Upper bounds on the bit-error probability of space-time trellis codes using generating function techniques

Generating function techniques have been extensively used to analyze the performance of both convolutional and trellis codes over AWGN and Rayleigh fading channels. We apply the generating function technique with appropriate modifications in order to upper bound the bit-error probability of space-time trellis codes (STTC) over Rayleigh and Rician fading channels. We restrict our analysis to the important class of geometrically, uniform STTC, where the modified state diagram has no more states than the original code trellis. As examples, 4 and 8 state STTC with 2 transmit antenna elements and 1 or 2 receive antenna elements are considered. For these codes, the upper bound is found to be inversely proportional to the lth power of E¯_b¯/N ₀, where 1 corresponds to the diversity advantage of the scheme. Furthermore, comparing simulation results with the derived upper bounds, we conclude that these bounds are within 2 dB to the performance of STTC in Rayleigh or Rician fading channels