Log-Likelihood Ratio-based Relay Selection Algorithm in Wireless Network

Recent Advances in Electrical Engineering and Electronic Devices Log-Likelihood Ratio-based Relay Selection Algorithm in Wireless Network Ahmed El-Mahdy and Ahmed Walid Faculty of Information Engineering & Technology, German University in Cairo, Egypt ahmed.elmahdy@guc.edu.eg and ahmed.zenhom@student.guc.edu.eg Abstract Cooperative communication describes strategies to transfer the data from a source to a destination by employing relay nodes between them. It is considered as one of the most efficient techniques to overcome fading in wireless networks since it can achieve spatial diversity. Employing all the relays in the network to transfer the data, consumes high power and cost. Selection of one or more relays reduces the complexity, decreases the power consumption and reduces the interference. In this paper, with these goals in mind, a relay selection algorithm is proposed in a slow flat fading channel. The algorithm is based on evaluating the log-likelihood ratio of all relays and the relay which has the largest magnitude of log-likelihood ratio (LLR) is selected to help the source to transmit the data to the destination. The performance of the algorithm is evaluated by simulation and compared with other relay selection algorithms. The performance is measured in terms of bit error rate (BER) and outage probability. Both decode and forward and amplify and forward protocols are investigated. The performance is evaluated for known and estimated channel. The channel is estimated using least square algorithm. The performance of channel estimation algorithm is measured in terms of the mean square error. The results show that the LLR algorithm minimizes bit error probability (BEP) and BEP provided by LLR-based selection combining algorithm is lower than BEP provided by the conventional SNR-based selection combining schemes. Keywords Cooperative communication, Wireless Systems, log-likelihood ratio, generalized selection combining, selection combining. 1. Introduction Wireless communication has become the fastest growing segment of the telecommunications market nowadays. It was crucial to develop ways to improve the performance of the wireless systems in order to get better received signal to support high data rates with maintaining the required quality of service with less fading losses and power consumption. Fading in wireless communication can be overcome by the use of spatial diversity. It improves the performance of the digital communication systems by transmitting the same information over independent channels separated in space. Cooperative Communications can efficiently combat the severity of fading by the use of spatial diversity, increase spectrum efficiency, increase coverage area and improve the system performance in wireless communications through the assistance of the relays that are deployed between source and destination. Signals travelling via the relays experience less power attenuation thus improving the received signal strength. The relaying technology provide two main advantages where very low transmit radio frequency power is required and the use of multiuser diversity as diversity combining is an efficient method for improving the performance of communication systems over fading channels. Several algorithms are introduced to select one relay or more than one relay for power saving purposes. The conventional relay selection rule selects M out of L relays where L is the total number of relay branches providing the largest instantaneous signal to noise ratio (ISNR). This is called SNRbased relay selection algorithm or Best Relay Selection investigated in [1]. In [2], the authors proposed opportunistic relaying where the best relay node is selected based on the best end-to-end performance between the source and the destination nodes. This scenario happens when all the relay nodes are maintaining a listening mode so that the relays can over hear the ready-to-send (RTS) packet from the source node to all neighboring nodes and the destination node sends a clear-to-send (CTS) packet to its neighboring nodes through which the relay nodes collect the instantaneous channel state information (CSI) from the source to the relay and from the relay to the destination. The best relay k is chosen according to: { }, where is the fading amplitude of the channel between source and relay i and is the fading amplitude of the channel between relay i and destination. In [3], the authors proposed a relay selection algorithm called switched relay selection that chooses a relay node based on a predetermined threshold that guarantees a satisfying performance. This algorithm compares all the received instantaneous signal to noise ratio (ISNR) at the relay and at the destination which are denoted by and with a predetermined threshold which is chosen to guarantee a satisfying performance. Then, ISNR of each relay is compared to if is greater than or equal to then is compared to if is greater than or equal to then the chosen relay is. If the ISNR of all the relays fail to pass the threshold, the max min rule is used to select the relay according to the equation ( { }). In [4], the authors ISBN: 978-1-61804-266-8 157

Recent Advances in Electrical Engineering and Electronic Devices proposed partial relay selection algorithm which does not require knowing the whole channel state information. The algorithm is based only on the received SNR from the source to the relay, then the best relay k is chosen according to:. The authors in [5] use rate distortion theory to investigate the overhead performance tradeoff for relay selection in cooperative networks. The system considered in this paper has N relays, a single antenna and is only capable of half duplex transmission. In the first stage the information is sent from the transmitter to the relay nodes. Then in the second stage the relay with the maximum channel power gain from the relay to the destination is chosen which means that only one relay transmits the information according to the rule where j is the chosen relay and is the channel gain coefficient from the relay to the destination. In this paper, a relay selection algorithm is proposed and is based on the calculation of LLR which is not considered before. The algorithm selects M out of L relays providing the largest log-likelihood ratio (LLR) magnitude for retransmission and forwarding the information to the destination. The motivation for using LLR in selecting relays is that the magnitude of LLR provides the reliability of hard decision. LLR-based relay selection algorithm minimizes the bit error probability (BEP) and provides BEP lower than the BEP provided by the conventional SNR-based relay selection algorithm described above. LLR-based algorithm enhances the performance by choosing the most reliable relay for detection. The rest of the paper is organized as follows: In Section II, the system model is described including the used two relaying protocols. Section III, the proposed LLR-based relay selection algorithm is presented. Section IV, channel estimation algorithm is described. Simulation and results are presented in section V. Finally, the conclusions are explained in Section VI. 2. SYSTEM MODEL The system consists of a two-hop network model where there is one source, one destination and L relays as shown in Fig.1. The source, relays, and the destination are deployed with single antenna working in the half duplex mode. The system includes a direct communication link between the source and the destination. The considered noise is additive white Gaussian noise (AWGN). The fading channel coefficients from source-to-destination, source-to- relay, and relayto-destination links are respectively denoted by respectively. The channel coefficients are assumed to be independent and identically distributed slow flat Rayleigh fading channels [6]. Each transmission is divided into two time slots [7]. During the first time slot, the source sends the signal to the relays and also to the destination terminal (direct link). Therefore, the received signal at relay terminal from the source terminal is given by: Fig.1. System model where is the transmitted signal which is assumed to be BPSK signal with amplitudes either + and. The received signal at destination terminal from the source terminal due to direct communication link is given by: where are the independent complex Gaussian fading channel parameters of the S-D link and S-R link respectively with zero mean and variances of and respectively. are the additive white Gaussian noise of the S-D link and S-R link with zero mean and variances of and respectively. In the second time slot, each relay retransmits the signal to the destination using either decode and forward or amplify and forward protocols. A brief description of these protocols is presents as follows. 2.1 Decode and forward protocol (DF) During the second time slot in decode and forward technique (DF), each relay first demodulates and decodes the received signal. Upon success, each relay re-encodes the signal data and forwards it to the destination. The destination node will combine all the signals coming from all the relays for detection. Therefore the received signal at the destination from relay is given by: where (1) (2) (3) is the re-encoded signal at the relay terminals. is the independent complex Gaussian fading channel parameter of the R-D link with zero mean and variance of. is the additive white Gaussian noise of the R-D link with zero mean and variance of. The destination in DF receives less noisy versions of signal compare to AF. ISBN: 978-1-61804-266-8 158

Recent Advances in Electrical Engineering and Electronic Devices 2.2 Amplify and forward protocol (AF) During the second time slot in amplify and forward technique (AF), each relay multiplies its received signal by a gain and forwards the amplified signal to the destination. The disadvantage of this method is that the noise at the relay will get amplified. This method is often used when the relays have limited resources, e.g. processing time or power limitations or when the source-relay channel is weak. Therefore the received signal at the destination from relay is given by: [ ] [ ] where is the gain of relay which is given by [7] : (4) (5) where is the transmitted signal power and is the power spectral density. 3. PROPOSED LLR BASED RELAY SELECTION ALGORITHM 3.1 Derivation of the proposed algorithm At the first time slot the source broadcasts the BPSK signal to the relays and to the destination using equations (1) and (2). At the second time slot, the relays receive the transmitted signal from the source, the log-likelihood ratio (LLR) is calculated for each relay and it is given by: where the sign of is the hard decision value and the magnitude represents the reliability of the hard decision which is used to choose the most reliable relay for detection. and are the probability density function (pdf) of the observation at the relays given the channel and the transmitted signal. Using (1) and knowing that the additive noise is AWGN and the channel is complex, then these probability density functions can be written as: ( ) = ( ) = (6) (7) (8) Substituting (7) and (8) into (6), the LLR in its simplest form is given by { } { } Then, the magnitude of LLR written as in its simplest form can by { } (10) Where represents the real part, represents the complex conjugate and represents the magnitude of the equation. 3.2. Description of the algorithm In this section, the proposed relay selection algorithm is described. The algorithm starts with the calculation of the magnitude of the LLR given in (10) for each relay in the system. Then, the values of the LLR is arranged in descending order and we select the first M relays from L corresponding to the largest magnitude of the LLR (the first M values). These M relays are chosen to send the signal to the destination using either DF or AF. If M=1, only one relay is selected which has the maximum magnitude of LLR and this scenario is called LLR-based SC. This relay sends the signal to the destination and the destination combines its signal with the direct link signal coming from the source. Since increasing the number of operating relays reduces the BEP, the LLR-based SC has the worst performance among other scenarios that will be mentioned later but it has several advantages as it has low complexity and power consumption among the other scenarios. If M<L, only the best M relays are chosen which have the largest magnitude of LLR among all relays and this scenario is called LLR-based generalized selection combining (GSC). The selected relays send their signals to the destination in the second hope but in different time slots to prevent the interference between them. The destination combines the signals received from them with the signal received through the direct link (between the source and destination). LLR-based GSC is less complex than combining all relays and has better performance than LLR-based SC. The performance of LLR-based SC and LLR-based GSC is evaluated and compared with the performance with combining all the relays using maximal ratio combining (MRC). We mentioned that LLR-based relay selection algorithm in general has several benefits since it enhances the system performance by choosing the most reliable relay for detection therefore, reducing the bit error probability. ISBN: 978-1-61804-266-8 159

BER Recent Advances in Electrical Engineering and Electronic Devices BER for LLR-MRC BER for LLR-SC BER for LLR-GSC BER for SNR-MRC BER for SNR-GSC BER for SNR-SC Fig.2 Channel estimation 2 4 6 8 10 12 14 16 18 20 Fig.3. Comparison between the performance of relay selection algorithm based on LLR and relay selection algorithm based on SNR in DF mode. 4. CHANNEL ESTMATION In practical systems, the fading channel is unknown and the receiver estimates it. Channel estimation is performed by least square estimation (LSE) algorithm and its performance is measured in terms of mean square error (MSE). The scenario of channel estimation is performed as follows. The source sends a ready-to-send (RTS) request to all the relays and the relays respond by sending back a clear-to-send (CTS) request in order for the source to be able to send a training sequence as shown in Fig.2. The received training sequence at the relays in vector form signal vector can be written as: (11) where is a training sequence vector which contains the training bits. is the true channel between the source and relay i, and is the noise vector between the source and relay i. Since the relays know the training sequence, then the relays obtain the estimated channels of the S-R link using the LSE algorithm given by: (12) The same procedure is used to obtain the estimated channels between the relays and the destination and in the direct link between the source and the destination. The performance of the least square algorithm is measured in terms of mean square error (MSE). MSE calculates the average of the error difference between the true and estimated fading channels in the system. The MSE is given by: (13) where is the estimated channel fading parameter, is the true channel fading parameter. L is the total number of relay branches. 2L is the number relay channels used on both sides of the relays. (2L+1) is the total number of channels used including channels on both sides of the relays added to the direct link channel from the source to the destination. 5. SIMULATION AND RESULTS In this section, numerical results are presented to evaluate the performance of the proposed relay selection algorithm based on Log Likelihood ratio (LLR). The performance of the system is measured in terms of the bit error rate (BER) versus SNR. The results are obtained for perfect and estimated channels. The channels are modeled by slow flat fading Rayleigh channels. Both decode and forward (DF) and amplify and forward (AF) protocols are investigated. The simulation parameters are as follows. The number of bits for the transmitted signal is =10,000, the type of modulation used is binary phase shift key (BPSK), the number of relays L=4 and the length of the training sequence used for channel estimation is 10 bits. Number of GSC combined branches = L/2 = 2. Fig.3 and Fig.4 show a comparison between BER performance of the proposed relay selection algorithm based on loglikelihood ratio and the conventional relay selection algorithm based on signal to noise ratio (SNR). Both GSC and SC schemes are provided and the MRC is also plotted as a lower bound in performance. Fig.3 is plotted for DF mode and Fig.4 is plotted for AF mode. The figures show that the BER of the schemes based on LLR algorithm is lower than the BER of the schemes based on SNR-based algorithm. Therefore LLRbased relay selection algorithm has better performance than the conventional SNR-based relay selection algorithm. These figures also show that LLR-GSC has the better performance than LLR-SC. This is because SC selects only one relay and ISBN: 978-1-61804-266-8 160

BER Recent Advances in Electrical Engineering and Electronic Devices BER for LLR-MRC BER for LLR-SC BER for LLR-GSC BER for SNR-MRC BER for SNR-GSC BER for SNR-SC 2 4 6 8 10 12 14 16 18 Fig.4. Comparison between the performance of relay selection algorithm based on LLR and relay selection algorithm based on SNR in AF mode. Fig.5. The absolute of perfect and estimated channel from source to first relay GSC system combines L/2 relays and this is enhances the performance. This is also the reason that the LLR-MRC is the best performance over all systems since it combines all the relays. All the channels between the source and the relays, between the relays and the destination and between the source and destination are estimated using least square algorithm. We present only one channel as an example. The absolute of perfect and estimated channel between the source and the first relay is shown in Fig.5. The figure shows that at low SNR, the noise is high and dominates the performance. Therefore there is a gap between the perfect and estimated channel. But as SNR increases, the estimated channel converges with the true one. Fig.6 shows Mean Square Error (MSE) between perfect and estimated channels. As SNR increases, the MSE decreases and the performance gets better. Fig.7 and Fig.8 express a comparison between the BER performance of LLR-based GSC and LLR-based SC with the MRC in both perfect and estimated channels. Fig.7 is plotted for DF mode and Fig.8 is plotted for AF mode. The figures show that the BER of the three for perfect channel outperforms the BER for estimated channel at the beginning. This is because of the channel estimation error that affects the BER. Therefore at low SNR values, the error is high so there is a gap between performance with perfect channel and performance with estimated channel. But as SNR increases, the estimated channel converges with the true one and the performance gets better. 6. CONCLUSION In this paper, the performance of relay selection based on loglikelihood ratio has been investigated through using GSC and SC schemes and their performance has been compared with the traditional MRC scheme. Therefore LLR-based relay selection algorithm has better performance than the Fig.6.The Mean Square Error (MSE) between perfect and estimated channels. conventional SNR-based relay selection algorithm. As the number of operating relays increases, the performance improves. Therefore, MRC has the best performance followed by LLR-based GSC followed by LLR-based SC. The results have been shown that a reduction in complexity, interference and power consumption is achieved when using LLR-based GSC and LLR-based SC at the expense of slight performance degradation compared to MRC. Channel estimation has been evaluated using least square algorithm and its performance has been measured in terms of men square error (MSE). The results of using channel estimation showed that due to strong noise at low SNR values, there was error and so the estimated channel doesn t converge with the perfect channel but as the SNR increases, the two channels finally converge. Therefore the performance gets better and the MSE between the estimated and true channel decreases. ISBN: 978-1-61804-266-8 161

BER BER Recent Advances in Electrical Engineering and Electronic Devices BER for LLR-based MRC BER for LLR-based MRC Estimate BER for LLR-based SC BER for LLR-based GSC BER for LLR-based GSC Estimate BER for LLR-based SC Estimate BER for LLR-based MRC BER for LLR-based MRC Estimate BER for LLR-based SC BER for LLR-based SC Estimate BER for LLR-based GSC BER for LLR-based GSC Estimate -5 0 5 10 15 20 25 Fig.7.Comparison between the performance of the three schemes based on LLR between perfect and estimated channel in DF mode. -5 0 5 10 15 20 25 30 Fig.8.Comparison between the performance of the three schemes based on LLR between perfect and estimated channel in AF mode. REFERENCES [1] A. Bletsas, A. khisti, D. P. Reed, and A. Lippman, " A simple Cooperative diversity method based on network path selection," IEEE Journal on Selected Areas in Communications, vol. 24, pp.659-672, March 2006. [2] Adam, H.; Bettstetter, C.; Senouci, S.M., "Adaptive relay selection in cooperative wireless networks," Personal, Indoor and Mobile Radio Communications, 2008. PIMRC 2008. IEEE 19th International Symposium on, vol., no., pp.1,5, 15-18 Sept. 2008 [3] Kyu-Sung Hwang; Young-chai Ko; Alouini, M.-S., "Low Complexity Cooperative Communication with Switched Relay Selection and Adaptive Modulation," Vehicular Technology Conference, 2009. VTC Spring 2009. IEEE 69th, vol., no., pp.1, 5, 26-29 April [4] A. Eksim, M. E. Celebi, " Comparison of Cooperative Path Selection Techniques, " IEEE 15th Signal Processing and Communications Applications, 2007. SIU 2007, pp.1-4, June 2007. [5] L. Pan; H. C. Cheng, and J. F. An, "ML-based selection relay with transmission power constraint," 12th International Conference on ITS Telecommunications (ITST), 2012,pp.242-247, Nov.2012. [6] Theodore S. Rappaport, "Wireless Communications: Principles and Practice," 2nd Edition, Prentice Hall, pp.138-195, Dec. 31, 2001. [7] K. J. Ray Liu, A. K. Sadek, W. Su, and A. Kwasinski, "Cooperative Communications and Networking," pp.119-253, Cambridge University Press, 2009. ISBN: 978-1-61804-266-8 162