Optimum power allocation for sum rate improvement in AF multi-way relay networks

In this paper, we formulate and study the optimum power allocation problem in an amplify and forward (AF) multi-way relay network (MWRN). We derive closed-form analytical expressions for the optimum power allocation coefficients for the data power and the pilot power of the users and the relay to maximize the sum rate. We assume that only long term statistical channel state information (CSI) (i.e., channel variance) are available to each user and the relay. Our results show that to achieve the same sum rate, optimum power allocation requires 7-9 dB less transmit power compared to equal power allocation depending on users' channel conditions. In addition, we show that for optimum power allocation, the reduction in the sum rate due to channel estimation errors, becomes less compared to the case of equal power allocation.