Recently, a quasi-orthogonal space–time block code (QSTBC) capable of achieving a significant fraction of the outage mutual information of a multiple-input–multiple-output (MIMO) wireless communication system for the case of $n_{T}=4$ transmit and $n_{R}=1$ receive antennas was proposed. We generalize these results to $n_{T}=2^{n}$ transmit and an arbitrary number of receive antennas. Furthermore, we completely characterize the structure of the equivalent channel for the general case and show that for all $n_{T}=2^{n}$ and $n_{R}$ the eigenvectors of the equivalent channel are fixed and independent from the channel realization. Furthermore, the eigenvalues of the equivalent channel are independent identically distributed random variables each following a noncentral chi-square distribution with $4n_{R}$ degrees of freedom. Based on these important insights into the structure of the QSTBC, we derive tight lower and upper bounds for the outage probability achieved with QSTBC. Finally, by utilizing the special structure of the QSTBC, we propose a new transmit strategy, which decouples the signals transmitted from different antennas in order to detect the symbols separately with a linear ML-detector rather than joint detection, an up to now only known advantage of orthogonal space–time block codes (OSTBC).
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