MIMO capacity scaling and saturation in correlated environments

The capacity of MIMO systems under ideal (i.i.d.) channel conditions has been shown to increase linearly with the number of antennas. Capacity scaling in a correlated channel environment as well but the constant of scaling is shown in Chee-Nee Chuah, D.N. C. Tse, J.M. Khan, R.A. Valanzuela [2002] to be less than that of the i.i.d. scaling factor. Using a channel representation motivated by physical scattering considerations, the virtual channel representation, we show this effect does occur provided the number of effective scattering paths keeps asymptotically increasing with the increase in the number of antennas. Otherwise we show that saturation of capacity occurs. Using random banded matrix theory results, we also show that the effect of correlation is to reduce the effective received SNR according to the degree of correlation. This also yields a closed form expression for the asymptotic capacity of correlated MIMO channels.