A Modified Levenberg–Marquardt Method for the Bidirectional Relay Channel

This paper presents an optimization approach for a system consisting of multiple bidirectional links over a two-way amplify-and-forward relay. Improvement to the fairness of the system is desired. All user pairs exchange information over one relay station (RS) with multiple antennas. Due to the joint transmission to all users, the users are subject to mutual interference. A mitigation of the interference can be achieved by max-min fair precoding optimization where the relay is subject to a sum power constraint. The resulting optimization problem is nonconvex. This paper proposes a novel iterative low-complexity approach based on a modified Levenberg-Marquardt (LM) method to find near optimal solutions. The presented method finds solutions close to the standard convex-solver-based relaxation approach.