The estimation of channel coefficients constitutes a major function of the receiver. It is also an important step in the signal detection process at the receiver, in a wireless communication system. To describe the space-time channel from multiple transmitters to a single receiver, many parameters are required. This means that in order to perform channel estimation and signal detection, the order P say, of the required filter will be very large. Since the channel is time varying thus the filter adaptive, a large P implies a slow response to changing channel conditions. This is one motivation for reduced-rank adaptive filtering. In this project, several aspects of space-time channel parameter estimation, and signal detection, are examined. Three methods have been studied. A maximum likelihood channel estimation method and two different subspace-based, reduced-rank methods - the "cross-spectral" method and the "residual correlations" method.