Array gain and capacity for known random channels with multiple element arrays at both ends

Two arrays with M and N elements are connected via a scattering medium giving uncorrelated antenna signals. The link array gain relative to the case of one element at each end is treated for the situation where the channels are known at the transmitter and receiver. It is shown that the maximum mean gain achieved through adaptive processing at both the transmitter and the receiver is less than the free space gain, and cannot be expressed as a product of separate gains, First, by finding the singular values of the transmission matrix, fundamental limitations concerning the maximum gain and the diversity orders are given, indicating that the gain is upper hounded by (rootM + rootN)(2) and the diversity order is MN. Next an iterative technique for reciprocal channels which maximizes power at each stage transmitting back and forth is described. The capacity or spectral efficiency of the random channel is described, and it is indicated how the capacity is upper bounded by N parallel channels of gain M(N < M) for large values of N and M.