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 givi ng uncorrelated antenna signals. The link array gain relative to the case o f one element at each end is treated for the situation where the channels a re 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 pro duct of separate gains, First, by finding the singular values of the transm ission matrix, fundamental limitations concerning the maximum gain and the diversity orders are given, indicating that the gain is upper hounded by (r ootM + rootN)(2) and the diversity order is MN. Next an iterative technique for reciprocal channels which maximizes power at each stage transmitting b ack and forth is described. The capacity or spectral efficiency of the rand om channel is described, and it is indicated how the capacity is upper boun ded by N parallel channels of gain M(N < M) for large values of N and M.