This project has three specific areas of study: Efficient Channel-Based Equalization, the computation of the equalizer via channel characterization derived from embedded training data; Interference Rejection for Code-Division Multiple Access, near-far and intersymbol interference and interference from disparate users; and Multicarrier Methods for Broadcast Transmission, for mitigation of time-varying fading effects. The focus of the study is on the time-varying multipath data channel. At relatively low data rates, the time-varying nature of wireless communication channels often leads to channel variation over a small number of symbol intervals. In this case a significant amount of training data can be embedded in the transmitted packets of data to enable adjustments to be made at the receiver. An alternative, perhaps forced by the need for higher data rates, is to increase the bandwidth of the transmitted signal. Then the relative rate of channel variation is less compared to the symbol rate, and the fraction of training is reduced. As wider bandwidths are used, multipath effects become more important and more sophisticated receiver structures need to be used. The research studies both narrow and wideband transmission, for applications in digital cellular radio and digital broadcast channels.