An exact union bound on the BER for the combined system of ideal beamforming and Alamouti´s STBC

The simplest Alamouti´s space-time block code is coupled with a larger number of transmit antennas via ideal beam-forming to achieve higher diversity gain compared to the conventional Alamouti scheme with only two transmit antennas. An exact union bound on the bit error rate (BER) is derived for the combined system of ideal beamforming and Alamouti´s space-time block code based on the exact calculation of the pairwise error probability (PEP) for the same system. To calculate the exact PEP, the Gauss-Chebyshev quadrature rule and the moment-generating function (MGF) approach is adopted. The analysis is carried out for the slow Rayleigh flat fading channels and binary phase shift keying (BPSK) modulation.