A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users

In this letter, we derive the scaling laws of the sum rate for fading multiple-input multiple-output Gaussian broadcast channels using time sharing to the strongest user, dirty-paper coding (DPC), and beamforming, when the number of users (receivers) n is large. Throughout the letter, we assume a fix average transmit power and consider a block-fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like MloglognN for DPC, and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of time sharing to the strongest user scales like min(M,N)loglogn. Therefore, the asymptotic gain of DPC over time sharing for the sum rate is (M/min(M,N)) when M and N are fixed. It is also shown that if M grows as logn, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum-rate capacity of time -sharing scales like Nloglogn

[1]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[2]  Andrea J. Goldsmith,et al.  Optimality of zero-forcing beamforming with multiuser diversity , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[3]  Harish Viswanathan,et al.  Downlink capacity evaluation of cellular networks with known-interference cancellation , 2003, IEEE J. Sel. Areas Commun..

[4]  Andrea J. Goldsmith,et al.  Dirty paper coding vs. TDMA for MIMO broadcast channels , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[5]  Andrea J. Goldsmith,et al.  Capacity limits of MIMO channels , 2003, IEEE J. Sel. Areas Commun..

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

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

[8]  Andrea J. Goldsmith,et al.  Dirty-paper coding versus TDMA for MIMO Broadcast channels , 2005, IEEE Transactions on Information Theory.

[9]  Wei Yu,et al.  Sum-capacity computation for the Gaussian vector broadcast channel via dual decomposition , 2006, IEEE Transactions on Information Theory.

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

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

[12]  Yongzhe Xie,et al.  Some results on the sum-rate capacity of MIMO fading broadcast channels , 2006, IEEE Transactions on Wireless Communications.

[13]  A. Edelman Eigenvalues and condition numbers of random matrices , 1988 .

[14]  F. G. Tricomi,et al.  Asymptotische Eigenschaften der unvollständigen Gammafunktion , 1950 .

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

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

[17]  Patrick P. Bergmans,et al.  Random coding theorem for broadcast channels with degraded components , 1973, IEEE Trans. Inf. Theory.

[18]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[19]  A. Sridharan Broadcast Channels , 2022 .

[20]  Bertrand M. Hochwald,et al.  Space-Time Multiple Access: Linear Growth in the Sum Rate , 2002 .

[21]  Thomas L. Marzetta,et al.  Multiple-antenna channel hardening and its implications for rate feedback and scheduling , 2004, IEEE Transactions on Information Theory.

[22]  Andrea J. Goldsmith,et al.  Capacity and optimal resource allocation for fading broadcast channels - Part I: Ergodic capacity , 2001, IEEE Trans. Inf. Theory.

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

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