On the Capacity Limit of Wireless Channels Under Colored Scattering

It has been generally believed that the multiple-input multiple-output channel capacity grows linearly with the size of antenna arrays. In terms of degrees of freedom, linear transmit and receive arrays of length L in a scattering environment of total angular spread \\Ω asymptotically have \\ΩL degrees of freedom. In this paper, it is claimed that the linear increase in degrees of freedom may not be attained when scattered electromagnetic fields in the underlying scattering environment are statistically correlated. After introducing a model of correlated scattering, which is referred to as the colored scattering model, we derive a capacity upper bound, assuming that the channel is known perfectly at the receiver and in distribution at the transmitter. Unlike the uncorrelated case, the prelog factor of the capacity, i.e., the number of degrees of freedom, in the colored scattering channel is asymptotically limited by \\Ω\\·min{L, 1/ ΓI} where Γ is a parameter determining the extent of correlation. In other words, for very large arrays in the colored scattering environment, degrees of freedom can get saturated to an intrinsic limit rather than increasing linearly with the array size.