Broadcast in MIMO Systems Based on a Generalized QR Decomposition: Signaling and Performance Analysis

A simple signaling method for broadcast channels with multiple-transmit multiple-receive antennas is proposed. In this method, for each user, the direction in which the user has the maximum gain is determined. The best user in terms of the largest gain is selected. The corresponding direction is used as the modulation vector (MV) for the data stream transmitted to the selected user. The algorithm proceeds in a recursive manner where in each step, the search for the best direction is performed in the null space of the previously selected MVs. It is demonstrated that with the proposed method, each selected MV has no interference on the previously selected MVs. Dirty-paper coding is used to cancel the remaining interference. For the case that each receiver has one antenna, the presented scheme coincides with the known scheme based on Gram-Schmidt orthogonalization (QR decomposition). To analyze the performance of the scheme, an upper bound on the cumulative distribution function (CDF) of each subchannel is derived which is used to establish the diversity order and the asymptotic sum-rate of the scheme. It is shown that using fixed rate codebooks, the diversity order of the jth data stream, 1 les j les M, is equal to N(M - j + 1)(K - j + 1), where M, N, and K indicate the number of transmit antennas, the number of receive antennas, and the number of users, respectively. Furthermore, it is proven that the throughput of this scheme scales as M log log(K) and asymptotically (K rarr infin) tends to the sum-capacity of the multiple-input multiple-output (MIMO) broadcast channel. The simulation results indicate that the achieved sum-rate is close to the sum-capacity of the underlying broadcast channel.

[1]  C. Khatri.  Distribution of the Largest or the Smallest Characteristic Root Under Null Hypothesis Concerning Complex Multivariate Normal Populations , 1964 .

[2]  Shlomo Shamai,et al.  The capacity region of the Gaussian MIMO broadcast channel , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[3]  Gerard J. Foschini,et al.  Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas , 1996, Bell Labs Technical Journal.

[4]  Stephan ten Brink,et al.  A close-to-capacity dirty paper coding scheme , 2004, IEEE Transactions on Information Theory.

[5]  Shlomo Shamai,et al.  Capacity and lattice strategies for canceling known interference , 2005, IEEE Transactions on Information Theory.

[6]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[7]  Ross D. Murch,et al.  A transmit preprocessing technique for multiuser MIMO systems using a decomposition approach , 2004, IEEE Transactions on Wireless Communications.

[8]  Rick S. Blum,et al.  Multiuser diversity for a dirty paper approach , 2003, IEEE Communications Letters.

[9]  Babak Hassibi,et al.  On the capacity of MIMO broadcast channels with partial side information , 2005, IEEE Transactions on Information Theory.

[10]  Zhiyong Xu,et al.  An analysis of cache performance of multimedia applications , 2004, IEEE Transactions on Computers.

[11]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[12]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[13]  W. Yu,et al.  Degrees of freedom in wireless multiuser spatial multiplex systems with multiple antennas , 2006, IEEE Transactions on Communications.

[14]  Babak Hassibi,et al.  A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users , 2007, IEEE Transactions on Communications.

[15]  Wei Yu,et al.  A Dual Decomposition Approach to the Sum Power Gaussian Vector Multiple Access Channel Sum Capacity Problem , 2003 .

[16]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[17]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[18]  G. A. Mack,et al.  Order Statistics (2nd Ed.) , 1983 .

[19]  Shlomo Shamai,et al.  On the achievable throughput of a multiantenna Gaussian broadcast channel , 2003, IEEE Transactions on Information Theory.

[20]  Martin Haardt,et al.  Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels , 2004, IEEE Transactions on Signal Processing.

[21]  Andrea J. Goldsmith,et al.  On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming , 2006, IEEE Journal on Selected Areas in Communications.

[22]  G. Pólya,et al.  Problems and theorems in analysis , 1983 .

[23]  Wei Yu,et al.  Sum capacity of Gaussian vector broadcast channels , 2004, IEEE Transactions on Information Theory.

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

[25]  S. Brink,et al.  Approaching the Dirty Paper Limit for Canceling Known Interference , 2003 .

[26]  Wonjong Rhee,et al.  Degrees of freedom in multi-user spatial multiplex systems with multiple antennas , 2004 .

[27]  David Tse,et al.  Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality , 2003, IEEE Trans. Inf. Theory.

[28]  Andrea J. Goldsmith,et al.  Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels , 2003, IEEE Trans. Inf. Theory.

[29]  H. A. David,et al.  Order Statistics (2nd ed). , 1981 .

[30]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[31]  A. Lee Swindlehurst,et al.  A vector-perturbation technique for near-capacity multiantenna multiuser communication-part I: channel inversion and regularization , 2005, IEEE Transactions on Communications.

[32]  Raymond Knopp,et al.  Information capacity and power control in single-cell multiuser communications , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[33]  Babak Hassibi,et al.  On the capacity of MIMO broadcast channel with partial side information , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[34]  Mohamed-Slim Alouini,et al.  Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems , 2003, IEEE J. Sel. Areas Commun..

[35]  Shlomo Shamai,et al.  The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel , 2006, IEEE Transactions on Information Theory.