Tight Error Bound for Coded Unitary Space-Time Modulation

This paper studies the bit error probability (BEP) of coded unitary space-time modulation with iterative decoding where neither the transmitter nor the receiver knows the channel fading coefficients. The tight error bound on the asymptotic performance is first analytically derived for given unitary constellation and mapping rule. Design criterion regarding the choice of unitary constellation and mapping is then established to achieve the best asymptotic performance. Furthermore, using the unitary constellation obtained from orthogonal design and 4-PSK, two mapping rules are proposed. In particular, one mapping is the best mapping for systems with iterative decoding, whereas the other mapping is most suitable for systems that do not implement iteration process. The latter mapping is similar to Gray mapping considered for coherent channels. Analytical and simulation results show that with the proposed mapping of the unitary constellation obtained from orthogonal design, the error performance of the iterative systems can approach very near the performance of the ideal unitary constellation and mapping.