WLC11-1: A New Approach to the Capacity Distribution of MIMO Rayleigh Fading Channels

The distribution of the capacity of multiple input multiple output (MIMO) fading depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant of a Wishart matrix. Based on the distributions of the determinant and the trace of the Wishart matrix, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the capacity of MIMO Rayleigh fading channels. The new bounds on capacity CCDF provide further insights into the channel capacity, and show the effects of the system parameters on the capacity distribution explicitly. These bounds can be used to evaluate the mean capacity as well.

[1]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[2]  Mansoor Shafi,et al.  On a Gaussian approximation to the capacity of wireless MIMO systems , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[3]  Lee M. Garth,et al.  Exact capacity distributions for MIMO systems with small numbers of antennas , 2003, IEEE Communications Letters.

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

[5]  Rohit U. Nabar,et al.  Introduction to Space-Time Wireless Communications , 2003 .

[6]  Byeong Gi Lee,et al.  New bounds of pairwise error probability for space-time codes in Rayleigh fading channels , 2002, 2002 IEEE Wireless Communications and Networking Conference Record. WCNC 2002 (Cat. No.02TH8609).

[7]  John G. Proakis,et al.  Digital Communications , 1983 .

[8]  Moe Z. Win,et al.  On the capacity of spatially correlated MIMO Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.

[9]  Thomas L. Marzetta,et al.  Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading , 1999, IEEE Trans. Inf. Theory.

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

[11]  N. R. Goodman.  The Distribution of the Determinant of a Complex Wishart Distributed Matrix , 1963 .