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ABBA codes are an important class of quasi orthogonal space-time block codes proposed by Tirkkonen et al.. Recently, they have become more attractive for practical applications because Yuen et al. have shown that ABBA codes allow pair-wise real-symbol decoding (or equivalently, single-complex symbol decoding) complexity; it is the Minimum Decoding Complexity (MDC) achievable by any non-OSTBC. Additionally, MDC-ABBA codes can achieve full diversity while their code rate is higher than that of OSTBC. In this paper, the authors present a new, general, simple, and closed-form method to decode MDC-ABBA codes. They explicitly derive the equivalent channel of MDC-ABBA codes and the maximum mutual information of MDC-ABBA.
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