Adaptive robust beamformer formulti-pair two-way relay networks with imperfect channel state information

Abstract

In wideband multi-pair two-way relay networks, the performance of beamforming at a relay station (RS) is intimately related to the accuracy of the channel state information (CSI) available. The accuracy of CSI is determined by Doppler spread, delay between beamforming and channel estimation, and density of pilot symbols, including transmit power of pilot symbols. The coefficient of the Gaussian-Markov CSI error model is modeled as a function of CSI delay, Doppler spread, and signal-to-noise ratio, and can be estimated in real time. In accordance with the real-time estimated coefficients of the error model, an adaptive robust maximum signal-to-interferenceand- noise ratio (Max-SINR) plus maximum signal-to-leakage-and-noise ratio (Max-SLNR) beamformer at an RS is proposed to track the variation of the CSI error. From simulation results and analysis, it is shown that: compared to existing non-adaptive beamformers, the proposed adaptive beamformer is more robust and performs much better in the sense of bit error rate (BER); with increase in the density of transmit pilot symbols, its BER and sum-rate performances tend to those of the beamformer of Max-SINR plus Max-SLNR with ideal CSI.

Keywords

Multi-pair two-way relay / Adaptive robust beamformer / Channel state information (CSI) / Maximum signal-to-interference-and-noise ratio (Max-SINR) / Maximum signal-to-leakage-and-noise ratio (Max-SLNR)

References

[1] Aziz, A., Thron, C., Cui, S.G., , 2014. Linearized robust beamforming for two-way relay systems. IEEE Signal Process. Lett., 21(8):1017–1021. http://dx.doi.org/10.1109/LSP.2014.2322118

[2] Baddour, K.E., Beaulieu, N.C., 2003. Nonparametric Doppler spread estimation for flat fading channels. Proc. IEEE Wireless Communications and Networking Conf., p.953–958. http://dx.doi.org/10.1109/WCNC.2003.1200500

[3] Chalise, B.K., Vandendorpe, L., 2009. MIMO relay design for multipoint-to-multipoint communications with imperfect channel state information. IEEE Trans. Signal Process., 57(7):2785–2796. http://dx.doi.org/10.1109/TSP.2009.2018610

[4] Chen, Y., Shu, F., Wang, J., , 2014. High-performance beamforming and spatial channel pairing schemes at relay station for AF-based multi-pair two-way relay networks. Proc. 6th Int. Conf. on Wireless Communications and Signal Processing, p.1–4.http://dx.doi.org/10.1109/WCSP.2014.6992011

[5] Cover, T., Gamal, A.E., 1979. Capacity theorems for the relay channel. IEEE Trans. Inform. Theory, 25(5):572–584. http://dx.doi.org/10.1109/TIT.1979.1056084

[6] Degenhardt, H., Klein, A., 2012. Self-interference aware MIMO filter design for non-regenerative multi-pair twoway relaying. Proc. IEEE Wireless Communications and Networking Conf., p.272–276. http://dx.doi.org/10.1109/WCNC.2012.6214264

[7] Holtzman, J.M., Sampath, A., 1995. Adaptive averaging methodology for handoffs in cellular systems. IEEE Trans. Veh. Technol., 44(1):59–66. http://dx.doi.org/10.1109/25.350270

[8] Ijaz, A., Awoseyila, A.B., Evans, B.G., 2011. Low-complexity time-domain SNR estimation for OFDM systems. Electron. Lett., 47(20):1154–1156. http://dx.doi.org/10.1049/el.2011.2014

[9] Knopp, R., 2007. Two-way wireless communication via a relay station. GDR-ISIS Meeting.

[10] Kramer, G., Gastpar, M., Gupta, P., 2005. Cooperative strategies and capacity theorems for relay networks. IEEE Trans. Inform. Theory, 51(9):3037–3063. http://dx.doi.org/10.1109/TIT.2005.853304

[11] Laneman, J.N., Wornell, G.W., 2003. Distributed spacetime-coded protocols for exploiting cooperative diversity in wireless networks. IEEE Trans. Inform. Theory, 49(10):2415–2425. http://dx.doi.org/10.1109/TIT.2003.817829

[12] Mao, J.L., Gao, J.C., Liu, Y.A., , 2012. Robust multiuser MIMO scheduling algorithms with imperfect CSI. Sci. China Inform. Sci., 55(4):815–826. http://dx.doi.org/10.1007/s11432-011-4388-3

[13] Popovski, P., Yomo, H., 2006. Bi-directional amplification of throughput in a wireless multi-hop network. Proc. IEEE 63rd Vehicular Technology Conf., p.588–593. http://dx.doi.org/10.1109/VETECS.2006.1682892

[14] Rankov, B., Wittneben, A., 2007. Spectral efficient protocols for half-duplex fading relay channels. IEEE J. Sel. Areas Commun., 25(2):379–389. http://dx.doi.org/10.1109/JSAC.2007.070213

[15] Sadek, M., Tarighat, A., Sayed, A.H., 2007. A leakagebased precoding scheme for downlink multi-user MIMO channels. IEEE Trans. Wirel. Commun., 6(5):1711–1721. http://dx.doi.org/10.1109/TWC.2007.360373

[16] Sendonaris, A., Erkip, E., Aazhang, B., 2003. User cooperation diversity. Part I: system description. IEEE Trans. Commun., 51(11):1927–1938. http://dx.doi.org/10.1109/TCOMM.2003.818096

[17] Shen, H., Wang, J.H., Levy, B.C., , 2013. Robust optimization for amplify-and-forward MIMO relaying from a worst-case perspective. IEEE Trans. Signal Process., 61(21):5458–5471. http://dx.doi.org/10.1109/TSP.2013.2278819

[18] Shu, F., Chen, Y., You, X.H., , 2014a. Low-complexity optimal spatial channel pairing for AF-based multi-pair two-way relay networks. Sci. China Inform. Sci., 57(10):1–10. http://dx.doi.org/10.1007/s11432-014-5102-z

[19] Shu, F., Lu, Y.Z., Chen, Y., , 2014b. High-sumrate beamformers for multi-pair two-way relay networks with amplify-and-forward relaying strategy. Sci. China Inform. Sci., 57(2):1–11. http://dx.doi.org/10.1007/s11432-013-4980-9

[20] Tepedelenlioglu, C., Giannakis, G.B., 2001. On velocity estimation and correlation properties of narrow-band mobile communication channels. IEEE Trans. Veh. Technol., 50(4):1039–1052. http://dx.doi.org/10.1109/25.938579

[21] Wang, C., Au, E.K.S., Murch, R.D., , 2007. On the performance of the MIMO zero-forcing receiver in the presence of channel estimation error. IEEE Trans. Wirel. Commun., 6(3):805–810. http://dx.doi.org/10.1109/TWC.2007.05384

[22] Wang, C.Y., Liu, T.C.K., Dong, X.D., 2012. Impact of channel estimation error on the performance of amplifyand-forward two-way relaying. IEEE Trans. Veh. Technol., 61(3):1197–1207. http://dx.doi.org/10.1109/TVT.2012.2185964

[23] Wang, J., Wen, O.Y., Li, S.Q., 2008. Soft-output MMSE MIMO detector under imperfect channel estimation. Proc. IEEE Wireless Communications and Networking Conf., p.1334–1338. http://dx.doi.org/10.1109/WCNC.2008.240

[24] Yilmaz, E., Zakhour, R., Gesbert, D., , 2010. Multipair two-way relay channel with multiple antenna relay station. Proc. IEEE Int. Conf. on Communications, p.1–5. http://dx.doi.org/10.1109/ICC.2010.5502396

[25] Zhang, R., Liang, Y.C., Chai, C.C., , 2009. Optimal beamforming for two-way multi-antenna relay channel with analogue network coding. IEEE J. Sel. Areas Commun., 27(5):699–712. http://dx.doi.org/10.1109/JSAC.2009.090611

[26] Zheng, F., Hua, Y., Koshy, J.C., 2006. Joint source and relay optimization for a non-regenerative MIMO relay. Proc. 4th IEEE Workshop on Sensor Array and Multichannel Processing, p.239–243. http://dx.doi.org/10.1109/SAM.2006.1706129

[27] Zhong, B., Zhang, X., Li, Y., , 2013. Impact of partial relay selection on the capacity of communications systems with outdated CSI and adaptive transmission techniques. Proc. IEEE Wireless Communications and Networking Conf., p.3720–3725. http://dx.doi.org/10.1109/WCNC.2013.6555166

[28] Zhou, B.L., Jiang, L.G., Zhang, L., , 2011. Impact of imperfect channel state information on TDD downlink multiuser MIMO system. Proc. IEEE Wireless Communications and Networking Conf., p.1823–1828. http://dx.doi.org/10.1109/WCNC.2011.5779410