Union Bounds for BER Evaluation and Code Optimization of Space-Time codes in 2-by-2 MIMO systems

n this paper, an exact closed-form formula for the pair-wise error probability (PEP) is derived for two transmit and two receive antennas MIMO systems using the probability density function (PDF) of the modified Euclidean distance. An exact union bound formed by this formula, together with the asymptotic union bound, are studied for optimization and bit-error rate (BER) evaluation of space-time (S-T) codes. Numerical calculations and Monte Carlo computer simulation have been used to study these two union bounds on a 2-by-2 MIMO system using a rotation-based diagonal S-T code (D code) in a block fading channel. Results show that the exact union bound is a very tight bound for BER evaluation while the asymptotic union bound is very accurate for code optimization