ML Performance Analysis of the Decode-and-Forward Protocol in Multi-hop Networks

We analyze the maximum-likelihood (ML) performance of the decode-and-forward protocol in a cooperative diversity network which consists of a source, a relay, and a destination with a direct path signal.We first present an approximated ML detection rule by adopting max-log approximation. Then we obtain decision regions in a form without union and intersection.Finally, based on the decision regions,we derive a very accurate closed-form BER approximation for M-pulse amplitude modulation (PAM) and M-quadrature amplitude modulation (QAM).