Abstract
Multiple input multiple output (MIMO) dual-hop relay systems in delay spread channels are analyzed in this work. The delay spread channel caused by multipath phenomenon in radio propagation is a major reason of intersymbol interference (ISI), increasing bit error ratio (BER) significantly at large enough delay time. To solve this problem, a joint of linear precoder and decoder is designed using unweighted minimum mean-squared error (MMSE) criterion for the system in two proposed schemes. The relay in Scheme 1 has none of the precoder and the decoder whereas that in Scheme 2 has both of them. System performance is evaluated in both perfect and imperfect channel state information (CSI) conditions. With the perfect CSI, the system is analyzed under effects of parameters such as modulation order, data block size, and delay tap numbers to form the basis for selecting their values. With the imperfect CSI, factors including correlation coefficients and estimation error variances are considered to evaluate their effects on the system performance. Simulation results show that BER of Scheme 1 is better with the perfect CSI but more sensitive to CSI errors than that of Scheme 2 is. Which scheme is suitable for a practical system it depends on a trade-off between complexity of the system and accuracy of the channel estimation.







Similar content being viewed by others
References
Kaur, H., Khosla, M., & Sarin, R. K. (2018). Channel estimation in a MIMO relay system: Challenges & approaches. The 2nd international conference on inventive systems and control. https://doi.org/10.1109/ICISC.2018.8399065.
Ubaidulla, P., & Chockalingam, A. (2011). Relay precoder optimization in MIMO-relay networks with imperfect CSI. IEEE Transactions on Signal Processing, 59(11), 5473–5484.
Mo, R., Chew, Y. H., & Yuen, C. (2012). Information rate and relay precoder design for amplify-and-forward MIMO relay networks with imperfect channel state information. IEEE Transactions on Vehicular Technology, 61(9), 3958–3968.
Lee, N., Park, H., & Chun, J. (2008). Linear precoder and decoder design for two-way AF MIMO relaying system. IEEE vehicular technology conference. https://doi.org/10.1109/VETECS.2008.258
Jayasinghe, L. K. S., Rajatheva, N., & Latva-aho, M. (2012). Joint pre-coder and decoder design for physical layer network coding based MIMO two-way relay system. IEEE international conference on communications. https://doi.org/10.1109/ICC.2012.6364770
Tseng, F.-S., & Wu, W.-R. (2010). Linear MMSE transceiver design in amplify-and-forward MIMO relay systems. IEEE Transactions on Vehicular Technology, 59(2), 754–765.
Toding, A. (2019). Minimum MSE criteria design of amplify-and-forward MIMO relay wireless communication system. Journal of Advanced Research in Dynamical & Control Systems, 11(07), 644–649.
Arslan, H., & Yücek, T. (2003). Delay spread estimation for wireless communication systems. The 8th IEEE symposium on computers and communications. https://doi.org/10.1109/ISCC.2003.1214135.
Pahlavan, K., & Levesque, A. H. (2005). Characterization of radio propagation. Wireless information networks (pp. 55–64). New Jersey: Wiley.
Sampath, H., Stoica, P., & Paulraj, A. (2001). Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion. IEEE Transactions on Communications, 49(12), 2198–2206.
Mo, R., Chew, Y. H., & Yuen, C. (2011). Relay precoder designs for amplify-and-forward MIMO relay networks with imperfect channel state information. The 73rd IEEE vehicular technology conference. https://doi.org/10.1109/VETECS.2011.5956488.
Liang, X., Ding, Z., & Xiao, C. (2012). On linear precoding of non-regenerative MIMO relays for QAM inputs. IEEE international conference on communications. https://doi.org/10.1109/ICC.2012.6364642
Huang, Y., Yang, L., Bengtsson, M., & Ottersten, B. (2010). A limited feedback joint precoding for amplify-and-forward relaying. IEEE Transactions on Signal Processing, 58(3), 1347–1357.
Rong, Y., & Hua, Y. (2009). Optimality of diagonalization of multi-hop MIMO relays. IEEE Transactions on Wireless Communications, 8(12), 6068–6077.
Zhang, Y., Li, J., Pang, L., & Ding, Z. (2011). On precoder design for amplify-and-forward MIMO relay systems. IEEE vehicular technology conference. https://doi.org/10.1109/VETECF.2011.6092954
Benkhelifa, F., & Alouini, M.-S. (2017). Precoding design of MIMO amplify-and-forward communication system with an energy harvesting relay and possibly imperfect CSI. IEEE Access. https://doi.org/10.1109/ACCESS.2016.2646387
Danaee, A., & Bahrami, H. R. (2011). Precoder and decoder design for SNR maximization in amplify-and-forward (AF) MIMO relay systems. IEEE vehicular technology conference. https://doi.org/10.1109/VETECF.2011.6093265
Zhang, J., Bao, W., Zhang, P., & Wang, Q. (2012). Joint source-relay precoder and decoder designs for amplify-and-forward MIMO relay system with imperfect channel state information. IEEE vehicular technology conference. https://doi.org/10.1109/VTCFall.2012.6398988
Singh, K., Ku, M.-L., & Lin, J.-C. (2013). A two-dimensional MMSE equalizer for MIMO relay networks in multipath fading channels. IEEE wireless communications and networking conference. https://doi.org/10.1109/WCNC.2013.6555081
Ying, K., Qian, H., Baxley, R. J., & Yao, S. (2015). Joint optimization of precoder and equalizer in MIMO VLC systems. IEEE Journal on Selected Areas in Communications, 33(9), 1949–1958. https://doi.org/10.1109/JSAC.2015.2432515
Rottenberg, F., Mestre, X., Horlin, F., & Louveaux, J. (2017). Single-tap precoders and decoders for multiuser MIMO FBMC-OQAM under strong channel frequency selectivity. IEEE Transactions on Signal Processing, 65(3), 587–600. https://doi.org/10.1109/TSP.2016.2621722
Castanheira, D., Teodoro, S., Simões, R., Silva, A., & Gameiro, A. (2019). Multi-user linear equalizer and precoder scheme for hybrid sub-connected wideband systems. Electronics. https://doi.org/10.3390/electronics8040436
Doanh, B. Q., Quan, D. T., Hiep, P. T., & Hieu, T. C. (2019). A combining design of precoder and equalizer based on shared redundancy to improve performance of ISI MIMO systems. Wireless Networks, 25, 2741–2750.
Doanh, B. Q., Quan, D. T., Hiep, P. T., & Hieu, T. C. (2019). An efficient design of precoding and equalization to reduce BER of multi-path MIMO channels. The 3rd international conference on recent advances in signal processing, telecommunications & computing (SigTelCom). https://doi.org/10.1109/SIGTELCOM.2019.8696166.
Doanh, B. Q., Hiep, P. T., & Hieu, T. C. (2019). Impact of imperfect CSI on Capacity of ISI MIMO systems based on joint precoding and equalization designs. The 19th international symposium on communications and information technologies (ISCIT). https://doi.org/10.1109/ISCIT.2019.8905137.
Doanh, B. Q., Hieu, T. C., Nam, T. S., Anh, P. T. P., & Hiep, P. T. (2020). Performance analysis of joint precoding and equalization design with shared redundancy for imperfect CSI MIMO systems. Advances in Science, Technology and Engineering Systems Journal, 5(3), 142–149.
Xing, C., Ma, S., & Wu, Y.-C. (2010). Robust joint design of linear relay precoder and destination equalizer for dual-hop amplify-and-forward MIMO relay systems. IEEE Transactions on Signal Processing, 58(4), 2273–2283.
Athaudage, C. R. N., & Jayalath, A. D. S. (2004). Delay-spread estimation using cyclic-prefix in wireless OFDM systems. IEE proceedings-communications. https://doi.org/10.1049/ip-com:20040551
Krivochiza, J., Merlano-Duncan, J. C., Chatzinotas, S. & Ottersten, B. (2019 ). M-QAM modulation symbol-level precoding for power minimization: Closed-form solution. The 16th international symposium on wireless communication systems (ISWCS). https://doi.org/10.1109/ISWCS.2019.8877286.
Musavian, L., Nakhai, M. R., Dohler, M., & Aghvami, A. H. (2007). Effect of channel uncertainty on the mutual information of MIMO fading channels. IEEE Transactions on Vehicular Technology, 56(5), 2798–2806.
Funding
The authors declare that they have no funding.
Author information
Authors and Affiliations
Contributions
Ms Huong implemented Matlab simulation and Mr Hiep introduced system model.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Huong, T.T.T., Hiep, P.T. Joint Precoder and Decoder for MIMO Dual-Hop Relay Systems in Delay Spread Channels. Wireless Pers Commun 124, 1247–1261 (2022). https://doi.org/10.1007/s11277-021-09404-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-021-09404-0