Error rate analysis and optimal power allocation in multiple access relay channels with Analog Network Coding

In this paper, we examine multi-source multi-relay systems that employ Analog Network Coding for which we provide a two-fold contribution: i) We derive a closed-form upper bound of the average symbol error rate (SER) per source of the system, which is shown to be tight in the high-Signal-to-Noise Ratio (SNR) region, especially for an adequate number of relays, and ii) based on this bound, for a given total power budget to be distributed among the source and relay nodes we formulate the power allocation optimization problem with the aim of minimizing the SER per source. Results show that for a common target SER among the sources, an increase in their number results in an increase in the expected energy gains over the equal power allocation for all the nodes policy.