An Optimal One-shot Multiuser Detector for Flat Rayleigh Fading Channels

In this study 1 we derive the general form of an optimal one-shot multiuser detector given any density for the users' amplitudes. It is shown that well-known multiuser receivers such as the maximum likelihood detector, the decorrelating detector and even the MMSE detector are special cases of the above receiver, each optimal given a particular assumption about the density of the users' amplitudes. Finally, when it is assumed that the amplitudes obey a Rayleigh distribution, we obtain the optimal one-shot multiuser detector for at Rayleigh fading channels. Results show that, as expected, the resulting receiver has superior performance. With the advent of multiuser detectors 1], CDMA has proven to be a viable technology for the next generation of wireless systems (see, for example, 2]). However, one of the many challenges unique to the wireless channel, and one that has not been fully resolved, is the fact that the multipath fading environment is time-varying. Even though the statistics of the channel variations may be known, most multiuser detectors do not incorporate this knowledge into the detection process. Any such knowledge is most often used for tracking the channel variations. The minimum P e (probability of bit error) receiver, however, is a MAP (Maximum a-posteriori) receiver, that is, a receiver that directly incorporates the density of the channel variations into the bit decisions. To explore the potential gains of a multiuser MAP receiver, this study focuses on at fading environments. The attenuation suuered by the transmitted signal is well-modeled as being composed of three components: deterministic path loss, large (time) scale fading, and small (time) scale fading. The latter component is well-modeled as a Rayleigh random variable. Therefore, over a small time scale, since the deterministic and the large time scale components remain approximately constant, the received amplitude may be modeled as a Rayleigh r.v. with a xed mean. This mean is time-varying, but only over larger time scales, thus making it easier to track by the receiver.