Joint relay weighting and power allocation for a two-way amplify-and-forward relay system

In this paper, we propose a joint relay weighting (RW) and power allocation (PA) algorithm for a two-way amplify-and-forward relay system, in which each participating node is equipped with a single antenna, to minimize the sum of mean-squared errors (sum-MSE) of the received signals at two source nodes. The algorithm alternates between two parts: obtaining the optimal RW for a specific PA, which is derived as a closed-form solution, and searching the optimal PA under an obtained RW that minimizes the sum-MSE via a gradient-descent algorithm. It is shown that the diversity order of the system is one-half of the total number of relays. Computer simulation results show that the proposed RW-PA algorithm has better sum-MSE and sum of bit-error rates than the equal PA scheme.