Low-Complexity Decoding in DF MIMO Relaying System

We derive a maximum-likelihood (ML) decoder for decode-and-forward (DF) based multiple-input-multiple-output (MIMO) cooperative systems having an equal number of antennas at the source and relay nodes, and utilizing an arbitrary complex-valued M-ary constellation. The DF-based MIMO cooperative system considered in this paper utilizes orthogonal space-time block codes (OSTBCs) for the transmission of data of the source to the destination. To reduce the decoding complexity, a suboptimal piecewise linear (PL) decoder is also derived, which performs close to the ML decoder. The proposed ML and PL decoders are applicable to arbitrary complex-valued M-ary constellations and require the destination node to possess knowledge of the channel statistics of the source-relay (S-R) links, whereas the existing decoder of multi-antenna-based DF cooperative systems needs to know the exact channel coefficients of the S-R link at the destination. The proposed decoders outperform an amplify-and-forward (AF)-protocol-based multi-antenna cooperative system. We obtain an expression of the average probability of error of the proposed PL decoder using an M-phase-shift keying (M-PSK) constellation and a single MIMO relay. The approximate symbol error rate (SER) of the proposed PL decoder is derived with multiple MIMO relays, M-PSK constellation, and asymptotically high signal-to-noise ratio (SNR) of the S-R links. It is analytically shown that the proposed ML and PL decoders achieve maximum possible diversity in the multi-antenna cooperative system with a single relay.