On the capacity of MIMO wireless channels

In this paper, we present a new closed-form formula for the ergodic capacity of multiple-input multiple-output (MIMO) wireless channels. Assuming independent and identically distributed (i.i.d.) Rayleigh flat-fading between antenna pairs and equal power allocation to each of the transmit antennas, the ergodic capacity of such channels is expressed in closed form as finite sums of the exponential integrals which are the special cases of the complementary incomplete gamma function. Using the asymptotic capacity rate of MIMO channels, which is defined as the asymptotic growth rate of the ergodic capacity, we also give simple approximate expressions for the MIMO capacity. Numerical results show that the approximations are quite accurate for the entire range of average signal-to-noise ratios.