Optimal cooperative relay beamforming for interference minimization

We consider a wireless cellular network with multiple amplify-and-forward (AF) relays in each cell, assisting the communication of multiple source-destination pairs with relay transmission beamforming. Our objective is to minimize the maximum interference power among all active receivers in a neighboring cell subject to per-relay power and minimum received SNR constraints. We propose an efficient algorithm to obtain the optimal relay beamforming vectors. We show that even though the optimization problem is non-convex, it has zero Lagrange duality gap and can be converted to a semi-definite programming problem. The performance of the proposed algorithm is studied numerically, both for the case where the interference channel information is exactly known and for the case of inaccurate channel information due to either limited feedback or channel estimation error. It is demonstrated that the min-max interference approach substantially outperforms the alternative where we simply minimize the maximum relay transmission power.