Suboptimum detection for the two-wave Rayleigh-fading channel

Indoor wireless communication in the 20-60 GHz band requires schemes that are biased toward power efficiency rather than bandwidth efficiency and use simple, robust detectors. Using the two-wave Rayleigh-fading channel as a model for the indoor wireless channel, the optimum detector structure is derived, and a simple suboptimum detector is developed. This suboptimum detector is a straightforward extension of the optimum detector for the single-wave Rayleigh-fading channel. The suboptimum detector is optimum for the channel when the delay of the second wave is known, and whenever the equal energy signals have a normalized complex autocorrelation of either zero or unity at that delay. The performance of this suboptimum detector on the two-wave Rayleigh-fading channel with known delay is studied. An exact expression for the probability of error is derived for uniformly orthogonal, equal energy, binary signals. This expression, which is in terms of the average signal-to-noise ratios in the waves and the complex autocorrelation of the signals, explicitly exhibits the presence of a diversity-like effect when the delay between the waves is non zero, and is an approximation for the probability of error when the complex cross-correlation is small. When the suboptimum detector is used, wideband signals, such as chirp signals and variants, perform well on this channel, enhancing the diversity-like effect. Such signals are also shown to make the suboptimum detector nearly optimal in structure.>