Amplify-and-forward on a multiaccess relay channel with computation at the receiver

We consider a communication system in which two sources communicate with a destination with the help of a common relay. We assume that the relay operates in half-duplex mode; and concentrate on the symmetric-rate case. We study and analyse the performance of a simple strategy in which the relay simply amplifies its output and retransmits it. However, unlike standard amplify-and-forward, the destination recovers the sent messages by computing and inverting two appropriate linear combinations of the sources´ messages, obtained using what it gets from the sources and the relay. We discuss the design criteria and establish the sum-rate allowed by this strategy. Also, we consider, and solve, the problem of maximizing the sum-rate by properly optimizing the power values and the integer-valued coefficients of the recovered linear combinations. It should be emphasized that although the coding strategy described in this paper performs only as good as standard amplify-and-forward, it has the advantage of utilizing simpler linear codes; and, so, is more relevant in practical collaborative systems.