Optimal amplify and forward strategy for two-way relay channel with multiple relays

An iterative algorithm is proposed to achieve the optimal rate region in a two-way relay channel, where two nodes want to exchange data with each other using multiple relays, and each relay employs an amplify and forward strategy. The iterative algorithm solves a power minimization problem at every step, subject to minimum signal-to-interference-and-noise ratio constraints, which is non-convex, however, for which the Karush Kuhn Tucker conditions are sufficient for optimality. Using simulations, the achievable rate region of the iterative algorithm is compared with the cut-set upper bound; the gap is shown to be quite small for most cases.