Maximum-likelihood decoding in decode-and-forward based MIMO cooperative communication systems

We derive a maximum-likelihood (ML) decoder for a multiple antenna based decode-and-forward (DF) cooperative system utilizing an arbitrary complex-valued M-ary constellation. A sub-optimal piece-wise linear (PL) decoder is also derived, which works close to the ML decoder with significant reduction in decoding complexity. The proposed ML and PL decoders work for arbitrary complex-valued M-ary constellations with knowledge of the channel statistics of the source-relay links in the destination contrary to existing decoder of multi-antenna DF based systems which needs to know the exact source-relay channel coefficient. The proposed decoders outperform an amplify-and-forward protocol based multi-antenna cooperative system. We also derive the analytical symbol error rate (SER) of the PL decoder with multiple relays, M-PSK constellation, and asymptotically high signal-to-noise ratio (SNR) of the source-relay links.