How Accurate are the Gaussian and Gamma Approximations to the Outage Capacity of MIMO Channels

Recent results showed that the capacity of a multiple-input-multiple-output (MIMO) fading channel can be approximated by a Gaussian random variable. This Gaussian approximation method has been used to approximate MIMO capacity complementary cumulative distribution functions, or equivalently, the outage capacity, for various fading scenarios where the exact moment generating functions (thus the moments) can be obtained. This paper studies and compares the accuracy of this Gaussian approximation with a newly proposed Gamma approximation for the cases in absence or presence of co-channel interference. It shows that while both approximations are very accurate even for a small number of antenna elements, various fading conditions, and a wide range of transmitting signal-to-noise ratio (TSNR), the MIMO capacity can be better approximated by a Gamma random variable for Rician channels especially for low to medium TSNR values.