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In this paper, the authors 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. They also show that the error performance is dominated by the relay-destination channel, thus the best relay position should be close to the destination. They 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.
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