Design criteria and performance of space-frequency bit-interleaved coded modulations in frequency-selective Rayleigh fading channels

In this paper, we investigate design criteria and the performance of the space-frequency bit-interleaved coded modulation (SF-BICM) systems in frequency-selective Rayleigh fading channels. To determine the key parameters that affect the performance of SF-BICM, we derive the pairwise error probability (PEP) in terms of the determinant of the matrix corresponding to any two codewords. We prove that the bit-interleavers do the function of distributing the nonzero bits uniformly such that two or more nonzero bits are seldom distributed into the symbols that are transmitted in the same frequency bin. This implies that the bit-interleavers transform an SF-BICM system into an equivalent 1-antenna system. Based on this, we present design criteria of SF-BICM systems that maximizes the diversity order and the coding gain. Then, we analyze the performance of SF-BICM for the case of 2-transmit antennas and 2-multipaths by deriving a frame error rate (FER) bound. The derived bound is accurate and requires only the distance spectrum of the constituent codes of SF-BICM. Numerical results reveal that the bound is tight enough to estimate the performance of SF-BICM very accurately.