Success-Probability-Based Power Allocation for Downlink PNC in Multi-way Relay Channels

In this paper, we propose a novel power allocation scheme for physical-layer network coding (PNC) in downlink multi-way relay channels (MWRC). The power allocation is formulated as a constrained optimization problem, where the aim is to maximize the success probability under a total power constraint when using Babai estimation for signal detection. Optimizing over this metric allows us to maximize the probability of successfully decoding a chain of network codes, which is of crucial importance in downlink multi-way PNC. Specifically, to meet the different requirements for transmission quality in applications, we consider different aggregate measures of success probability over the participating user terminals, i.e., the arithmetic mean, the geometric mean, and the maximin. For each measure, we formulate a constrained optimization and demonstrate the concavity of the objective, allowing us to obtain solution efficiently via iterative means. The performance of the proposed power allocation schemes for downlink PNC in MWRC is evaluated by means of computer simulations over Raylegih fading channels. The results demonstrate the effectiveness of the proposed schemes in improving the success probability in the reception of a chain of network codes.