Distributed Alamouti Full-duplex Relaying Scheme with Direct Link

Transcription

1 istributed Alamouti Full-duplex elaying Scheme with irect Link Mohaned Chraiti, Wessam Ajib and Jean-François Frigon epartment of Computer Sciences, Université dequébec à Montréal, Canada epartement of Electr Eng, Ecole Polytechnique de Montréal, Canada s: and Abstract In full duplex relaying, the direct link and the decode and forward processing delay are not always negligible The signal transmitted by the source thus interferes, at the destination, with the delayed signal retransmitted by the relay This paper presents a novel full duplex transmission scheme based on distributed Alamouti encoding denoted by FAE that eliminates the interference problem and combines efficiently each transmitted signal and its delayed copy at the destination for decode and forward relaying The performances of FAE are compared to the full duplex system with interference at the destination denoted by FI and to the conventional half duplex relaying The simulation results show the harmful effect of the interference problem on the end-to-end achievable data rate and on the bit error rate They also show that our proposed scheme provides a highest end-to-end achievable data rate and lower bit error rate than FI due to its ability to take advantage of full duplexing while eliminating interference Index Terms Full duplex relaying, direct link, processing delay, distributed Alamouti encoding I INTOUCTION Cooperative relaying in wireless transmission systems has attracted attention due to its diverse applications and numerous advantages such as extending the cell coverage [] and the enhancing transmission diversity [] In half-duplex H relaying, the relay receives and transmits signals in orthogonal channels on frequency frequency division duplexing or time time division duplexing domains This results in an inefficient spectrum use and hence the end-to-end capacity degrades ecently, full-duplex F relaying has been investigated as a promising technique to enhance the system capacity []-[7] F relays exploit the space domain to transmit and receive signals in the same spectrum band and time However, F relaying is limited by the relay s self-interference due to the transmitted signal leakage which interferes with the received signal A comparison between H relaying and F relaying performances []-[4], without considering the effect of the direct link, shows that F relaying achieves higher end-to-end data rates However, these works consider an ideal F relay with no self-interference ecent works [5]-[7] show that selfinterference mitigation for a multi-antenna relay is feasible through signal processing techniques, where the relay antennas are partitioned into receiver and transmitter antennas In [5], self-interference is mitigated using null-space beamforming and it shows how a finite computational error can affect the F transmission feasibility A range of self-interference mitigation techniques has been investigated in [7] It combines spatial processing, null-space beamforming, and time domain processing through a minimum mean square error filtering The results show that self-interference is also mitigated when side information acknowledgement is imperfect However, all the previous works ignore the processing delay at the relay or the direct link between the source and the destination Hence no interference is perceived by the destination between the direct signal from the source and the delayed signal forwarded by the relay In realistic scenarios, the direct link between the source and the destination, and the processing delay at the relay may not be negligible Then, at the destination, the signal transmitted by the source acts as interference to the desired signal transmitted by the relay The exact outage probability of full-duplex relaying, where the relay operates in decode-andforward mode F, is derived in [8] It shows the harmful effect of the previous interference problem at the destination on system outage probability and that F relaying outperforms H relaying only in high signal to interference ratio SI The problem of direct link interference must thus be adressed In this paper we consider a multi-antenna relay operating in F mode The antennas at the relay are partitioned into receive and transmit antennas The processing delay at the relay and the direct link between the source and the destination are considered We specifically address in this paper the problem of interference avoidance at the destination Our main motivation is to combine, at the destination, the signal received via direct link and its delayed copy to enhance the end-to-end achievable data rate We thus propose a novel F relaying transmission scheme based-on distributed Alamouti Encoding [9] referred to as FAE This scheme ensures that the signal from the source and its delayed copy are efficiently combined while eliminating the interference The self-interference at the relay, due to F transmission, is mitigated using zero forcing beamforming ZFBF technique The performances of our transmission scheme, in terms of end-to-end achievable data rate and bit error rate BE, are compared to both conventional H relaying and the conventional F relaying with interference problem at the destination FI Simulation results show that our proposed scheme provides the highest end-to-end achievable data rate and lower BE than FI for all ranges of SI The rest of this paper is organised as follows In the //$00 0 IEEE 400

2 Fig FI transmission process during a TS Fig Full duplex transmission process second section, the system model is described The full-duplex relaying schemes are presented in section III Simulation results are provided in section IV and conclusions are drawn in section V Throughout this paper, denotes the -norm, [] T and []* denote the transpose and the conjugate transpose operators respectively denotes the modulo operator A complex Gaussian random variable Z with mean μ and variance σ is denoted as Z CNμ, σ h X,Y denotes the channel coefficient between two antennas X and Y The argument of a complex number is denoted by arg II SYSTEM MOEL We consider a F relaying system consisting of a single antenna source S, a multi-antenna relay and a single antenna destination, where the source and the relay transmit in the same band The relay is equipped with at least three antennas which may either transmit or receive signals If the relay has more than three antennas, then it may select the best three from the antennas for transmitting and/or for receiving We assume that the source transmits data to the destination via the relay as well as via the direct link S The relay decodes and forwards the received signal from the source with a processing delay τ>0 ue to F transmission, the relay suffers from self-interference problem Therefore, the relay antennas are partitioned into one receiver antenna r and two transmitter antennas t and t Furthermore, the relay uses ZFBF spatial processing technique to send data toward the destination while nulling it out on r direction It is assumed that the relay has a perfect knowledge of the channel coefficients between its antennas Fig shows the relaying system considered in this paper, where s n and r n denote the codewords transmitted during time n by the source and the relay respectively The link between a transmitter antenna X and a receiver antenna Y, where the two antennas belong to different nodes, is assumed to be ayleigh fading channel Thus the channel coefficients are given by h X,Y CN0,d α X,Y, where α is the path loss component and d X,Y is the normalized distance between X and Y The relay antennas are close to each other, thus the channel gain between two relay antennas follows a ice distribution We consider that each receiver generates an additive white gaussian noise AWGN with zero mean and variance To mitigate the F self-interference using the ZFBF technique, the relay multiplies the transmitted codeword of symbols denoted by x with the weight vector w [0] formed as follows ht,, w = r h t, r, h t, h t, thus we obtain h t, r, h t, r w =0and also we have ht,, h t, w = Consequently, the self-interference is completely mitigated The signal received by the destination is written as: P y = w x + n, where P is the relay transmit power and n is the AWGN at the destination In this paper, we assume that time is divided into time slots TS We consider that the state of the channels stays invariant during a TS, but it may change independently from a TS to another The processing delay to decode and retransmit a codeword at the relay is denoted by τ Without loss of generality, we consider that the TS duration denoted by d TS is an integer multiple of τ Thus, during one time slot, the source can transmit N = d TS τ codewords We assume that each TS is divided in N + sub-slot with equal durations III FULL-UPLEX ELAYING SCHEMES In this section, we describe in details the two F transmission schemes considered in this paper, namely: F relaying with interference FI and the novel F relaying with distributed Alamouti encoder FAE that we propose in this work In both schemes, the relay uses the ZFBF technique to mitigate the relay self-interference and the relay operates in F mode A Full-duplex relaying with interference FI Fig shows the transmission process of the FI scheme In this scheme, the source sends a codewords x n at the n th subslot n =,,N, and the relay decodes and retransmits x n at the n + th sub-slot uring F transmission, the relay selects one antenna to receive x n r while two other antennas t and t retransmit x n and mitigate selfinterference using ZFBF technique For the first sub-slot, the 40

3 source transmits the codeword x while r, t and t are operating as receivers Hence, the relay uses the maximal ratio combining MC [] to combine the three signal copies Thus, the signal to noise ratio SN at the relay at the n th sub-slot is written as: P S h S,i, if n = γ n = i {t,t,r} P S h S,r, otherwise At the last sub-slot N + th sub-slot, the relay retransmits x N while the source stays silent The relay can thus use the transmit maximal ratio combining technique [] which provides the highest SN for the Multi-Input Single-Output MISO system The relay then multiplies the transmitted signal by the weight vector v formed as follows: v = h, h,, 4 where h, = T h r,, h t,, h t, The vector of signals received by the destination during a TS can be written as follows: y y Ḍ y N+ = z 0 0 P z P z 0 0 P h, x n x + n Ḍ, 5 x N n N+ where z = P h s, and n n CN0, n {,,, N +} In this scheme, the destination treats the signal received via the direct link S as interference, except at the first sub-slot where the destination combines the first received signal with its delayed copy, that is associated with direct link interference, using optimum combining OC [] which is optimal in presence of interference Hence, at the destination, the signal to interference plus noise ratio SIN associated to the n th codeword is given by: γ n = P S h S, P + + P S h S,, if n = P + P S h S,, if n {, N } P h,, if n = N 6 The relay operates in decode and forward mode, so it requires to correctly decode each codeword before retransmission Hence, the end-to-end achievable data rate is given by: FI = N + N n= log +min γ n,γn 7 It is important to note that depends on which relay antenna is selected to receive the source signal during the full duplex transmission Therefore, at the beginning of each TS, the relay selects the receiver and transmitter antennas { r, t, t } that maximise the end-to-end achievable data rate In H relaying, the relay receives the source signal and it retransmits the received signal in two successive sub-slots Therefore, H relaying process is identical to FI scheme when τ = d TS B Full-duplex relaying with Alamouti Encoding FAE The proposed FAE scheme is based on the Alamouti coding technique to eliminate the direct link interference and efficiently combine both copies of each signal at the destination, hence improving the end-to-end achievable data rate In this section, we start by explaining this transmission scheme for a processing delay equal to τ = d TS Afterwards, we generalise the FAE transmission process to any value of τ It is assumed that the relay has a perfect knowledge of the S link channel coefficient Considering that τ = d TS, the source then transmits N = codewords x and x at each TS The transmission of the proposed FAE scheme occurs in three phases Transmission phase At the first sub-slot, the source transmits the codeword x The relay antennas { r, t, t } operate as receivers and the relay uses MC to combine the received signal copies Hence, the SN at the relay is given by: γ = P S h S,t + h S,t + h S,r, 8 and the received signal by the destination is written as: y = h S,x + n 9 Transmission phase At the second sub-slot, the source transmits x while the relay retransmits x The relay uses ZFBF to avoid selfinterference as explained in Sec II Hence, the SN at the relay is given by: γ = P S h S,r, 0 and, from, the signal at the destination is written as: y = P x + P S h S, x + n, where is the power assigned by the relay to retransmit x Transmission phase At the third sub-slot, the relay encodes and transmits weighted versions of x and x in order to perform, with 40

4 y, an orthogonal matrix of signals at the destination Alamouti code Let us define α and α as the weight components assigned to x and x respectively Their energy is equal to unity Let also define P and P as the power assigned to transmit the codewords x and x respectively at the third sub-slot The vector of signals received by the destination at the second and third sub-slots is then given by: y y = + x PS h S, P h, α P h, α x P n n The relay suitably adjusts the weight components α and α and the transmit powers, P and P to get an orthogonal equivalent channel matrix as follows We start by adjusting the transmitted signals arguments by solving the following system: { arg α =arghs, arg α =0 α = h S, h S, α = The total energy used by the relay during two sub-slots is equal to P The relay adjusts the transmit powers, P and P, with respect to the previous energy constraint, by solving the following system: P h, = P S h S, P h, = + P + P =P h S, = P h, P S h, + h, P = P S h S, h, P = h, 4 At the beginning of each TS the relay calculates and it applies FAE scheme when is strictly greater than zero Note that the transmit power is most of the times strictly greater than zero, since h S, h, is usually smaller than one and P is the same order of magnitude than P S Otherwise, the FI scheme is applied and the transmit powers are set to = P P =0 5 P = P When FAE is applied, the received vector of signals during one TS can be obtained by combining 9, and as y y Fig FAE transmission process follows: y PS h S, 0 P = PS h S, PS h S, + x x n n n 6 We denote by H the equivalent channel matrix defined in 6 It can be observed that as desired H is orthogonal The destination then uses the Alamouti detector to decode the codewords That is, the destination multiplies the vector of received signals by H Hence, the signal to interference plus noise ratio SIN associated with the n th codeword γ n is given by: γ n = +P S h S,, if n = + P S h S,, if n = 7 Note that indeed the interference of the direct link has been removed From equations 8, 0 and 7, the achievable end-toend data rate is given by FAE/τ= d TS = n= log +min γ n,γn 8 It is important to note that the system performance remains the same as when a pseudo-inverse channel matrix is applied at since H is orthogonal This transmission scheme can be extended to the general case as follows Without loss of generality, we assume that the number of transmit codewords N is even if N is odd, the relay just retransmits at the last sub-slot the last received codewords The vector of transmit codewords during one TS is divided into blocks of two codewords The transmission process of each block of codewords follows the three transmission phases described above However, at the third transmission phase of the k th k =,, N block, the source simultaneously starts the first transmission phase for the k + th block which is treated as interference by the destination as shown in Fig At the third transmission phase of the last block of codewords block N, the relay uses all its antennas as transmitter Accordingly, the relay adjusts the transmit powers and the weight components exactly as in and 4 Otherwise for blocks,, N, the relay uses two antennas to transmits signal t and t and one antenna to receive signal r at the third transmission phase, then the relay uses the ZFBF technique to mitigate self-interference Consequently, the relay 40

5 assigns the powers, P and P to transmit x, x and x respectively, which are obtained by substituting h, by in 4 In this case, the transmit powers are adjusted as follows: P = P P S h S, P = P S h S, 9 P = At the end of each TS, the relay multiplies the received signals vector with a pseudo-inverse matrix M =H H H to separate the codewords Hence, the SNs of the n th codewords at the destination and at the relay are γ n = γ n = 0 M n,i N+ i= i {t,t,r} P S h S,i, if n = P S h S,r, otherwise where M i,j is the component of matrix M located at the i th line and j th column The relay operates in F mode Consequently it is necessary for each transmission that the relay decodes correctly the received signal Hence, from 0, the end-to-end achievable data rate of the systems is given by: FAE = N + N log +min n= IV SIMULATION ESULTS γ n,γn In this section, we performed Monte Carlo simulations to evaluate the performance of the FAE scheme Then we compare it to FI scheme and H relaying scheme performances The performances are evaluated in terms of end-toend achievable data rate and BE The noise variance is set to = The distances between S and are equals The path loss component is set to α =4 We assume that the link between the S is poor but it is not negligible Indeed, the path loss ratio of link to S link is set to η = d α, =db d α S, Figures 4 and 5 show the end-to-end achievable data rate versus P S and P respectively for low d TS τ ie τ = d TS and high d TS τ ie τ = d TS Fig 4 considers a fixed value of P we assume P =0dB and Fig 5 considers a fixed value of P S we assume P S =0dB The FI results show the harmful effect of the interference signal received via direct link on the end-to-end achievable data rate It can be observed that at higher P to P S ratio, FI outperforms H relaying On the other hand, when P is much lower than P S, the direct link becomes considerable and hence the interference at the destination becomes higher In this case H relaying outperforms FI scheme For both figures, we observe that FAE End to end achievable data rate FAEτ=/ FAEτ=/ FIτ=/ FIτ=/ H relaying Transmit power of the source db Fig 4 End-to-end achievable data rate versus the transmission power of the source P =0dB End to end achievable data rate FAEτ=/ FAEτ=/ FIτ=/ FIτ=/ H relaying Transmit power of the relay db Fig 5 End-to-end achievable data rate versus the transmission power of the relay P S =0dB outperforms both FI scheme and H relaying scheme for all P S and P values We observe also that if P S to P ratio increases, the difference between FAE and FI on the endto-end achievable data rate becomes more important Indeed, at low P S, the end-to-end achievable data rate is limited by S link capacity, as explained in sub-section III-A Furthermore, when P S increases, the interference increases which harmfully affect the FI performance In FAE, when the processing delay τ decreases, the part of TS used by the relay to transmit signals increases and hence the achievable data rate increases, which is shown in Figs 4 and 5 However in FI, the endto-end achievable data rate increases as τ decreases, at low P to P S ratio, this is because the interference is high Thus, in this case, it is better that the relay transmits and receives 404

6 0 0 End to end achievable data rate 5 5 FAEτ=d TS / FAEτ=d TS / FIτ=d TS / FIτ=d TS / H relaying Path loss ratio of link to S link BE 0 0 FAEτ=d TS / FAEτ=d TS / FIτ=d TS / FIτ=d TS / Tranmit power of the relay db Fig 6 End-to-end achievable data rate versus the path loss ratio of link to S link P S = P =0dB Fig 7 BE versus the transmission power of the relay P S =0dB signals in orthogonal channels Fig 6 shows the end-to-end achievable data rate as function of η, the path loss ratio of link to S link, where the relay transmit powers and the source are set to P =0dB and P S =0dB respectively We observe that our proposed scheme FAE combines efficiently each signal and its delayed copy, when the path loss ratio of the to S link is low and medium when η<5db However, at very high η when η > 0dB, the direct link becomes negligible and hence the FAE scheme has a performance close to H relaying scheme Fig7 shows the BE versus the transmit power of the relay for the FAE and FI transmission schemes where the transmit power of the source is set to P S =0dB We observe that FAE outperforms FI We see also that the BE decreases and the diversity increases as τ increases V CONCLUSION In full duplex relaying, the destination suffers from interference caused by the received signal via direct link when the processing delay is not negligible In order to enhance the system end-to-end achievable data rate, we proposed a novel F relaying scheme based-on distributed Alamouti encoding which efficiently combines each signal and its delayed copy The relay operates in decode and forward mode The simulation results shows that H relaying outperforms FI at low relay transmit power to source transmit power ratio They also demonstrated that our proposed scheme FAE ensures the highest end-to-end achievable data rate and lower BE than FI for all ranges of source and relay transmit powers for wireless and mobile broadband radio, IEEE Commun Mag, vol 4, no 9, pp 80 89, Sept 004 [] A Sendonaris, E Erkip, and B Aazhang, User cooperation diversity part I & II, IEEE Trans Commun, vol 5, no, pp , Nov 00 [] T iihonen, S Werner, and Wichman, Comparison of full-duplex and half-duplex modes with a fixed amplify-and-forward relay, in Proc IEEE on Wireless Communications and Networking Conference WCNC, 009 [4] Y Y Kang and J H Cho, Capacity of MIMO wireless channel with full-duplex amplify-and-forward relay, in Proc IEEE on Personal, Indoor and Mobile adio Communications PIMC, 009 [5] Senaratne and C Tellambura, Beamforming for space division duplexing, in Proc IEEE International Conference on Communications ICC, 0 [6] T iihonen, A Balakrishnan, K Haneda, S Wyne, S Werner, and Wichman, Optimal eigenbeamforming for suppressing selfinterference in full-duplex MIMO relays, in Proc IEEE Conference on Information Sciences and Systems CISS, 0 [7] T iihonen, S Werner, and Wichman, Mitigation of loopback selfinterference in full-duplex MIMO relays, IEEE Trans Signal Process, vol 59, no, pp , ec 0 [8] T Kwon, S Lim, S Choi, and Hong, Optimal duplex mode for F relay in terms of the outage probability, IEEE Trans Veh Technol, vol 59, no 7, pp 68 64, Sept 00 [9] S Alamouti, A simple transmit diversity technique for wireless communications, IEEE J Sel Areas Commun, vol 6, no 8, pp , oct 998 [0] E riouch and W Ajib, Efficient scheduling algorithms for multiantenna cdma systems, IEEE Trans Veh Technol, vol 6, no, pp 5 5, Feb 0 [] K Marvin and M Alouini, igital Communication Over Fading Channels John Wiley and Sons, 000 [] Paulraj, A Nabar and Gore, Introduction to Space-Time Wireless Communications Press, 00 [] J Winters, Optimum combining in digital mobile radio with cochannel interference, IEEE J Sel Areas Commun, vol, no 4, pp 58 59, July 984 EFEENCES [] Pabst, B Walke, Schultz, P Herhold, H Yanikomeroglu, S Mukherjee, H Viswanathan, M Lott, W Zirwas, M ohler, H Aghvami, Falconer, and G Fettweis, elay-based deployment concepts 405