Error performances of multiple access system using analog network coding

In this work, we study the error performances of the multiple access system using analog network coding (ANC), where all the users broadcast their data to the relays and destination simultaneously in the first phase, and the relays forward the source messages that have been mixed in the air in the second phase. Depending on the type of relay power constraint, both the variable gain relaying and fixed gain relaying are considered. We show that the error rates of both schemes scale as O(log P/P²) at high signal-to-noise ratio (SNR), where P is the transmitted power. We also show that the error performance is dominated by the relay-destination channel, thus the best relay position should be close to the destination. We also demonstrate that ANC may be outperformed by the conventional amplify-and-forward scheme when the data rate is low and the user number is not large. Finally, we propose a relay selection strategy based on Min-Max criterion that can achieve full diversity when there are multiple relays.