Interference Minimization in Cooperative Relay Beamforming With Multiple Communicating Pairs

Abstract

We consider a cellular network where each cell contains multiple source–destination pairs communicating through multiple amplify-and-forward relays using orthogonal channels. We propose an optimal relay beamforming design that minimizes the maximum interference at the neighboring cells subject to per-relay power limits and minimum received signal-to-noise ratio (SNR) requirements. Even though the problem is non-convex, we show that it has zero Lagrange duality gap, and we convert its dual problem to a semi-definite programming problem. Depending on the values of the optimal dual variables, we study three cases to obtain the optimal beam vectors accordingly. This results in an iterative algorithm that provides a semi-closed-form optimal solution. We extend our algorithm to the problem of maximizing the minimum SNR subject to some pre-determined maximum interference constraints at neighboring cells, by the solution to the min-max interference problem along with a bisection search. The solution to this max-min SNR problem gives insight into the worst-case signal-to-interference-and-noise ratio given some maximum interference target. The performance of the proposed algorithm is studied numerically, both for when the knowledge of interference channel is perfect and for when it is imperfect due to either limited feedback or channel estimation error.