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Analog Network Coding in the Multiple Access Relay Channel: Error Rate Analysis and Optimal Power Allocation

In this paper, we consider Analog Network Coding (ANC) in the Multiple Access Relay Channel (MARC) with multiple relays, and provide the following three-fold contribution: 1) we introduce a tractable mathematical framework for computing the Symbol Error Rate (SER) of Maximum-Likelihood (ML), Zero-Forcing (ZF), and Minimum Mean Square Error (MMSE) receivers; 2) by capitalizing on this tractable mathematical framework, we formulate a power allocation problem that is proved to be convex for ML, ZF and MMSE receivers; and 3) we provide closed-form expressions of the optimal power to be allocated to the sources and the relays for ZF and MMSE receivers. With the aid of Monte Carlo simulations, we validate the accuracy of the proposed mathematical framework for various network topologies and channel conditions, as well as study the effectiveness of optimal power allocation. It is shown, in particular, that power optimization is beneficial as the number of sources increases and if the quality of the source-relay links is better than the quality of the relay-destination links.