MSMSE-based optimal beamforming design and simplification on AF MIMO two-way relay channels

Abstract

An optimal cooperative beamforming for the amplify-and-forward (AF) MIMO two-way relay channels was designed. Supposing the channel state information (CSI) was perfectly known by the receiver and transmitter as well as the relay, optimal beamforming vectors (matrices) of all nodes were jointly designed based on the criterion of minimizing the sum mean square errors (MSMSE). The analysis result shows that the performance effect of transmitting and receiving beamforming pairs is to maximize the receive signal-to-noise ratio (SNR) at two communication nodes, and the rank of the optimal relay beamforming matrix is no larger than two when there is only one data stream at each source node. A simplified algorithm was put forward to accomplish the design based on the analysis conclusions. Simulation results provide that the system performance, which is characterized in terms of bit error rates (BER), is significantly improved by cooperative beamforming, and the performance of the simplified method is not only very close to the optimal one but also with faster iteration speed and much lower computational complexity.

Keywords

beamforming / two-way relay channels / amplify-and-forward / multiple input multiple output

References

[1] LanemanJ. N., TseD. N. C., WornellG. W.. Cooperative diversity in wireless networks: Efficient protocols and outage behavior [J]. IEEE Transaction Information Theory, 2004, 50(12): 3062-3080

[2] BolcskeiH.. Capacity scaling laws in MIMO relay networks [J]. IEEE Trans Wireless Commun, 2006, 5(6): 1433-1444

[3] WYREMBELSKI R, OECHTERING T, BJELAKOVIC I. Capacity of Gaussian MIMO bidirectional broadcast channels [C]// IEEE International Symposium on Information Theory. 2008: 584–588.

[4] VAZE R, HEATH R. Optimal amplify and forward strategy for two-way relay channel with multiple relays [C]// IEEE Information Theory Workshop on Networking and Information Theory. 2009: 181-185.

[5] ShiH., AbeT., AsaiT., YoshinoH.. Relaying schemes using matrix triangularization for MIMO wireless networks [J]. IEEE Trans Commun, 2007, 25(2): 1683-1688

[6] YiZ., KimI. M.. Joint optimization of relay-precoders and decoders with partial channel side information in cooperative networks [J]. IEEE J Select Areas Commun, 2007, 25(2): 379-389

[7] KramerG., GastparM., GuptaP.. Cooperative strategies and capacity theorems for relay networks [J]. IEEE Transaction Information Theory, 2005, 51(9): 23037-3063

[8] LIANG Ying-chang, ZHANG Rui. Optimal analogue relaying with multi-antennas for physical layer network coding [C]// IEEE International Conference on Communication, 2008: 3893–3897.

[9] ZhengL., TseD. N. C.. Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels [J]. IEEE Transaction Information Theory, 2003, 49(5): 1073-1096

[10] WangB., ZhangJ., Host-madsenA.. On the capacity of MIMO relay channels [J]. IEEE Transaction Information Theory, 2005, 51(1): 29-43

[11] JingY.-d., JafarkhaniH.. Network beamforming using relays with perfect channel information [J]. IEEE Transaction Information Theory, 2009, 55(6): 2499-2517

[12] JING Yin-di, JAFARKHANI H. Network beamforming using relays with perfect channel information [C]// IEEE International Conference on Acoustics, Speech and Signal Processing, 2007: 473–476.

[13] KIM S, CHUN J. Network coding with linear MIMO pre-equalizer using modulo in two-way channel [C]// IEEE Wireless Communications and Networking Conference. 2008: 517–521.

[14] ZhangR., LiangY., ChaiC. C., CuiS.. Optimal beaforming for two-way multi-antenna relay channel with analogue network coding [J]. IEEE J Select Areas Commun, 2009, 27(5): 699-712

[15] JoungJ., SayedA. H.. Multiuser two-way amplify-and-forward relay processing and power control methods for beamforming systems [J]. IEEE Transaction Signal Process, 2010, 58(3): 1833-1846

[16] SampathH., StoicaP., PaulrajA.. Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion [J]. IEEE Transaction Commun, 2001, 49(12): 2198-2206

[17] LEE N, PARK H, CHUN J. Linear precoder and decoder design for two-way of MIMO relaying system [C]// IEEE Vehicular Technology Conference. 2008: 1221–1225.

[18] LEE K, LEE K W, SUNG H, LEE I. Sum-rate maximization for two-way MIMO amplify-and-forward relaying systems [C]// IEEE Vehicular Technology Conference. 2009: 26–29.

[19] LeeK., SungH., ParkE., LeeI.. Joint Optimization for one and two-way MIMO AF multiple-relay systems [J]. IEEE Transaction Wireless Commun, 2010, 9(12): 3671-3681

[20] LutkepohlH.Handbook of matrices [M], 1996, New York, Wiley