Optimal design of non-regenerative MIMO wireless relays

Given a multiple-antenna source and a multiple-antenna destination, a multiple-antenna relay between the source and the destination is desirable under useful circumstances. A non-regenerative multiple-antenna relay, also called nonregenerative MIMO (multi-input multi-output) relay, is designed to optimize the capacity between the source and the destination. Without a direct link between the source and the destination, the optimal canonical coordinates of the relay matrix are first established, and the optimal power allocations along these coordinates are then found. The system capacity with the optimal relay matrix is shown to be significantly higher than those with heuristic relay matrices. When a direct link is present, upper and lower bounds of the optimal system capacity are discussed.