Algebraic Relationship between Amicable Orthogonal Designs and Quasi-Orthogonal STBC with Minimum Decoding Complexity

We show that there exists an interesting relationship between the algebraic constraints of Amicable Orthogonal Design (AOD) matrices and the dispersion matrices of Quasi-Orthogonal Space-Time Block Code with minimum decoding complexity (MDC-QOSTBC). This insight leads to a novel concept of "Preferred AOD Pair", and we show that MDC-QOSTBC can be constructed from two AODs that form a Preferred AOD Pair. With the Preferred AOD Pair concept, we are able to derive the lower bound on code rate of square MDC-QOSTBC, and show them to be 1 and ¿ for four and eight transmit antennas respectively. We also present a systematic method to construct Preferred AOD Pair and use them to obtain new MDC-QOSTBCs.