Physical-Layer Multicasting by Stochastic Transmit Beamforming and Alamouti Space-Time Coding

Consider transceiver designs in a multiuser multi-input single-output (MISO) downlink channel, where the users are to receive the same data stream simultaneously. This problem, known as physical-layer multicasting, has drawn much interest. Presently, a popularized approach is transmit beamforming, in which the beamforming optimization is handled by a rank-one approximation method called semidefinite relaxation (SDR). SDR-based beamforming has been shown to be promising for a small or moderate number of users. This paper describes two new transceiver strategies for physical-layer multicasting. The first strategy, called stochastic beamforming (SBF), randomizes the beamformer in a per-symbol time-varying manner, so that the rank-one approximation in SDR can be bypassed. We propose several efficiently realizable SBF schemes, and prove that their multicast achievable rate gaps with respect to the MISO multicast capacity must be no worse than 0.8314 bits/s/Hz, irrespective of any other factors such as the number of users. The use of channel coding and the assumption of sufficiently long code lengths play a crucial role in achieving the above result. The second strategy combines transmit beamforming and the Alamouti space-time code. The result is a rank-two generalization of SDR-based beamforming. We show by analysis that this SDR-based beamformed Alamouti scheme has a better worst-case effective signal-to-noise ratio (SNR) scaling, and hence a better multicast rate scaling, than SDR-based beamforming. We further the work by combining SBF and the beamformed Alamouti scheme, wherein an improved constant rate gap of 0.39 bits/s/Hz is proven. Simulation results show that under a channel-coded, many-user setting, the proposed multicast transceiver schemes yield significant SNR gains over SDR-based beamforming at the same bit error rate level.

[1]  Anthony Man-Cho So,et al.  Rank-two transmit beamformed Alamouti space-time coding for physical-layer multicasting , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[2]  Hao Zhu,et al.  Precoder Design for Physical Layer Multicasting , 2011, IEEE Transactions on Signal Processing.

[3]  Marius Pesavento,et al.  Distributed Beamforming for Multi-Group Multicasting Relay Networks , 2012, IEEE Transactions on Signal Processing.

[4]  Anna Scaglione,et al.  Randomized Space-Time Coding for Distributed Cooperative Communication , 2007, IEEE Transactions on Signal Processing.

[5]  Zhi-Quan Luo,et al.  SDP relaxation of homogeneous quadratic optimization: Approximation bounds and applications , 2009 .

[6]  I. M. Pyshik,et al.  Table of integrals, series, and products , 1965 .

[7]  David James Love,et al.  Optimal and Successive Approaches to Signal Design for Multiple Antenna Physical Layer Multicasting , 2011, IEEE Transactions on Communications.

[8]  N.D. Sidiropoulos,et al.  Broadcasting with channel state information , 2004, Processing Workshop Proceedings, 2004 Sensor Array and Multichannel Signal.

[9]  Raymond W. Yeung,et al.  A First Course in Information Theory (Information Technology: Transmission, Processing and Storage) , 2006 .

[10]  Angel Lozano,et al.  Long-Term Transmit Beamforming for Wireless Multicasting , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[11]  Wolfgang Utschick,et al.  Design of Single-Group Multicasting-Beamformers , 2007, 2007 IEEE International Conference on Communications.

[12]  Emil Björnson,et al.  Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies With Instantaneous and Statistical CSI , 2010, IEEE Transactions on Signal Processing.

[13]  Amos Lapidoth,et al.  Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels , 2003, IEEE Trans. Inf. Theory.

[14]  David Tse,et al.  Opportunistic beamforming using dumb antennas , 2002, IEEE Trans. Inf. Theory.

[15]  Zhi-Quan Luo,et al.  Capacity Limits of Multiple Antenna Multicast , 2006, 2006 IEEE International Symposium on Information Theory.

[16]  Raymond W. Yeung,et al.  A First Course in Information Theory , 2002 .

[17]  Hao Zhu,et al.  Precoder design for physical layer multicasting , 2012, ICC.

[18]  Daniel Pérez Palomar,et al.  A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization , 2006, IEEE Transactions on Signal Processing.

[19]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[20]  J. Kent The Complex Bingham Distribution and Shape Analysis , 1994 .

[21]  Michael D. Zoltowski,et al.  Improved space-time coding for multiple antenna multicasting , 2006, 2006 International Waveform Diversity & Design Conference.

[22]  K. J. Ray Liu,et al.  Transmit diversity techniques for multicasting over wireless networks , 2004, 2004 IEEE Wireless Communications and Networking Conference (IEEE Cat. No.04TH8733).

[23]  Arogyaswami Paulraj,et al.  Optimal linear precoders for MIMO wireless correlated channels with nonzero mean in space-time coded systems , 2006, IEEE Transactions on Signal Processing.

[24]  David James Love,et al.  Capacity Limits of Multiple Antenna Multicasting Using Antenna Subset Selection , 2008, IEEE Transactions on Signal Processing.

[25]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[26]  Mikael Skoglund,et al.  Combining beamforming and orthogonal space-time block coding , 2002, IEEE Trans. Inf. Theory.

[27]  Anthony Man-Cho So,et al.  Optimal Spectrum Sharing in MIMO Cognitive Radio Networks via Semidefinite Programming , 2011, IEEE Journal on Selected Areas in Communications.

[28]  Nikos D. Sidiropoulos,et al.  Multiple-Antenna Multicasting Using Channel Orthogonalization and Local Refinement , 2010, IEEE Transactions on Signal Processing.

[29]  A. Goldsmith,et al.  Capacity of Rayleigh fading channels under different adaptive transmission and diversity-combining techniques , 1999, IEEE Transactions on Vehicular Technology.

[30]  E. Masoud,et al.  Space-Time Block Coding for Wireless Communications , 2008 .

[31]  Shuzhong Zhang,et al.  Complex Matrix Decomposition and Quadratic Programming , 2007, Math. Oper. Res..

[32]  Shlomo Shamai,et al.  Fading Channels: Information-Theoretic and Communication Aspects , 1998, IEEE Trans. Inf. Theory.

[33]  Anthony Man-Cho So,et al.  Convex Optimization in Signal Processing and Communications: Probabilistic analysis of semidefinite relaxation detectors for multiple-input, multiple-output systems , 2009 .

[34]  Anthony Man-Cho So,et al.  Achievable Rate Derivations and Further Simulation Results for "Physical-Layer Multicasting by Stochastic Transmit Beamforming and Alamouti Space-Time Coding" , 2013, ArXiv.

[35]  Paul Tseng,et al.  Approximation Bounds for Quadratic Optimization with Homogeneous Quadratic Constraints , 2007, SIAM J. Optim..

[36]  Zhi-Quan Luo,et al.  Semidefinite Relaxation of Quadratic Optimization Problems , 2010, IEEE Signal Processing Magazine.

[37]  Anthony Man-Cho So,et al.  A Unified Theorem on Sdp Rank Reduction , 2008, Math. Oper. Res..

[38]  Gregory W. Wornell,et al.  Efficient use of side information in multiple-antenna data transmission over fading channels , 1998, IEEE J. Sel. Areas Commun..

[39]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[40]  S. Kotz,et al.  Symmetric Multivariate and Related Distributions , 1989 .

[41]  Holger Boche,et al.  Majorization and Matrix-Monotone Functions in Wireless Communications , 2007, Found. Trends Commun. Inf. Theory.

[42]  Stefania Sesia,et al.  LTE - The UMTS Long Term Evolution, Second Edition , 2011 .

[43]  D. Owen Handbook of Mathematical Functions with Formulas , 1965 .

[44]  Xin Wen,et al.  Rank-two beamforming for single-group multicasting networks using OSTBC , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[45]  Marius Pesavento,et al.  A convex inner approximation technique for rank-two beamforming in multicasting relay networks , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

[46]  Xiang-Gen Xia,et al.  On the nonexistence of rate-one generalized complex orthogonal designs , 2003, IEEE Trans. Inf. Theory.

[47]  Nikos D. Sidiropoulos,et al.  Transmit beamforming for physical-layer multicasting , 2006, IEEE Transactions on Signal Processing.

[48]  Sergio VerdÂ,et al.  Fading Channels: InformationTheoretic and Communications Aspects , 2000 .

[49]  L. C. Godara,et al.  Handbook of Antennas in Wireless Communications , 2001 .