Optimum detection of Walsh-Hadamard multiplexed antipodal signals over Rayleigh fading channels

This paper proposes and analyzes a maximum aposteriori probability (MAP) coherent detector for Walsh-Hadamard multiplexed binary antipodal signals, based on vector detection at the code-length size of the Walsh-Hadamard codes. Tight bounds on the bit error probability that are analytically derived or numerically computed, together with simulation results, show significant performance gain over symbol-by-symbol MAP detection for either one-dimensional or two-dimensional system configurations that lead to pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) rectangular constellations, respectively. In addition, the proposed system with MAP vector detection, presents great performance enhancement compared to standard binary phase shift keying (BPSK) modulation under identical information bit rate and mean power constraints, at a cost of higher instant power and moderate detection complexity.