BICM-ID with Signal Space Diversity for Keyhole Nakagami-m Fading Channels

This paper generalizes the application of bit interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) over keyhole Nakagami-m fading channels. The tight union bound on the asymptotic error performance is first analytically derived. The optimal rotation matrix with respect to both the asymptotic performance and the convergence behavior is then determined. In particular, it is demonstrated that the most suitable rotation matrix is the one that has i) all entries equal in magnitude, ii) high diversity order, and iii) large minimum product of the ratios between squared distances and log-squared-distances of the rotated constellation scaled by factors of SNR and the parameter m. Various analytical and simulation results show that by employing SSD with a sufficiently large dimension, the error performance can closely approach that over an AWGN channel, even in the worst case of keyhole fading.