On the Relation of OSTBC and Code Rate One QSTBC: Average Rate, BER, and Coding Gain

Recently, the statistical properties of the equivalent channel representation of a multiple-input-multiple output (MIMO) system employing code rate one quasi-orthogonal space-time block codes (QSTBC), which are constructed by using orthogonal space-time block codes (OSTBC) as building elements, was characterized. Based on these characterizations we analyze the average rate (or mean mutual information), the bit-error-rate performance, and the coding gain achieved with QSTBC for any number of receive and
nT
=2
n
,
n
ges 2 transmit antennas. First, we study constellation rotation using a systematic approach in order to maximize the coding gain and to achieve full diversity QSTBC. Moreover, we present an upper bound on the coding gain. We derive a lower and upper bound on the BER-performance for QSTBC. Furthermore, we analyze the average rate achievable with QSTBC in case of an uninformed transmitter and also the case, in which the transmitter knows the mean channel matrix whereas the receiver has perfect CSI. Along with the analysis, we compare all the results of these performance measures with the results achieved with OSTBC, revealing important connections between OSTBC and QSTBC. For example, the coding gain of a QSTBC is upper bounded by the coding gain of the underlying OSTBC. Also, the BER of a QSTBC for
nT
transmit and
nR
receive antennas is tightly lower bounded by the BER of a full-diversity providing intersymbol-interference free system. In addition to that, we show that gains in terms of average rate by using a QSTBC (and, thus, with higher
nT
) instead of the underlying OSTBC are only attainable, if the available channel state information at the transmitter (CSIT) is utilized. Finally, we illustrate our theoretical results using numerical simulations.