Universal space-time trellis codes

This article gives practical examples of space-time trellis codes performing as predicted by Root and Varaiya´s (1968) compound channel theorem. Specifically, 32-state and 64-state 2×2 space-time trellis codes are presented that provide a bit-error rate (BER) of 10^-5 on all 2×2 matrix channels with an excess mutual information (MI) within 8% of the excess MI required by standard trellis codes of the same complexity operating only in additive white Gaussian noise (AWGN). Not surprisingly, the universal space-time trellis-coded modulations (ST-TCMs) provide average bit- and frame-error rates in quasi-static Rayleigh fading (QRF) that are comparable to those achieved by ST-TCMs designed specifically for QRF as well as standard TCMs followed by the Alamouti (1998) space-time block code. However, all of these other schemes require more excess MI in the worst case, and some have a significantly wider variation in the required excess MI. The article also compares the universal and quasi-static Rayleigh fading design approaches analytically and bounds the worst case distance of a trellis code on a 2×2 channel using the distances of the code on singular and unitary channels. This bound is extended to the more general n_T×n_R scenario.