Performance and optimization of network-coded cooperative diversity systems

In this paper, we study network-coded cooperative diversity (NCCD) systems comprising multiple sources, one relay, and one destination, where the relay detects the packets received from all sources and performs Galois field (GF) network coding over rm GF(2m) before forwarding a single packet to the destination. Assuming independent Rayleigh fading for all links of the network, we derive simple and accurate closed-form approximations for the asymptotic symbol and bit error rates of NCCD systems. The derived error rate expressions are valid for arbitrary numbers of sources, arbitrary modulation schemes, and arbitrary constellation mappings and provide significant insight into the impact of various system and channel parameters on performance. Moreover, these expressions can be exploited for optimization of the constellation mapping as well as for formulation of various NCCD system optimization problems including optimal power allocation, relay selection, and relay placement.