Generalized Union Bound for Space-Time Codes

⎯Gallager’s second bounding technique, also known as the generalized union bound, is employed to derive a new upper bound on the error probability of space-time codes with maximum-likelihood (ML) decoding on quasi-static Rayleigh fading channels. The new bound is distinguished by two characteristics: unlike the classical union bound, the new bound is rapidly convergent and is only a few decibels away from simulation results; compared to Gallager’s first bound, it has better computational efficiency and numerical stability. Hence, the new bound is a useful tool for performance analysis and computer search of good space-time codes. Moreover, the correlation between fading coefficients is easily accommodated by the new bound. The application of the new bound to convolutional coding on block fading channels is also demonstrated, and an improved version is derived for the bit error probability of maximum a posteriori probability (MAP) decoding. 1 Index Terms⎯Gallager bounds, optimization, space-time coding, union bound, weight spectrum.