equalizer (DFE) can catch the delaydiscrepancy well and recover the asynchronous MISO signalas synchronous copies. If the over-sampling factor is small,the DFE can not catch delay discrepancy because the delaydiscrepancy is much smaller than the sampling time intervalfor each tap in DFE equalizer. The performance will benear to the performance without DFE. However, larger over-

sampling factor results in large amount of sampled data andlonger processing time. The trade-off in bit error rate (BER)performance and processing complexity is illustrated in Figure5.

In Figure 5 we consider the performance with over samplingfactor 8,12, 16, and 20. When the over sampling factor is 8,the decision feedback equalizer (DFE) does not catch the delaydiscrepancy in received MISO signal. The performance is closeto the performance of direct signal detection without decisionfeedback equalizer (DFE). The bit error rate remains high indifferent SNR scenario due to the asynchronous MISO signal.The delay discrepancy dominates the performance and noisepower becomes a minor factor. As the over sampling factorincreases, the decision feedback equalizer (DFE) becomeseffective and delay discrepancy no longer affects bit error rate.Noise power becomes the major factor of bit error rate. AsSNR increases, the performance improves. When SNR is 20dBand the over sampling rate is 20, the bit error rate approaches

-I-cooperativ.MIMOy E* Direct Transmission

4 - MIMO3by-3* K~ MIMO2-by-2

N~~~~~~~

tPo~rsamplF 8.4- bversamplel

16

oversample -20

-I.u .u

4

inU

16-4

inU

to 0, which means perfect signal transmission.

IV. SYSTEM CAPACITY ANALYSIS

From simulation result, the performance of proposed coop-erative MIMO scheme is close to MIMO system with corre-sponding number of antennas. However, cooperative MIMOscheme needs to deal with intra cluster transmission in bothsource cluster and destination cluster. Although cooperativeMIMO scheme provides spatial diversity, the transmissioncapacity decreases due to node cooperation.

In this section we would like to consider the capacity inproposed cooperative MIMO system. We start the analysiswith a simple model, where only one transmitting clusterand one receiving cluster exist. The system assumption is asfollows:

1) Only one transmitting cluster and one receiving cluster.We do not consider interference and opportunity costhere.

2) The size of transmitting cluster is M + 1 and the sizeof receiving cluster is N + 1 (including the source nodeand destination node).

3) The channel bandwidth is W and each node in trans-mitting cluster transmits with power P/(M + 1).

4) The channel is AWGN channel with power spectraldensity N0o2 and is assumed quasi-static fading.

5) Signals degrade due to Pathloss. The pathloss constanta is usually between 2 and 4.

6) The distance between node i and node j is denoted as

dij.7) The gain of channel between node i and node j is

denoted as Aij8) The radius in cluster recruiting algorithm is r.9) The number of quantization levels for soft symbol is 2Q,

which means each soft-symbol is represented by Q bits.

Suppose the system transmits K bits and the cooperativetransmission consists of three parts. The first phase is broad-casting, in which the source node sends information to itscluster member and the destination cluster. The second phaseis inter-cluster transmission. All members of source clusterrelay information to destination cluster. The third phase isintra-cluster transmission in destination cluster. Each memberof destination cluster relay the soft symbols to destinationnode. We use the three-phase cooperative transmission andanalysis channel capacity in each phase.

A. Phase I. Broadcasting

Broadcasting, as shown in Figure 1 (a), indicates that thesource node sends information to its cluster member anddestination cluster. The intra-cluster transmission in sourcecluster can be approximated as SIMO channel model sincethe source node broadcasts information to all of its clustermembers.By using SIMO channel model approximation, the channel

capacity for the first phase is

C1 Wlog(1+ SNR)

Wlog(1 + NoW(M + 1) ds=

> Wlog(1 +M A2

and-tm r e tofiNW(M + 1) pha i

and the time required to finish the first phase is

K£1= <

1,2, ,M

K(4)C1 Wlog(1 + NoW(M±1) Z1r)

B. Phase II: Inter-Cluster Transmission

The second phase is inter-cluster transmission. All membersof transmitting cluster relay information to the destinationcluster. Each channel is assumed to be independent with eachother. For each receiver node j, the channel is MISO channeland the channel capacity is

M+ 1 V.C2j M10±l+ : 13

WlOg(l + W(M1) E dij

> Wlog(1 + NOW(M +1) (dSD + 2r)

The capacity for Phase II is C2 = f+ll C2j. Thus thetime required to transmit K bits in the second phase is

K Kt2 N-(M1)ZMl 2C2 ZN+l Wlog(l + = (dD2rW)

(5)

C. Phase III: Intra-cluster Transmission to Destination

In third phase, each member in receiving cluster makessoft-symbol decision and send the soft symbols to destinationnode. For K bits information, each receiving cluster memberwill make soft-symbol decision and transmit KQ bits to thedestination node. The destination node will wait until receivinginformation from all cluster members and then combine thesoft symbols to make hard decision. We assume each nodeuse power PIN for intra cluster transmission. For each clustermember j, the channel capacity is

C3j = Wlog(1 + PDANN0Wda)

And the transmission time for cluster member j to relayinformation to destination node is

t3jKQ

PA2Wlog(l-HNNjfD_

Thus the time required to finish the third phase will beN

t3 = Z t3jj=l

(6)KQ N, I

w j=l log(l +NN jD )

v, I1

Therefore, to transmit K bits by cooperative MIMO scheme,the total transmission time T is

T tl +t2 +t3

<K

Wlog(l + NoW(M±1) A)

K

1 Wl(1 + NoW(M1))=1 (dSD+2r))

w=1 log(1 + jD';)

The actual capacity for cooperative MIMO scheme willbe K/T since the systems require no larger than time T tocomplete the transmission for K bits. Thus the capacity is

Ccoop

KT

lo(1+

1 NoW(M =1 (dSD+2r)

N

+Q(Z: p\2 ))(8)

j=1 log(lI+ IjD' ) 8+NNoWd"

If we consider the non-cooperative case where the systemtransmits information directly from source node to destinationnode, the capacity of direct transmission with channel gain Awill be

Cdirect = Wlog(1 +A

Wd3D' (9)

Comparing equation 8 and 9, we can estimate the systemcapacity ratio as

Ccoop

CDT

log(1 + pW2d )

log(1 + NoW(M±1)Z1NW)

+ log(1 + NoWdDi)

log(1 NoW(M±l) (ds+±2rN1 flog(1 + ) ) (IO)'+J SD(

N Qlog(1 p'Wd2

By equation 10 we can estimate the improvement in capac-

ity due to node cooperation. The relation of system capacityratio, which is defined in equation 10 and other major systemfactors is shown in Figure 6, Figure 7 and Figure 8. FromFigure 6 we can find the capacity radio is not affectedmuch by SNR. But the sizes of transmission cluster andreceiving cluster play an important rule for capacity ratio. Asthe size of cooperative cluster increases, the capacity ratiodecreases because the increase in diversity gain compensatestransmission delay which is caused by three-phase cooperative

transmission. In figure 6 the capacity ratio for M = 3, N = 4is smaller than it for M = 4,N = 3. This is becauseeach receiving cluster member makes soft symbol decisionafter inter cluster transmission. For each receiving clustermember, the transmission can be modeled as MISO channel.In phase II, the channel capacity is equivalent to sum ofMISOchannels. When the size of transmission cluster M increases,it only provides possibly larger diversity gain for each MISOchannels. On the other hand, the increase of receiving clustersize N increases the number of MISO channels and offerslarger capacity. Thus, with the same number of nodes joiningcooperation M + N, larger receiving cluster size has smallersystem capacity ratio.The capacity ratio provided in equation 10 is also compared

to the conventional MIMO systems in Figure 7. Similar toequation 10, the capacity ratio of the conventional MIMOsystems is defined as CMIMO/CDT, the capacity of theconventional MIMO systems divided by the capacity of directtransmission. In Figure 7 the capacity ratio of the conventionalMIMO systems is fixed. SNR does not affect the capacityratio of the conventional MIMO systems because there is nodelay from intra-cluster transmission. The conventional MIMOsystems transmit and receive signals by multiple antennasand do not need broadcasting (phase I) and the intra-clustertransmission to destination (phase III) in the cooperativeMIMO systems. So the capacity ratio is fixed and proportionto the number of antennas on the devices. But SNR affects thecapacity ratio of the cooperative MIMO systems. When SNRis low, the capacity ratio is larger because node cooperationprovides transmission diversity and thus better performance inbit error rate(BER). As SNR increases, the channel quality isbetter and the performance of one-to-one direct transmissionis acceptable. Diversity gain from node cooperation onlyimproves the performance a little. Consider the sacrifice incapacity due to intra-cluster transmission delay, cooperativeMIMO system is not so attractive in high SNR environment.

The effect of transmission cluster size is also clearly ob-served in Figure 8. In Figure 8 we discuss how the transmis-sion distance and cluster radius affect system capacity ratio.The X-axis in Figure 8 is defined as distance ratio , whichis dsD. The equation 10 considers the path-loss, fading andspatial diversity gain provided by node cooperation. When thedistance ratio is low, the system capacity ratio is dominated bythe intra-cluster transmission. The short distance transmissiondoes not encounter much signal power degradation due topath-loss effect. Thus, the short distance direct transmissionis more preferred than cooperative MIMO scheme. In longdistance transmission, the path-loss is much higher and nodecooperation to obtain spatial diversity is more desirable. FromFigure 8 the capacity ratio is approximately stable when thedistance ratio is larger than 15.

V. SYSTEM CAPACITY FOR HETEROGENEOUS NETWORK

In this section we consider the system Capacity for thenetwork that nodes may have more than one antenna. Thenumber of antenna in node i is denoted as ai and we

10 15Scaled transmit signal to noise ratio (SNR) in cB

Fig. 6. Capacity ratio of different transmitting/receiving cluster size withscaled SNR. (Note: scaled SNR is defined as PTIra, r is cluster radius andPT is transmission power)

iCapao-ity ratio with quantization leveIB

Di-stance ratio rNote (Distarice between SD)f(cluster radius))

Fig. 8. Capacity ratio with distance ratio (Note: scaled SNR is defined as

PTI ra, where r is cluster radius and PT is transmission power. Distance ratiois defined as dSDIr, where dSD is distance between source and destinationnode)

10 15Scaled transmit signal to noise ratio (SNR) in cB

20

Using Singular Value Decomposition (SVD) with the as-

sumption as is larger than EN ai and donating the singularvalues as Ai, the above equation becomes

as PA2C1> ZWlOY(1+gNWair)

i=l

(1 1)

The transmission time for K bits is

tl

<Fig. 7. Capacity ratio compared to conventional MIMO system with scaledSNR (Note: scaled SNR is defined as PTIra, r is cluster radius and PT istransmission power)

KCl

K

E.as1 Wlog(1 + NoWaSr')

(12)

B. Phase II. Inter-Cluster Transmission

assume each node transmits with power P for both inter-cluster and intra-cluster transmission. The transmission poweris equally applied to each antenna in node i, which means thetransmission power for each antenna in node i is P/ai. Theassumption of wireless environment and other symbol notationis the same as previous section.

A. Phase I.Broadcasting

The source node sends information to its cluster memberand destination cluster. Assume the source node has as

antennas and each cluster member i has ai antennas. Thechannel matrix H is a as x yN1 ai matrix. If all channelsare i.i.d Rayleigh fading, the MIMO capacity is

C1 > logdet[las + N W HH*]NoWasrez,H

For each node in receiving cluster, the MISO channel modelbecomes MIMO channel model due to multiple receivingantennas. For node j in receiving cluster, the correspondingMIMO channel matrix Hj is a (ZM+1 ai) x aj matrix. Weassume all nodes in transmitting cluster have the same numberof antennas and each antenna use power P/a to transmitsignal. Apply SVD decomposition to H. and the channelcapacity for node j is

ai PA2Ci = 1:WIog(l+jkfw)ZWl NoWa)

>E WIg(l PA2

k=log1+NoWa(dSD +2r>)a (13)

4

365

-- MJ llbO a3x

IMIAMO 4X4

ffi 4 s s s .,,, ,., ,,., ,,0 IXse-0Ps w<wT+e_

E~~~~~~~~~~~~~~~~~~~~~~~~~~

-- -+ <- - -I

i;;

b

4.s

Thus, the capacity and the transmission time is

N+1

C2 = 1:Cjj=lN+1 a3j PA2

-j1 k 1 NoWa(dsD + 2r)a

t2

<

K

C2K

EN+71 Ea Wlog(1 + NoWak(dsD±2r)

fo=

>d

4(15)

where Aj,k is the singular values for Hj.

C. Phase III: Intra-Cluster Transmission to Destination

Here each member in destination cluster transmits softsymbols to the destination node. For node j, the transmissionis MIMO with channel matrix Hj, which is a aj x aD matrix.The channel capacity is

Ci

min(aj ,aD)

5: Wlog(1 +

k=l

min(aj ,aD)

> Wlog(1 +k=l

PA2

Pj,kNoWa --10

PA2NoWa -ro

C;apality ratio with quantizatibn leveI8

5 10 15Scaled transmit signal to noise ratio (SNR) in cB

20

Fig. 9. Capacity ratio with scaled SNR (Note: each node has 2 antenna)

Thus the system Capacity ratio is

CCoop

CDT

(16)

Thus, the transmission time is

Z=ila log(1 +NoWTc *asd1:)ppA2

-1 log(1 + NoWasrsx)

min(as aD) log(1 + PadEi=l ~~NoWasdTD)

A p/2

Z)=i Z=a log(1 + NoWa(d D±2r

N Q Zmnl(ss, aD) log(1 + Wa

NoW as)(2O)N mZin(as,aD) log(I +

t3j

<

QKCi

QK

W Zrmin(aj,aD) log(l + <nWjr,)

N

t3 = E t3jj=1NQK I

j.=1 k=l(aJ aD) log(1 + NoWajr")

The total transmission time T is

T = tl +t2 +t3K

pA 2

a-s Wlog(1 + NoWasr )

K+ N+ -pA2k

zjv.+il ZLaV 1 Wlog(1 + NoWa(d.sD±2r>)

N QK 1

E W ,mtnl(aj,aD) log(1 + N WsPA2

j= minif(aj,aD) log(1 + j,W k~

In Figure 9 we assume two antennas per node. The systemCapacity ratio is much smaller due to the improvement indiversity gain and degree of freedom. Multiple antennas pro-vide MIMO transmission for all three phases of cooperative

(17) transmission and thus improve the channel capacity.

VI. CONCLUSION

We propose a new method for asynchronous cooperativeMIMO communication. The nodes in transmitting cluster relaythe information after they receive information from source

node. In receiver nodes, a decision feedback equalizer (DFE) is

(18) used to correct the delay discrepancy in asynchronous MISOsignals. The equalized signals are then represented by softsymbols. The destination node combines soft symbols to makesignal detection.The performance of proposed system is shown and the

comparison of proposed system with conventional MIMOsystems is illustrated. The major performance factors, such as

over sampling rate and SNR, are also discussed and shown infigures. The proposed system can precisely correct the asyn-chronous signals and has performance close to conventionalMIMO systems. However, the over sampling rate must belarge enough to achieve such performance. We also analyze

(19) capacity ratio for proposed system and extend the analysis toheterogeneous network. On one hand, the cooperative system

-El*- Mh2AN=4

---M-3N=4-. -M=4N-3G---M=4N=4

,.,,.,; .... m0sI

k~ ~~~~~~~~~~~~~~~~ +s, ~ ~ ¼

l |

q3 Il

has a larger capacity than does direct transmission. On theother hand, the capacity is smaller than that of conventionalMIMO due to node cooperation.

ACKNOWLEDGEMENTS

This work was funded by MIT Lincoln Labs/AFOSR GrantLetter No. 14-S-06-0206, AT&T Labs Research and NSF-ITR0313095.

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