Joint Power Allocation for Multicast Systems with Physical-Layer Network Coding

This paper addresses the joint power allocation issue in physical-layer network coding (PLNC) of multicast systems with two sources and two destinations communicating via a large number of distributed relays. By maximizing the achievable system rate, a constrained optimization problem is first formulated to jointly allocate powers for the source and relay terminals. Due to the nonconvex nature of the cost function, an iterative algorithm with guaranteed convergence is developed to solve the joint power allocation problem. As an alternative, an upper bound of the achievable rate is also derived to modify the original cost function in order to obtain a convex optimization solution. This approximation is shown to be asymptotically optimal in the sense of maximizing the achievable rate. It is confirmed through Monte Carlo simulations that the proposed joint power allocation schemes are superior to the existing schemes in terms of achievable rate and cumulative distribution function (CDF).