  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 four transmit and one receive antennas was proposed. We generalize
these results to $n_T=2^n$ transmit and an arbitrary number of receive antennas
$n_R$. 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
an analytical lower bound for the fraction of outage probability achieved with
QSTBC and show that this bound is tight for low signal-to-noise-ratios (SNR)
values and also for increasing number of receive antennas. We also present an
upper bound, which is tight for high SNR values and derive analytical
expressions for the case of four transmit antennas. 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).
