Performance Analysis of Two-Hop Cooperative MIMO Transmission with Relay Selection in Rayleigh Fading Channel

Performance Analysis of Two-Hop Cooperative MIMO transmission with relay Selection in Rayleigh Fading Channel

Ahasanun Nessa1, Qinghai Yang2 Sana Ullah1, Md Huamaun Kabir1, Kyung Sup Kwak1 1Graduate School of Information Technology and Telecommunications, Inha University, #253 Yonghyun-dong, Nam-gu, Incheon, 402-751, Korea. Email: [email protected] 2School of Telecommunications Engineering, Xidian University, No.2 Taibainan-lu, Xi’an, 710071, Shaanxi, China. Email: [email protected]

Abstract— Wireless Relaying is one of the promising modes. But all this analysis all nodes have only one antenna solutions to overcome the channel impairments and consideration. Dual hop transmission of multiple antenna provide high data rate coverage that appears for beyond equipped relays has been analyzed in paper [7]. In this paper, 3G mobile communications. In this paper we present an our aim is to analyze the system with multiple relay nodes end to end BER performance analysis of dual hop where each relay node has one transmit and one receive wireless communication systems equipped with multiple antenna and source transmitting data using more than one Decode and Forward relays over the Rayleigh fading transmit antenna . We assume the two hop experience channel with relay selection. We select the best relay independently, not necessarily identically distribute Rayleigh fading reliability by averaging over independent channel based on end to end channel conditions. We apply realization and would be more efficient to combat fading and Orthogonal Space Time Block coding (OSTBC) at shadowing.. Moreover in this paper at the receiver end we source, and also present how the multiple antennas at are not considering all received signal passing through the source terminal affects the end to end BER different relay stations. We are selecting signal from one of performance. This intermediate relay technique will the best relay stations to assist the communication like a cover long distance where destination is out of reach single source destination pair. It will reduce the decoding from source. complexity at receiver side and also in the same time will achieve diversity gain. Keywords-Bit error rate (BER), amplify and forward (AF), multiple input multiple output (MIMO), decode- The paper is outlined as follows: Section II introduces and-forward (DF),probability density function (PDF). the system and channel model. Section III derives the probability density function and moment generation function I. INTRODUCTION of the received SNR per bit and analyzes the BER performance when M-ary PSK constellations are used. Relay Dual hop transmission is a technique by which the selection protocol is described in Section IV. Simulation channel from source to destination is split into two possibly results of our end to end BER performance are presented in shorter links using a relay. In this case the key idea is that the Section V. Finally Section VI presents conclusion and future source relays a signal to destination via a third terminal that work. acts as a relay [1]. It is an attractive technique when the direct link between the base station and the original mobile II. SYSTEM AND CHANNEL MODEL : terminal is in deep fade or heavy shadowing or when the destination is out of reach of the source. h11 R1 HSR HRD Cooperative relaying is a promising extension to relay g h 1 networks where several relay stations transmit jointly to 1t TX h21 same destination yielding diversity gain [2].Depending on 1 R2 g2 the nature and complexity of the relays cooperative D h transmission system can be classified into two main 2t hr1 g categories, namely regenerative or non regenerative systems. TXt r The performance of both systems has been well studied in h [3], [4], [5]. In [5] it is shown that outage probability may be rt Rr reduced via a variety of cooperation protocols. In [5] and [6] various protocols for ergodic capacity have been analyzed but they all are for fixed single relay system with AF Figure 1. Two-hop relay network with antenna arrays (Amplify-and-Forward) and DF (Decode-and-Forward) at source and r relays are relaying signal to D.

Authorized licensed use limited to: Inha University. Downloaded on November 8, 2009 at 05:29 from IEEE Xplore. Restrictions apply. iii= ªº Eee1..L (4) Consider a wireless network with r relay nodes which ¬¼«» are placed randomly and independently according to some yi and ei denote the received signal and the additive distribution. The source is equipped with multiple transmit l l antennas and each relay node has a single antenna which complex white Gaussian noise with mean zero and variance σ 2 can be used for both transmission and reception. After A respectively, at the ith relay during the l th symbol receiving the signal from source each relay node decodes it duration where the block length of the OSTBC is denoted by and among them only one transmits it to destination. We L . After receiving the signal each relay decodes them with assume there is no direct link from source to destination. We an efficient ML detector and take decision among them who are applying OSTBC at the source. No channel information is more opportunistic for relaying signal to destination and is available at source. So no power or bit loading is then transmit it to destination. We are discussing the relay performed at source. Each transmit antenna of source is selection protocol in Section IV. Let i th relay is the most appropriate the for relaying signal to destination .Then the σ 2 = P assumed to use the same transmit power s , where P is received signal at destination is t the total transmission power of the source and t is the DD=+ YXegi1 (5) number of antennas at source. At first time slot the source transmits the signals over the uplink matrix channel HSR to where X1 is the transmitted signal matrix from relay to the relays. After receiving the signal each relay decode the destination and eD is the complex additive white Gaussian σ 2 σσσ222== signal and find out the best relay among them and then noise with mean zero and variance B . Let AB . transmits it to destination. From (2) the received SNRs at each relay for the first hop can be given as III. BER ANALYSIS t 2 We are considering the dual hop wireless communication γρRi= ρα = ρ 2 () c = ch¦ ij (6) in which source equipped with multiple antennas and j=1 communication with destination via number of relay nodes. = ρ = σ 2 In order to achieve spatial diversity we are applying OSTBC where cLtKLogM/( . .2 ) and P / . K is number of at source. We assume there are r relays and number of complex signal is transmitted by OSTBC code X. And for transmit antennas at source is t. So the channel matrix for the the second hop it is like a SISO channel. For M order first hop is given by modulation the SNR of second hop can be given by

§·hh.. D 2 ¨¸11 1t γρρ()= gM /log (7) = i 2 H SR ¨¸##hij (1) ¨¸ R ©¹hhrrt1 .. So the MGFs of the first hop and second hop for γρ() and γ D are respectively obtained by where the element hij denotes the channel gain between the − i th relay and the j th transmit antenna of source, == + βρ t Msγ R ()() 1 cs1 (8) ir=1,2,... and j = 1, 2, . ..t . We assume that each element of SR =+γ D H is an independent and identically distributed complex Msγ D () 1/(1 s ) (9) β Gaussian random variable with zero mean and 1 variance. If By taking the inverse Laplace transform of (8) and (9) The we notice carefully we observe each row of H SR represents the channel coefficient between source and relay. So the PDFs of γρR () and γρD ()are respectively given by channel matrix for each relay can be represented by 1 −γβρ/ c fcteR ()γβρ= ( ) 1 (10) α = = γρ() 1 − ii()hh1.. it for i= ir1,2,... (1)!t

1 −γγ/()D ρs And for the second hop g is the individual relay to feD ()γ = (11) i γρ() γ destination fading amplitude. θ When OSTBC X is used at the source the signals BER of M-ary PSK constellation : The PDF of phase of received at each relay are given by the received signal with SNR γ is given by in [10]

11−γγθª 2 §·º ii=+α i θγ=+log22MM θ π γ log cos − γ θ YXE (2) feθ (|)π « 1cos4log22 MeerfcM¨¸ 1() log cos » 22¬« ©¹¼» where (12)

Yyyiii= ªº.. (3) ¬¼«»1 L and

Authorized licensed use limited to: Inha University. Downloaded on November 8, 2009 at 05:29 from IEEE Xplore. Restrictions apply. ∞ α is the fading amplitude from relay to destination. Since 2 id 1 − y where erfc(xedy )= . Then the exact probability that the π ³ the two hops are both important for end to end performance x each relay calculates corresponding hi based on the two θ phase of the received signals lies in a decision region decision rules and broadcast the measured values among ªºθϑ ¬¼lu, is given by them

∞ θ = αα22 u Rule 1: hisiidmin{} , (19) Pr{}θθϑρ∈=[] ;fθγρ ( θγ | )fdd ( γθγ ) 0 lu,()³³ θ 0 l 22 (13) 2 αα ==2 si id Rule 2: hi (20) The BERs of M-ary PSK constellation for the first and 11αα22+ + siid αα22 second are respectively obtained by si id

M ∞ θ − 1 uj The relay i that maximizes function h is one with the “best” PeffddMPSK()ρ = (|)θ γγ ()θ γ i Rjϑ γρR () (14) log2 M ¦ ³³0 θ end to end path between initial source to destination. j=1 lj After discovered best relay then it relaying to destination. M ∞ θ − 1 uj In this paper it is assumed the destination have perfect PeffddMPSK()ρ = (|)θ γγ ()θ γ Djϑ γρD () (15) log2 M ¦ ³³0 θ channel information available for decoding the received j=1 lj signal. where θπ=−(2jM 3) / and θπ=−(2jM 3) / for j=1,…M l j u j V. SIMULATION RESULT and e j is the number of bit errors in the decision region. In this section, we are presenting our simulation result about BER performance. We consider QPSK and 16QAM IV. RELAY SELECTION constellation for 2 and 4 transmit antenna equipped source. In this paper, all relay stations are not relaying signal to We are assuming the channels are Rayleigh fading channel. destination. At the receiver end we are only getting signal Two sorts of simulation are performed one for decision rule1 which are coming form the best station. We are assuming and another for decision rule2. And performances are nearly source to relay and relay to destination channel state same for both two cases. information is available to each relay. The relay nodes monitor the instantaneous channel conditions. After receiving the signals, each relay decodes hem with an 0 2 transmit antenna equiped source efficient ML detector and find out among them which one is 10 more opportunistic for relaying signal to destination. The term opportunistic has been widely used in various different -1 context. In previous work opportunistic relay is defined 10 considering distance toward source or destination [9] or sometimes considering the channel condition [8]. The relay -2 10 selection based on distance is not a good selection since BER R=1 communication link between transmitter and receiver R=2 Rule=1 R=2 Rule=2 locating in the same distance might have enormous R=3 Rule=1 -3 difference in terms of received signal due to fading and 10 R=3 Rule=2 R=5 Rule=1 shadowing. In this paper we are assuming all relays can R=5 Rule=2 R=7 Rule=1 listen to each other. After monitoring the instantaneous -4 R=7 Rule=2 10 channel condition each relay also broadcast the information 0 2 4 6 8 10 12 14 16 18 20 to other relay nodes. And they come to know among them SNR [dB] Figure 2. BER vs SNR for Relay selection. which one is more opportunistic in this time. Tx=2,modulation=QPSK. In our study we denote the relay to destination channel In Fig2 and Fig3 we consider 2 transmit antenna and 4 state information H and H . Let α and α is the SR RD si id transmit antenna at source respectively. By comparing Fig 2 channel state information to ith relay from source to ith relay and Fig 3 we illustrate how BER performance can be and ith relay to destination respectively. The channel improved by increasing the number of antennas and relays. If α α estimates si , id describe the quality of the wireless path we select more relays than it is possible to improve BER α between source-relay -destination to each relay. Where si is performance instead of using more transmit antennas at calculated by relay i by the following equation. source. It will reduce the cost of implementing more antennas at base station. Modulation order also affects the α =+ + si()hht i1 ... it / . (16) difference between the BER performances, that is shown in Fig 4 and Fig 5. If the modulation order gets higher, the

Authorized licensed use limited to: Inha University. Downloaded on November 8, 2009 at 05:29 from IEEE Xplore. Restrictions apply. difference becomes egligible. Comparing Fig 2 and Fig 4 and Fig 3 and Fig 5, it is easily noticeable. VI. CONCLUSION In this paper, we presented end to end BER performance

0 4 transmit antenna equiped source of dual hop wireless transmission employing transmit 10 diversity with OSTBC and receiver diversity by using multiple relays where the destination is out of reach from

-1 source. We show the BER performance by varying the 10 number of antennas and number of relays. But this performance improvement is not too much if the channel is

-2 10 noisy. In our design we are only considering the best signals BER R=1 those are coming from best relay station for reducing R=2 Rule=1 R=2 Rule=2 receiver complexity. In future our work will be evaluated

-3 R=3 Rule=1 10 under more advanced receiver structure for realistic channel R=3 Rule=2 R=5 Rule=1 consideration and we will continue our work for multi hop R=5 Rule=2 R=7 Rule=1 transmission for covering long distance. -4 R=7 Rule=2 10 0 2 4 6 8 10 12 14 16 18 20 SNR [dB] ACKNOWLEDGEMENT Figure 3. BER vs SNR for Relay selection. This research was supported by the MKE(Ministry of Tx=4,modulation=QPS Knowledge Economy), Korea ,under the ITRC( Information Technology Research Center ) support program supervised by the IITA( Institute of Information Technology 0 2 transmit antenna equiped source 10 Assessment )" (IITA-2008-C1090-0801-0019)

REFERENCES -1 10 [1] H. S. Ryu, C. Gu Kang and D. S won,“Transmission Protocol for Cooperative MIMO with Full Rate:Design andAnalysis,” IEEE 65th -2 10 Vehicular Technology Conference,April 22-25 ,2007, pp-934-938. BER R=1 R=2 Rule=1 [2] M. O. Hasna and M.-S. Alouini, “A performance Dual tansmissions R=2 Rule=2 with fixed gain relays,” IEEE Trans. Wireless Commun.,vol. 3, -3 R=3 Rule=1 10 R=3 Rule=2 pp. 1963-1968, Nov. 2004. R=5 Rule=1 R=5 Rule=2 [3] M. O. Hasna and M.-S. Alouini, “Application of the harmonic mean R=7 Rule=1 statistics to the end-to-end performance of transmissionsystems with -4 R=7 Rule=2 10 relays,” in Proc. IEEE Global Communications Conf., Taipei, 0 2 4 6 8 10 12 14 16 18 20 SNR [dB] Taiwan, Nov.2002, pp.1310-1314. [4] M. O. Hasna and M.-S. Alouini, “Optimal power allocation for Figure 4. BER vs SNR for Relay selection. relayed transmissions over Rayleigh-fadingchannels,,IEEE Trans. Tx=2,modulation=16QAM Wireless Commun., vol.3, no.6, pp.1999-2004, Nov. 2004. [5] Cooperative Diversity in Wireless Networks: Efficient Protocols and 4 transmit antenna equiped source 100 OutageBehavior,” IEEE Transactions on Information Theory, vol. 50, no. 12, pp. 3062–80, Dec.2004. [6] R.U. Nabar, H. Bölcskei, and F.W. Kneubühler, “Fading Relay Channels: Performance Limits and Space-Time Signal Design,” IEEE -1 10 Journal on Selected Areas in Communications, vol. 22, no. 6, pp. 1099-109, Aug. 2004. [7] I.-H. Lee and D. Kim, “Exact end-to-end analysis fordual-hop

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BER Dec. 2005 R=1 R=2 Rule=1 [8] A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, “A simple R=2 Rule=2 cooperativemethod based on network path selection,” IEEE Journ. R=3 Rule=1 10-3 Selec. Areas onComm. (JSAC), Special Issue on 4G, Jan. 2005. R=3 Rule=2 R=5 Rule=1 [9] M.Zori and R. R. Rao,”Geographic random forwarding for adhoc and R=5 Rule=2 sensor Networks: Multihop performance,” IEEE Trans. Mobile R=7 Rule=1 Comput.,vol 2, no. 4, pp.337-348, Oct.-Dec.2003 -4 R=7 Rule=2 10 0 2 4 6 8 10 12 14 16 18 20 [10] J.G. Proakis, Digiatal Communications, McGrraw-Hill, 1995. SNR [dB]

Figure5. BER vs SNR for Relay selection. Tx=4,modulation=16QAM

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