The probability of error for optimum detection on the two wave Rayleigh fading channel

The indoor wireless channel (20-60 GHz) can be modeled by a two wave Rayleigh model. The authors consider the optimum detector for equal energy signals on the two wave Rayleigh fading channel with known delay. They obtain upper and lower bounds on the probability of error when communicating on this channel using signals with nonzero complex cross-correlation. The bounds obtained converge to an exact expression for uniformly orthogonal signals. The expression explicitly demonstrates the existence of a diversity like effect, present whenever the delay is nonzero. Numerical evaluation of the bounds indicate that when the complex cross-correlation of the signals is small, the performance is nearly the same as the performance of the detector when it uses signals with zero complex cross-correlation