Performance analysis on channel capacity in cooperative MIMO system

Journal of Harbin Instinute of Technology (New Series)，Vol. 19，No.3, 2012Performance analysis on channel capacity in cooperative MIMO systemTnungtan Nguyen, MENG Wei- xiao, WANG Hong-yu, L Zhuo-lin阮中迅,孟维晓，王宏宇,李卓霖(School of Eecronice and Informaion Engineering, Hacbin Insitule of Techuolugs , Habin 150001 , China)rate ( BER) and lower the transmit power in radio mobile networks, especially when the direct channel betweenthe source and the destination is poor. Cooperaive multiple input mulhiple output (Co-MIMO) is a kind of MI-MO technique, where the muliple inputs and outputs are frmed via coperaion.n The capacity of Co-MIMOsystem over wireless channel has been investigated a lot, however few papers pay attention to the loeations of thechannel that may afet the probability distributions of the variable and the efeet of antenna spatial correlation.The results can be achieved by choosing sub-channels that is not related to other sub channels. This paper focu-ses on this problem. The simulation resuts show that once we search the partner we should consider trade offscooperation get optimum system performance. It further investigates that cooperation between diferent terninalscan reduce antenna spatial correlation, thereby increase the capacity and throughput of the system, and evenreach the ideal capacity of MIMO Bsystem. .Key words : cooperative MIMO; channel capacity ; muliple -antenna terminalsCLC number: TN929. 53Document code: AArticle ID: 1005-9113(2012)03-0061-07Multiple input multiple output ( MIMO)wirelessresource allocation strategy. In the aspect of multi -an-communication technology is a combination of antennatenna Co-MIMO channel model, it proceeds with hier-diversity technology and space-time processing technol-archical cooperation to obtain the linear throughputogy and belongs lo smnart antenna technology. In wire-range in the fixed area networkHowever, it paysless channel , multipath transmission can cause fading,attention to the mixed network of cellular and ad-hocthus it is considered as a harmful factor. MIMO systemnetwork, where are cooperative links between. relaysuse multi-antenna in both transmitter and receiver, thusand mobile terminals to create communication betweenthe quality of service ( QoS) to each user can. be im-base station and cooperative node- .。The study focusesproved. A new spatial diversity technology-cooperativeon base station which has multiple antennas'. Whendivcrsityt' makcs the mobile terminal use single anten-the base station transmits signals to a node of the nodena to utilize spatial diversity. The study results showcluster, other nodes this cluster proceed to cooperativethat in the flat fading environment , cooperative diversi-transmission to assist the destination node to receive in-ty can increase the channel capacity, raise QoS and im-formation. The channel correlated degree is proved toprove system performance because partners share eachbe a furiction of angle spread , scattering material char-other's antenna. They form virtual MIMO system. Inacterstics, distance of array antenna, the physical pa-Ref. [2]， the cross-layer routing and resource alloca-rameter of array antenna and Doppler spread. There-tion problems of cooperative MIMO ( Co- MIMO) arefore, they affeet the channel capacity of MIM0 systemstudied. The gain and changing problems of Co-MIMOdirectly.capacity is studied in Ref. [3]. The basic idea of Co-This paper considers the channel model of multi-MIMO technology is greatly influenced in the study ofantenna terminal with Co-MIMO. .Then ingenuity dis-Virtual Antenna Array ( VAA) on the 4G technology.cusses the influence of antenna spatial correlation asDohler et al. proposed transmission strueture of VAAwell as multi-path number to the channel capacity theo-for cellular networks, and the base station is equippedretically. According to the analysis of channel capacitywith multi- antennas. A multi-hop relay VAA structureof different cooperative model, the functions of spatialof the cellular network system was studied in Ref.correlation and the number of multi-path are discussed.[4], proposed by some related agreements, which an-coopert中国煤化工he dir ofalyzcs the capacity of end to end system, and providesTYRCNMHGRecived 201-12-15.Sponsored by the National Natural Science Foundation of China( Grant No. 60872016) and Progam for New Century Excellent Talents in Univesity( Grant No. NCET08-0157).Coresponding author: MENG Wei-xiao, E-mail; wxmeng@ hit. edu. cn..61.Journal of Harbin Instinute of Technology (New Series), Vol. 19, No.3, 2012The rest of this paper is organized as follows.where SNR and SNR, are the normalized power ratiosSome basic theory is. described in Section II. Sectionof X, to the noise ( after fading) at each receiver anten-III discusses the Co- MIMO modcls, the efect of thena of the cooperative node and the destination node,number of relay, the effect of cooperative nodes distri-and SNRs is the normalized power ratio of X2 to thebution and the effect of antenna spatial correlation onnoise at each antenna of the destination node.Co-MIMO syslem. The simulalion resuls ure presented1.2 Capacity of Co-MIMO Channelin Section IV. Finally, the important conclusions areBo Wang et al. 9 provided the Rayleigh fadingdrawn in Section V.ase, and an upper bound on the ergodic capacity ofthe Co-MIMO channel is given by :1 PrelininaryC≤Cper = min(C,C2)(4)JC = E{log[det(IM, +ηH° H + nH* H2)]}1.1 Cooperative MIMO System ModelThe model of Co-MIMO systeml9l is shown in Fig. 1,lCz = E{log[de(I, +np]H; H2+nH:' H)]}whereX, and X2 are the transmitted signals from the(5)source node and the relay node ( cooperative node) rewhere the expectations are taken with respect to chan-spectively; Y and Y are the received signals at the co-nel matrices H, H, and Hj.operative node and the destination node; H，H, andA lower bound on the ergodic capacity of the Co-H, are the MIMO model channel fading coficient ma-MIMO relay channel is given by:trices from the source node to the cooperative node,C≥Cw = max(Cg,min(C,C2)) (6)from source node to the destination node, and from thejC, = E\log[det(IM + ηHH)]}(7)cooperative node to the destination node respectively;lC, = E{log[ det(I, + nη2HH')]}2 and Z are Gaussian white noise of the cooperativewhere the expectations are taken with respect to corre-node and the destination node.sponding channel matrices.2 System ModelReley cudinH,2.1 Coperation NodeXCo-MIMO channel with multi-node is shown inFig. 2. It is assumned that there is no direct path be-tween the source and the destination, when he sourceFig. 1 Cooperative MIMO system modelis far from the destination or the source is indoor butthe destination outdoor. In this situation, the coopera-It is assumed that the source node has M transmit-tive node is needed. It is assumed that the number ofted antennas; the cooperative node has Mz transnittedantenna at source and destination isM, = N, and theantennas and N; received antennas; the destinationnumber of receiving and sending antenna at relay is M2node has N received antenas. H is the MIMO model= N, and the number of rclay is K. Synchrunizationchannel fading coefficient and is defined as :happens at eyery node.(h.x hy,2 “hmH=h. h2.2 “hz.n e CYv*M (1)▼亡RSCRSOwhere h denotes the fading rate from the i-th transmit-ting antenna to the j-th receiving antenna.Therefore, the received sign can be writen as :[Y=分HX+Z2)Fig.2 Multi-node cooperation modelly=√nHX + ηHx+zThe relationship between source and relay can bewhereH, 12 andIIzareN xM, NxM. andN x M2expresorders of channel gain matrix respectively. η, η2 and中国煤化工η的are parameters related to the SNR(10] , which can beTYHCNMHG2..K (8)expressed as fllowsSNR:_ SNR2_ SNR,owhere rjis N; X 1 order receiving signal; E: is receivedη1 =M,n2“M,73=M，，(3)average power of the k-th relay from the source in a●62●Journal o[ Harbin Instiute of Technology (New Series), Vol. 19, No. 3, 2012symbol period; H, = [h.,h.,..,h.sn] is M order(厄channel matrix and independent between each other; sdu,=PNM= [S;,S2,"",sM]' is M; X 1 order sending signal√N| Ewhich meets the complex Gaussian distribution ,二(N, +M) +σ2)E{ss"! = IM; nxisN; X 1 urder space-limne complexGaussian white noise vector, E{nn"} = σ1u，P|jBi.BL. ht.n hu.sEach relay terminal processes its received vectorfo..m=、signal rk to produce theN x 1 vector signal 1k and thenE，transmit to the destinalion. The received signal at the( lB.s.mMVM(N, +M) +σ2)destination can be expressed by:(14)y= ENNGt+z(9)an, and bk.c.m are the noises :where P is the average received power of the k-th relayin a symbol period ( the path fading and shadow fadingN((N. +M,) +o)already considered). G。= [6rs1sr.r2.*"gs.]T isP.ih.21 gi.B'.12order channel matrix;Z= [2,"",au] isM.x1or-br.s.m =der space-time complex Gaussian white noise vector,N((N, +M) +o)M8umI'variance isE{zz"} = σ2 Iy.(15)It is assumned that the path fading and shadow fa-hj stands for the interference:ding are fixed positive independent random variablesduring this time, and the received power in the first喝=二xJ+三ww+。2( E 0..)hop {E,}KI and in the second hop {P%}X-1 are thecalculated the value. The characteristic of random re-(16)flects that the location of source and relay is random.The positive value reflects that the node located in aP。√Mfixed area. So, different locations of the node can af-xJj=JN.国fect the probabilily distribution of the variable.((N、+M) +σ; )If the node are independent between each otherand evenly distributed in a fixed area， { Ek-1 andER{PIK-1 are independent. If the nodes are distributed|Pr(-B.8i. Ih. I1'in different areas (such as a range between the sourceWO.J=NNto destination) , the mean of E and P: will change com-三(N, +M) +o。)pletely.It provided the upper and lower limits of eapacityto the channel modelThe upper limit is:↓M6.8L. hohn.NNC.. ={1ngie(1n, ++2 u”)}(N+M) +o2)(10)(17)The lower limit is:So, based on Eq. (15) we can acquire the upperand lower limits of capacity in multi-antenna Co-MIMOCn= EEI(11)with multi-relay.2.2 Antenna Spatial Correlationwhere, I; isIn this paper, Rayleigh fading is considered, and1 = -log(1 +1 h*|'x( 2 1明12+hence the comporuents of the channel matrix H as de-fined in Eq. (1) can be expressed as;o2(1+. 20..+2( .))")h(r) = 2A.8(τ-r,)，(18)(12)where中国煤化Ipgatio;A, iswhere | hj 12 stands for the signal:the amYHC N M H Gthe impulse func-tion, and T% Is uhe uclay ot n-tn paun. The random MI-h.“=.2du+ 2( Ef.)(13)MO channel matrix Hc is provided by:,RtEXmvee(H;) = Rivec(H),(19)●63●Journal of Harbin Insitule of Technology (New Series), Vol. 19, No. 3, 2012where R'2 is the mean square root of matrix R. R isp(φ,o,雨) =Noexp[-Jzlφ-中l], (25)defned by:R=R,8R,(20)where, No is defined by:R is autocorrelation matrix , showed byR, *R, R, andNi=J exp[-2lφ-中]φ(26)R, are given by:「1Pl2.Prm,]The spatial correlationpu is based on PAS, DOAR,(R,) =|P?!(21)and AS. To all pairs of antennas, the Pisj must be cal-culated to get the correlation matrix in Co-MIMO sys-tem._PM1 PM2The spatial correlation between transmitting anten-wherep; is the transmitting correlation cefficient be-na and receiving antenna depends on anlenna topulugy，tween the i-th antenna to the j-th antenna( or receivingarray elements space, wave exit angle, and direction ofcorrelation coeffcient) : .arfrival. Moreover, it depends on AS and PAS, andPus = Pis，(22) PAS is the most important factor among them.where (●)* means complex conjugate.Then Hc is mentioned by:3 Simulation ResultsTo describe MIMO channel, we can use DirectionH。=RHR?(23)3.1 Simulation EnvironmentThe simulation conditions are summarized in Tab.of Arrival ( D0A)，Angle Spread (AS), and PowerAzimuth Spectrum ( PAS) of the antenna to reflect the1. Coordination models given later is based on simulationenvironment common MIMOs system (2x2, 4 x4).space specifc and time specifie of MIMO.It is assumed that a spaced linear array consists ofTab. 1 Simulation conditionsN omnidirectional receiving antenna, and D is space,ParameterValueas shown in Fig. 3.Antenna number of source node2-4<吕Antenna number of cooperation nodes;DAntena number of destination nodeT2BThe number of coperation node .1-30"iAntena space/ wavelength0.5-1.The number of Rayleigh fading multipathSNR/dB0-30Direction of arivnl( DOA)/(*)0Fig.3 MIMO fading channel propagation modelAngular spread (AS)/(*)The signal is transnmitted by M transmitting anten-3.2 Simulation Results and Analysisnas, and then reflected by the receiving antennas scat-3.2 l Effect of the number of relayWhen the receiving and sending antennas are alltered around. Antenna array model in the receivingidentical , the capacity of single-relay MIMO and Multi-end should be shown to analye the model in Fig. 2relay MIMO is shown in Fig. 4.more clearly.Letφ be average arival angle, σ be AS, p(φ)20]be probability density function of AS. The correlation87. Number of relayfunction between signals is given by:_16[p = cos[ 2πD/Asin(中) ]p(中)d中(24)i 12710]sin[ 2πD/ Asin( φ) ]p(φ)dφ8]Source Relay Destinaliunwhere p。and pz are the real component and the imagi-nary components of the correlation function between the中国煤化工2two antennas.MYHCNMHG2530So the spatial correlation relales with p(0).SNRIdBIn this paper, ρ(0) is subject Laplace distribu. Fig4 Capacity of sngle-eay MIMO and mit-relay MI.MOtion. 'The probability density function is:Journal of Harbin Institue of Technology (New Series), Vol. 19, No.3, 2012In the simulation, the sum of all nodes transmit-where P(t) is transmitting power; P,(t) is receivingting power is fixed, so we can compare the capacity inpower; d is the distance between transmitting node andthe same situation.receiving node; a is path fading factor, in this paper,We can observe from Fig. 4 that the capacity ofa =4; g2(t) is multi-path fading coefficient. It is as-Multi-relay MIMO is higher than that of the single-re-sumed thatd = 10, the SNR of cooperative nodes arelay. However, when the number of relay is increasing,tethe capacity tends to a certain value.Fig. 6 shows the effect of distribution of coopera-From Fig. 5, when the SNR is 10 dB, the numbertive nodes to capacity of Co-MIMO, when the numberof relay can afct the capacity of Co-MIMO. As theof receiving and transmitting antenna is identical andnumber of relay has been increasing, the capacity of the number of xelay is ten. And also it can be seen thatCo-MIMO systerm with Muli-antenna terminals will in-the smaller the distance between the source and the re-crease accordingly. When the number of relay increa-lay is, the greater the capacity will be.ses from 0 to 5, the capacity inereases significantly;however, as the number of relay increases further, the30 TSource Relay Destinationcapacity has a small rate of increment until get a con-stant.25 1antennaNurber of relay: 10Distribution of relay盒20(5,25) Uniform15 to source是6.2530Number of2SNR/dBEJu=10dBFig. 6 Relationship between relay distribution and capacity1020Therefore, when the terminal search partner is dy-Number of relayFig.5 Relationship between the mmber of relay and capacitynamic, it should choose the partner which meels cer-tain conditions. From the perspective of distance, weTherefore, in Co-MIMO system with Multi-anten-should choose the partner close to the source. At thisna terminals，the terminal need search partner dynam-time, the transmission condition is most appropriate asic. From the simulatiou, it can be concluded that thewe can get the best transmission quality. So, we can a-number of cooperative partner has a signifcant effectchieve the goal that choose sub-channel which is noton the capacity. However, when the nuober increasesrelated to the other sub-channels and the ideal capacityto a cerlain value , the capacity will tend to a fixed val-as MIMO advantage can be achieved.ue. And, if the number is too large , the' system will be3. 2. 3 Effect of Antenna Spatial Correlationcomplicated and cause power consurmption, signal in-Fig.7 shows that the antenna space affects chan-terference and other problems. It reveals that .we neednel capacity of multi- antenna terminals Co-MIMO whento consider trade-ofs to get optimum system peform-the DOA is 30 degrees and AS is 10 degrees. It can beseen that the antenna spatial correlation decreases asance when we search the partner.antenna space increases. So the channel capacity of3.2.2 Effect of distribution of cooperative nodesAs already stated before, it is assumed that the .Co-MIMO will increase, but the level of the increase ispath fading and shadow fading are fixed positive inde-not obvious. It can be concluded that the channel ca-pendent random variables during this time, and the re-pacity is close to the ideal value when antenna space isceived power in the frst hop{ E}R1 has calculatedmore than one wavelength and the antenna spatial cor-the stipulated value. The characteristics of random re-relation has been small enough to not influence thflect that the location of source and relay is random.channel capacity.The positive value reflects that the node is located in a中国煤化工of Co-MIMO and?na spatial crrela-fixed arca. So, different locations of the node can af-tion. infect the probability distribution of the variable.traditidDHCNMHG.degrees and AS isWe just consider the path fading, the relationship10 degrcus.1nc Dun anlu n 1cuain the same in thesimulation process. It makes the nodes number inbetween receiving and transmitting power is:P,(t) = P.(t) xd~* xg'(t) .(27)multi-antenna terminal Co-MIMO system equal to the65●Journal of Harbin Instiute of Technology (Neve Series), Vol. 19, No. 3, 2012transmitting antenna number in traditional MIMO sys-and the number of receiving and transmitting antennastem and the receiving antenna number of base stationare different.equal to the traditional MIMO system. It can be seenfrom Fig. 8 that the channel capacity of cooperative35MIMO is larger than the traditional MIMO. The chan.Cooperation antenna soure cooperation destination30- number number: node inodenodenel capacity of traditional MIMO system is easily affect-ed by antenna spatial correlation. I anlenuna space de-Antenna spacing/wavelengthcreases , the channel capacity will degrade significant-ly9201二021s01Antenna spacing/wavclcngth10030 1DOA: 30AS: 10°5t15202530SNR/dB0tFg.9 Infuence of antenna spatial correlation to the chan.nel apacitySource node Cooperction DestinalionIn the process of simulation to Fig. 9, we consid-Antenna numberer two cooperative nodes and single cooperative node.202:3(In the case of two cooperation nodes, both the trans-mitting antenna nurmber and the receiving antennaFig.7 Relation between the channel capacity of Co-MIMOnumber of cooperative nodes are two. In the case ofsystem and antenna spacesingle cooperative node, both the transmiting antennanumber and the receiving antenna number of coopera-tive node are four. In these two cases, the rumber of35 十transmiting antenna and receiving antenna remains thesame in source node and destination node.It can be noticed from Fig. 9 that, in the case ofsingle cooperative node，the four antennas of the coop-，20十eralive node have spatial correlated. Therefore thechannel capacity reduced; in the case of two coopera-15十, Traditional NUNItive nodes , four anlennas are distributed in the two ter-)」Anlenna sapacing/wavelength。 Uneorelatedminals. Because of cooperative transmission in multi-antenna terminals, the correlation of sub channel de-creases greatly. And the channel capacity of transmis-30SNRJdBsion MIMO has increased. So, under the condition ofFig.8 Influence of antenna space for the channel capacityCo-MIMO with multi-partner, it is easy to decrease an-of traditional MIMO and Co-MMOtenna spatial corrclation and achieve the ideal capacityof MIMO system.'Thus, the salient feature of Co-MIMO system withmultiple-antenna terminals is to facilitate decreasing4 Conclusionsantenna spatial correlation in the traditional MIMO sys-tem, using the relay function of multiantenna mobileIn this paper, we analyzed the channel capacity ofterminals to form dynamic reconfigurable (o-MIMO.Co-MIMO with the cooperation node and the antennaUnder the condition of appropriate complexity, we canspatial correlation. The capacity of multi-relay MIMOachieve the optimal spatial uncorrelated sub channelis higher than that of the single relay. With the in-and the ideal capacity of MIMO systemn. In this sys-crease of relay numbers, the capacity tends to a certaintem, the correlation of traditional MIMO system subvalue. The number of cooperative partner has a signifi-channel could decrease greatly if sub channel is chosencant中国煤化工hen we search thereasonable, and the capacity can also increase.partne二Is to get optimumFig. 9 yields the efctse of receiving and transmit-systemAHCN M H G resuls higlightting antenna spatial correlation on the channel capacityhe great effect of spatial correlation on the channel ca-of Co-MIMO when the number nf cooperation nodespacity of Co-MIMO with multiple-antenna terminals..66.Journal of Harbin Instiute of Technology (New Series)，Vol. 19, No.3, 2012Cooperation between terminals can reduce the correla-[6] Shin W Y, JeonS W, Devroye N, et al. Improved capacitytion of antenna, and thus increase the channel capacityscaling in wireless networks with infrastructure. IEEETransactions on Information Thcory, 2011, 57(8) :5088 -of the system. The proposed scheme can economize the5102space, and lead to the increase of the channel capaci-[7] Jeon s W, Chung S Y. Capacity scaling of single -sourcewiteclcss networks: ffcct of multiple antennas. IEEE Trans-References:action on Information Theory, 2012 ,58(3) :1702 - 1715. .[8] Foschini C G J, Cans M J, Valenzuela R A. Keyholes,[1] Sendonaris A, Erkip E, Aazhang B. User cooperation di-correlations, and capacities of multielement Lransmit ancversity-Part l: system description. IEE Transaction otreceive antennas. EEE Trans Wireless Commun, 2002,1:Comm, 2003, 51(11): 1927- 1938.361 - 368.[2] Cui Shuguang, Goldsmith A J. Cross-layer design of ener-[9] Wang B, Zhang J, Host-Madsen A. On the eapacity of MI-gy-constrained netwarks using cooperative MIMO tech-MO relay charnels. IEEE Transactions on Information The-niques. Signal Processing, 2006, 86(8) :1804 - 1814.ory, 2005, 51(1):29 -43.[3] Shyy D J, Dunyak J， Melean M C. Cooperative MIMO[ 10]Marcelta T L, Hochwald B M. Capacity of amnobilemulit-gateways: A promising technique for fast handoff. 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