Performance of Relay Cyclic Delay Diversity in Multicarrier System N. Abdul Razak, F. Said and A. H. Aghvami Centre for Telecommunications Research King’s College London London, United Kingdom nur.abdul [email protected], [email protected], [email protected] Abstract—In this paper, the performance of a cooperative relaying scheme with cyclic delay diversity (CDD) for an orthogonal frequency division multiplexing (OFDM) system is investigated. The system under consideration consists of multiple singleantenna terminals acting as relays and cooperating to provide spatial diversity. Cyclic shift is introduced at each relay and thus increase the frequency selectivity of relay channels. To exploit a highly selective channel, convolutional code is employed together with OFDM. Simulations demonstrate the bit error performance of the proposed scheme with different numbers of relays as well as performance in flat and frequency selective fading channels. The performance of the system is also compared to conventional multiple-input multiple-output (MIMO) with CDD and a conventional amplify-and-forward (AF) relay system. The results indicate that the proposed scheme provides enhanced performance under various considerations. Index Terms—MIMO, OFDM, cooperative communication, relay, cyclic delay diversity. I. I NTRODUCTION OFDM has been a promising technology in wireless communication and can provide a better coverage, more capacity and flexibility to the system [1]. It is also employed for high data rate wireless communication and has been adopted in wireless standards such as digital video broadcasting (DVB), IEEE 802.11a and so on. In OFDM systems, the high rate serial data stream is divided and transmitted simultaneously over a large number of closely-spaced orthogonal subcarriers. Subsequently, each subcarrier will carry a lower data rate signal where symbol duration increases with respect to the number of subcarriers. The OFDM receiver is comparatively simple since each subcarrier will experience the channel as if it is flat and the equalization is done in the frequency domain with a single tap filter. This makes the OFDM system robust to the frequency selective channel and gives it a high spectral efficiency. Another tremendous technology brought to attention in wireless communication is multiple-input multiple-output (MIMO). In the MIMO system, several antennas are employed at the transmitter and/or receiver to provide diversity and multiplexing gains. Spatial diversity offered by MIMO can improve the link reliability and spectral efficiency compared to single antenna systems. Therefore, the combination of MIMO and OFDM can provide a diversity gain that increases system performance and capacity. While MIMO offers significant performance gains to a system, employing multiple antennas at terminals in a network can be tricky, if not impossible due to several constraints and limitations. For example, it is not practical for a mobile station to have several antennas due to its size, hardware complexity and power constraints. Alternatively, cooperative communications with a relaying technique can be used where several single antenna terminals cooperate and act as relays thus creating a virtual MIMO system [4]. The broadcast nature of wireless networks make relays an ideal method to improve error rate performance in wireless networks [4]. Information sent to the intended destination is broadcasted and conveyed through various routes via relays and combined at the destination. This way, diversity can be exploited and the end-to-end path loss can be reduced [7]. Typically, each relay channel consists of two hops although more are also possible. Relaying be accomplished through suitably designed relaying protocols, generally amplify-and-forward (AF) and decode-and-forward (DF). Relays can either amplify or decode the received signal before retransmitting to the destination, and hence are named AF and DF respectively. AF is a simple and non-regenerative protocol but the amplification factor will also amplify the noise whereas DF can provide an error free transmission but will need a decoder at the relay, thus increasing the hardware complexity. Therefore, [3] also introduces selection relaying where relays can choose an optimum relaying strategy based on channel quality measurement. In addition, there are also various other relaying protocols, for example compressand-forward [1] and coded cooperation [4]. Relaying is a duplex process where during the first time slot the source broadcasts the information and it is received by both relays and destination and in the second timeslot relays retransmit the signal to the destination. For the relaying effect to be more beneficial, CDD is adopted in cooperative transmission of relays. Cyclic delays are introduced at relays and hence several copies of signals with different delays will be received at the destination. For cooperative transmission based on OFDM systems, this increases the frequency selectivity of the relay channel without the need to increase the guard interval and receiver complexity. Coded OFDM (COFDM) is used to take advantage of the obtained frequency selective channel [8]. This signalling scheme is preferred over the single carrier system which needs a frequency domain equalizer at the receiver. The delays can be random but it is usually pre-determined so that the maximum separation of signals is obtained. Cooperative relaying with CDD was first proposed in [5] and is referred to as Relay Cyclic Delay Diversity (RCDD). Several works on cooperative relaying have been done based on the efficient relay protocols described in [3]. Performance analysis of CDD in the OFDM relay system with a DF protocol has been investigated [5] while performance in a single carrier system with frequency domain equalization is explored in [7]. In this paper, we study the performance of CDD cooperative relaying with an AF protocol in a multicarrier system. In the proposed system, the relays amplify the received signal, add pre-determined cyclic delays, and retransmit the signal. At the destination, the delayed versions of the signal received from the relays and the direct signal from the source are added together linearly, as if virtual echoes are inserted on the channel [6]. This increases the channel frequency selectivity and higher order of diversity can be achieved by exploiting the channel with a forward error correcting (FEC) code such as convolutional code, and hence COFDM is used for signalling.The system has been simulated in flat and frequency selective channel fading environments and compared to conventional transmit diversity and relay systems. Details of the system model in the time and frequency domains is described in the next section. In section III, simulation results of the system with various considerations are given. We also compare the system to other conventional systems such as CDD in transmit diversity and the conventional AF relay system. Finally, we conclude the work in section IV. II. S YSTEM MODEL ysd (t) = l=0 hsd,l x(t − τsd,l ) + zsd (t) ysm (t) = (1) L−1 X Two-hop relay network hsm,l x(t − τsm,l ) + zsm (t) (2) l=0 where x(t) is the equivalent lowpass of the transmitted signal and zpq (t) is the additive noise during the transmission from p to q modelled as zero-mean complex Gaussian process with power spectral density Npq . For a frequency selective channel with L taps, hpq,l represents the radio channel coefficient between the terminals p and q of path l and τpq,l is the corresponding delay. At the second time slot, the relays retransmit the amplified and cyclic-delayed version of their received signal. The received signal at the destination from M relays is given by yrd (t) = = The system under consideration is a wireless relay network with two-hops as shown in Figure 1 which consists of a source s, a destination d and a set of M relays (m = 1, ..., M ). It is assumed that the relays are operating with an AF protocol where the signal received from the source is amplified, cyclically-delayed and forwarded to the destination. Transmission to and from relays is done in time duplex mode where the first time slot is used to receive the signal from the source and the second is used to forward it to the intended destination. The relays are assumed to be far enough of each other so that the channel can be considered uncorrelated. During the first time slot, the source broadcasts the information and received by the destination and relays. Assuming a slowly varying frequency selective fading channel, the equivalent low pass received signal at the destination and relay from the source, ysd (t) and ysm (t) respectively are given by the equations below. L−1 X Fig. 1. + "L−1 M X X # βm hmd,l ysm (t m=1 l=0 M L−1 X X L−1 X − τm,cyc − τmd,l ) + zmd (t) βm hsm,k hmd,l x(t − τm,cyc − τsm,k − τmd,l ) m=1 k=0 l=0 "L−1 M X X # βm hmd,l zsm (t − τm,cyc − τmd,l ) + zmd (t) (3) m=1 l=0 where τm,cyc is the cyclic delay introduced by relay m and βm is the amplification factor of relay m which assumed to be 1 βm = q P (4) L−1 2 + N / |h | sm,l 0 s l=0 where s is the average energy per transmitted symbol. Equation (4) shows that the amplification factor depends on the channel coefficient between the source and relay, hsm so that more weight is assigned to ’good’ signal for retransmission to the destination. At the destination, the signals from the first and second time slot as given in equations (1) and (3) respectively are added and the total received signal can be written as yd (t) = ysd (t) + yrd (t) L−1 X = hsd,l x(t − τsd,l ) l=0 M L−1 X X L−1 X where zd corresponds to the FFT of the noise vector, and the βm hsm,k hmd,l x(t − τm,cyc − τsm,k − τmd,l ) first term corresponds to the diagonal form of the channel m=1 k=0 l=0 matrix, Hsd which is given by + zt (t) (5) ˜ FN Hsd FH (11) N = diag(hsd ) where zt (t) is the total noise, given by + zt (t) = M L−1 X X βm hmd,l zm (t − τm,cyc − τmd,l ) + zd (t) (6) and therefore ˜sd = h m=1 l=0 Since AF also amplifies the noise at relays as shown in (6), it is not suitable to be for the transmission scheme other than M-PSK constellation scheme, where the detection also relies on amplitude of the received signal. From (5), it can be seen that the frequency selectivity of the channel is increased even when the channel is flat (L = 1). Therefore, the receiver can take advantage of this selective channel to improve the overall channel by employing coded OFDM signal. Figure 2 shows the equivalent channel model with cyclic delay at relays. √ N FN hsd (12) where hsd = [hsd (0) hsd (1) ... hsd (L − 1) 0 ... 0]T corresponds to the impulse response of the channel from source to the destination, padded with zeros to form a vector of length N . Using this expression, the demodulated data vector can be rewrite in a simpler form which is ˜sd )x + zd y ˜sd = diag(h (13) During the second time slot, relay m retransmits the signal received during the first time slot as in equation (9). At each relay, y ˜sm is amplified with the amplification factor, βm as described by equation (4) and cyclically right shifted by δm position which is predetermined to ensure maximum signal separation, given as follows N (14) δm = m M Therefore the retransmitted signal will be x ˜md = βm Pδm ysm Fig. 2. Equivalent channel model Consider N BPSK modulated symbols, x = [x(0) x(1) ... x(N − 1)]T , corresponding to the number of subcarrier of an OFDM symbol. After the inverse fast Fourier transform (IFFT), the OFDM symbol can be written as x ˜ = FH N x with each element is given by 1 x ˜(n) = √ N N −1 X x(k)ej(2π/N )kn where Pδm = circ(eδm +1 ). P corresponds to an N xN permutation matrix performing a right cyclic shift of δm positions defined in (14) as a right circular matrix with eδm +1 in the first row. ek corresponds to a row vector of length N with all its positions equal to 0, except for position k which is equal to 1. The total received signal at the destination from M relays can be written as yrd = During the first time slot, the received signal at the destination and relay m from the source are given by respectively ysd = Hsd x ˜ + wmd (8) ysm = Hsm x ˜ + wmd (9) where Hpq and wpq are the channel matrix and the Gaussian noise vector from terminal p to q. At the destination, the cyclic prefix is removed and the FFT of ysd in equation (8) is performed in order to recover the N modulated symbols. This can be written as M X = (7) k=0 (15) = m=1 M X m=1 M X Hmd xmd + wrd βm Hmd Pδm ysm + wrd Hef f x ˜ + wrd (16) m=1 where Pδm corresponds to the cyclic delay introduced at the relay m and Hef f is the effective channel defined as Hef f = βm Hsm Hmd Pδm . wrd is the total noise from the relays at the destination which is given by wrd = M X (Hef f wm + wmd ) (17) m=1 y ˜sd = FN ysd = FN Hsd x ˜ + FN wsd = FN Hsd FH N x + zsd Next, FFT operation is performed on yrd in (16) resulting (10) y ˜rd = FN Hef f FH N x + zrd (18) TABLE I BASEBAND OFDM SIGNALLING PARAMETERS Parameters Channel bandwidth Modulation type FFT size Guard period Frame length FEC Coding rate Constraint length TABLE II FADING CHANNEL PARAMETERS Value 10 MHz BPSK 64 16 16 symbols Convolutional coding 1/2-rate (171,133) 7 Parameters Statistic distribution Doppler frequency Low frequency oscillator Guard period Tap Decoder Since Hef f is a summation of circulant matrices, (18) is also a circulant matrix and therefore it can be expressed as a diagonal matrix using the FFT decomposition. Finally, y ˜rd becomes ˜ef f )x + zrd y ˜rd = diag(h (19) ˜ef f is given by with the effective channel, h ˜ef f = h M X ˜sm h ˜md ˜em βm h (20) m=1 where represents the Hadamard product. Finally, the received signal in the first time slot given in equation (13) can be linearly added to the received signal in the second time slot as in (19). Value Rayleigh 50 Hz 12 16 1(flat), 8(frequency selective) Viterbi Figure 4 shows further performance of the COFDM in the proposed system with relays, M = 1 and M = 5, in flat and frequency selective channel with parameters as in Table II. The performance is best to be illustrated in the flat fading channel but it still gains reasonably in the frequency selective channel. At BER of 10−4 , the performance of the system gains 4dB and 8dB in the flat and frequency selective fading channel respectively. This shows that the introduction of different delays by several relays improves the system performance, even when the channel is already selective. This can be seen from the channel snapshots of the system effective channel with both flat and frequency selective channels shown in figures 5 and 6 respectively. 1E0 M=1, flat fading M=5, flat fading M=1, selective fading M=5 selective fading 1E-1 To illustrate the performance of this relay communication scheme, a COFDM signal with the parameters shown in Table I is considered. The simulations perform bit error rate (BER) analysis of the proposed system based on SNRs obtained under various cases. First, the behaviour of the system is investigated using coded and uncoded OFDM signals in the flat fading channel. It is observed in Figure 3 that increasing the number of relays increases the performance difference when a COFDM signal is used. On the other hand, uncoded OFDM in the proposed system does not give much gain in performance. Bit error rate, BER III. S IMULATION RESULTS 1E-2 1E-3 1E-4 1E-5 1E-6 0 Fig. 4. 2 4 6 8 10 Eb/No [dB] 12 14 16 18 Proposed scheme in frequency selective channel 2 M=1 M=3 M=5 M=1 M=3 M=5 uncoded 1E-1 1.6 1.4 1.2 channel gain 1E-2 Bit error rate, BER flat fading channel effective channel 1.8 1E0 1E-3 coded 1E-4 1 0.8 0.6 0.4 0.2 1E-5 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 1E-6 subcarrier index 0 2 4 6 8 10 12 14 16 18 20 Eb/No [dB] Fig. 3. Performance of the proposed system model with coded and uncoded OFDM signal Fig. 5. Snapshot of effective channel response in flat fading environment for M=1 relay system 2.5 frequency selective fading channel effective channel 2 1.5 channel gain Next, the obtained performance gain is assessed when cyclic delay is applied at the relays. Figure 7 shows the BER curve of the proposed relay system compared to CDD transmit diversity system [2] and AF relay system [3] in both fading environments with two diversity paths. It is observed that the proposed system model has better performance compared to the other two models. Figure 8 shows the BER of the AF relay system with and without cyclic delay. Generally, increasing the number of relays will increase the performance gain. The proposed scheme provides better performance gain when the number of relays is increased compared to the one without cyclic delay. 1 0.5 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 subcarrier index IV. CONCLUSION Fig. 6. Snapshot of effective channel response in frequency selective fading environment for M=1 relay system 1E0 CDD transmit diversity amplify-and-forward proposed model CDD transmit diversity amplify-and-forward proposed model 1E-1 flat fading channel 1E-2 Bit error rate, BER In this paper, performance of a cooperative relaying system with added CDD at relays was assessed. The obtained results show that applying CDD in cooperative communication with the COFDM signal increases the performance of the system even when the channel is already selective. This is an attractive scheme for future wireless communication since it does not increase the system complexity. The effect of various numbers of relays with pre-determined time delay is also considered. Considerable gain can be obtained with an increased number of relays in the system. This is due to the increases in the frequency selectivity of the channel. This frequency selectivity is exploited well by using COFDM signal in the system. 1E-3 frequency selective channel 1E-4 1E-5 1E-6 R EFERENCES 2 4 6 8 10 12 14 16 18 20 Eb/No [dB] Fig. 7. BER of conventional CDD, amplify-and-forward relay with and without cyclic delay 1E0 M=1, without CDD M=3, without CDD M=5, without CDD M=1, with CDD M=3, with CDD M=5, with CDD 1E-1 Bit error rate, BER [1] E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, and H. Vincent Poor. MIMO Wireless Communications. Cambridge University Press, 2007. [2] A. Dammann and S. Kaiser. Performance of low complex antenna diversity techniques for mobile ofdm systems. In In Proceedings 3rd International Workshop on Multi-Carrier Spread-Spectrum & Related Topics, 2001. [3] N. Laneman, D. Tse, and G. Wornell. Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Trans. Inform. Theory, 50:3062–3079, 2004. [4] A. Nosratinia, T.E. Hunter, and A. Hedayat. Cooperative communication in wireless networks. IEEE Communications Magazine, 42:68–73, 2004. [5] A. Osseiran, A. Logothetis, S. B. Slimane, and P. Larsson. Relay cyclic delay diversity: Modeling & system performance. In IEEE International Conference on Signal Processing and Communications, 2007. [6] M. I. Rahman, K. Witrisal, D. Prasad, O. Olsen, and R. Prasad. Performance comparison between mrc receiver diversity and cyclic delay diversity in ofdm wlan systems. In 6th Wireless Personal Multimedia Communications Symposium, 2003. [7] S. B. Slimane and A. Osseiran. Relay communication with delay diversity for future commuication systems. In IEEE Vehicular Technology Conference, 2006. [8] K. Witrisal, Y.H. Kim, R. Prasad, and L.P. Ligthart. Antenna diversity for ofdm using cyclic delays. In IEEE 8th Symposium on Communications and Vehicular Technology, 2001. 0 1E-2 1E-3 1E-4 1E-5 0 2 4 6 8 10 12 14 16 18 20 Eb/No [dB] Fig. 8. BER performance of relay system with and without cyclic delay