A continuous representation of multi-antenna fading channels and implications for capacity scaling and optimum array design

In this paper we introduce a continuous representation of multi-antenna (MIMO) fading channels that reveals the effect of array parameters and scattering characteristics on channel degrees of freedom and capacity. It is shown that the intrinsic degrees of freedom in the scattering environment provide an upper bound on the rank of the MIMO channel matrix (and hence the spatial multiplexing gain) and are determined by two key parameters: angular spreads and the scattering correlation scales seen by the transmitter and receiver. Similarly, the spatial signal spaces at the transmitter and receiver are determined by two key parameters each: the aperture size and the smallest scale of signal variation. For any given scattering environment, the continuous representation helps us determine the optimal number of antennas and the antenna spacings to maximize the spatial multiplexing gain (and hence capacity). In particular, we show that linear capacity scaling with the number of antennas is possible in ideally uncorrelated scattering environments with vanishing correlation scales. Conversely, for a non-vanishing scattering correlation scale, the capacity eventually saturates with the number of antennas.