New union bound on the error probability of bit-interleaved space-time codes with finite interleaver sizes

In this paper a new union bound on the bit error probability of bit-interleaved space-time (BI-ST) coded systems is derived. Unlike existing performance analysis tools for BI-ST systems, the new bound provides a general framework for analyzing the performance of BI-ST systems employing finite interleaver sizes. The derivation is based on the uniform interleaving assumption of the coded sequence prior to transmission over the multiple antennas. The new bound is a function of the distance spectrum of the code, the signal constellation used and the space-time (ST) mapping scheme. The bound is derived for a general BI-ST coded system and applied to two specific examples; namely, the BI space-time coded modulation (BISTCM) and the BI space-time block codes (BI-STBC). Results show that the analysis provides a close approximation to the BI-ST performance for a wide range of signal-to-noise ratios (SNR). The analysis can also accurately characterize the performance differences between different interleaver sizes, which is a breakthrough in the analysis of BI-ST coded systems.