Sum rate maximization for multi-pair two-way relaying with single-antenna amplify and forward relays

We consider a multi-pair two-way relay network with multiple single antenna amplify-and-forward relays. The sum rate maximization problem subject to a total transmit power constraint is studied for such network. The optimization problem is non-convex. First, we show that the problem is a monotonic optimization problem and propose a polyblock approximation algorithm for obtaining the global optimum. However, this algorithm is only suitable for benchmarking because of its high computational complexity. After observing that the necessary optimality condition for our problem is similar to that of the generalized eigenvalue problem, we propose to use the generalized power iterative algorithm which can approach the global optimum recursively. Finally, we propose the total signal-to-interference-plus-noise ratio (SINR) eigen-beamformer which is a closed-form suboptimal solution that reduces the computational complexity significantly. Simulation results show that the proposed algorithms outperform the existing scheme. Moreover, the total SINR eigen-beamformer almost achieves the performance of the optimal solution.