Diversity analysis of MIMO decode-and-forward relay network by using near-ML decoder

The probability of making mistakes on the decoded signals at the relay has been used for the maximum-likelihood (ML) decision at the receiver in the decode-and-forward (DF) relay network. It is well known that deriving the probability is relatively easy for the uncoded single-antenna transmission with M-pulse amplitude modulation (PAM). However, in the multiplexing multiple-input multiple-output (MIMO) transmission, the multi-dimensional decision region is getting too complicated to derive the probability. In this paper, a high-performance near-ML decoder is devised by applying a well-known pairwise error probability (PEP) of two paired-signals at the relay in the MIMO DF relay network. It also proves that the near-ML decoder can achieve the maximum diversity of M_S M_D + M_R min(M_S, M_D), where M_S, M_R, and M_D are the number of antennas at the source, relay, and destination, respectively. The simulation results show that 1) the near-ML decoder achieves the diversity we derived and 2) the bit error probability of the near-ML decoder is almost the same as that of the ML decoder.