Exact BER Analysis for Square Orthogonal Space-Time Block Codes on Arbitrary Fading Channels with Imperfect Channel Estimation

In this contribution, we examine the effect of imperfect channel estimation on the bit error rate (BER) performance of square orthogonal space-time block codes (OSTBCs). The propagation channels from the Nt transmit antennas to each of the N_t receive antennas are assumed to be affected by (possibly correlated) flat block fading with an arbitrary distribution. The transmitted symbols belong to a PAM or QAM constellation. The resulting average BER can easily be written as an expectation over 4N_tN_r real-valued random variables, but the computing time needed for its numerical evaluation increases exponentially with N_t and N_r. However, we point out that expressing the BER in terms of the distribution of the Frobenius norm of the channel matrix, allows to reduce the BER expression for any number of receive antennas to an expectation over only 2N_s + 2 random variables (with N_s denoting the number of information symbols in the OSTBC matrix). Due to the high diversity order of OSTBCs, the numerical evaluation of this expectation is much less time-consuming than a straightforward computer simulation. Moreover, the presented BER expression is useful not only when the fading distribution is given in closed form, but also when only experimental data (e.g. a histogram) on the fading are available.