Analytical Expression for the MIMO Channel Capacity

Abstract This paper presents analytical expressions for the multiple-input multiple-output (MIMO) channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the ergodic capacity for single-input multiple-output (SIMO) channels. The analysis shows that the SIMO channel capacity can be approximated by a Gaussian random variable and that the MIMO channel capacity can be approximated as the sum of multiple SIMO capacities. The SIMO channel results are used to derive approximate closed-form expressions for the MIMO channel ergodic capacity and the complementary cumulative distribution function (CCDF) of the MIMO channel capacity (outage capacity). Simulations show that these theoretical results are good approximations for MIMO systems with an arbitrary number of transmit or receive antennas. Moreover, these analytical expressions are relatively simple which makes them very useful for practical computations.

[1]  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.

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

[3]  Heinrich Meyr,et al.  Achievable rate of MIMO channels with data-aided channel estimation and perfect interleaving , 2001, IEEE J. Sel. Areas Commun..

[4]  Zhenming Feng,et al.  Generic procedure for tightly bounding the capacity of MIMO correlated Rician fading channels , 2005, IEEE Transactions on Communications.

[5]  Mansoor Shafi,et al.  Capacity of MIMO systems with semicorrelated flat fading , 2003, IEEE Trans. Inf. Theory.

[6]  Alfréd Rényi,et al.  Probability Theory , 1970 .

[7]  Chen-Nee Chuah,et al.  Capacity scaling in MIMO Wireless systems under correlated fading , 2002, IEEE Trans. Inf. Theory.

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

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

[10]  Babak Hassibi,et al.  How much training is needed in multiple-antenna wireless links? , 2003, IEEE Trans. Inf. Theory.

[11]  Reiner S. Thomä,et al.  Capacity of MIMO systems based on measured wireless channels , 2002, IEEE J. Sel. Areas Commun..

[12]  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).

[13]  Keith Q. T. Zhang,et al.  A simple capacity formula for correlated diversity Rician fading channels , 2002, IEEE Communications Letters.

[14]  Angel E. Lozano,et al.  Link-optimal space-time processing with multiple transmit and receive antennas , 2001, IEEE Communications Letters.