Jointly Optimal Precoder and Power Allocation for an Amplify-and-Forward Half-Duplex Relay System

Abstract

This paper investigates the optimal precoder design and power allocation between the source and relay for ahalf-duplex single-relay non-orthogonal amplify-and-forward (NAF) system. Based on the pair-wise error probability (PEP)analysis, an optimal class of 2 2 precoders is first derived for the traditional power allocation scheme, where one-third ofthe system power is spent at the relay node, while two-thirds are spent at the source node. Different from optimal unitaryprecoders proposed earlier, the derived class of precoders indicates that the source should spend all its power transmittinga superposition of the symbols in the broadcast phase, while being silent in the cooperative phase, for optimal asymptoticperformance. We then further address the problem of jointly optimal precoder and power allocation for the system underconsideration. It is shown that the total power should be equally distributed to the source and the relay, and the sourceshould again spend no power during the cooperative phase for the best asymptotic performance. Analytical and simulationresults reveal that the proposed precoders not only exploit full cooperative diversity, but also provide significant codinggain over the optimal unitary precoders. For instance, a coding gain of around 1dB can be attained at the practical BERlevel of 10 ? 5 for various modulation schemes.