Sum rate maximization model of non-regenerative multi-stream multi-pair multi-relay network

We consider the general MIMO relay network with K user pairs and R relays. The model to maximize the total signal to total interference plus noise ratio, with individual relay transmit power constraints, is set up. We constrain the precoding matrices to have orthogonal columns to guarantee multiple stream transmission. By alternating iteration method, we decompose the problem into several subproblems. For the precoding subproblem, which is a nonconvex matrix optimization problem, we apply the projected gradient method to its dual problem and prove there is zero duality gap between the primal and the dual problems. Simulation results show our proposed multiple stream model is efficient to achieve high sum rate and outperform the existing model in medium to high SNR scenarios.