A general method to decode ABBA quasi-orthogonal space-time block codes

ABBA codes, a class of quasi-orthogonal space-time block codes (STBC) proposed by Tirkkonen et al., allow low complexity pair-wise complex-symbol decoding. A refined version of ABBA codes with special signal mapping leads to pair-wise real-symbol decoding, i.e. with minimum decoding complexity (MDC) achievable by non-orthogonal STBC. Despite these advantages, a general simple closed-form method to decode ABBA and MDC-ABBA codes for an arbitrary number of transmit/receive antennas is not available. We thus derive an equivalent channel representation to address this issue. The maximum mutual information of ABBA/MDC-ABBA codes is also derived. We found that MDC-ABBA codes perform better than ABBA codes when using two 8QAM constellations.