This dissertation focuses on providing solutions to two of the most important problems in wireless communication systems design, namely, 1) the interference suppression, and 2) the channel parameter estimation in wireless communication systems over time-varying multipath fading channels. We first study the interference suppression problem in various communication systems under a unified multirate transmultiplexer model. A state-space approach that achieves the optimal realizable equalization (suppression of inter-symbol interference) is proposed, where the Kalman filter is applied to obtain the minimum mean squared error estimate of the transmitted symbols. The properties of the optimal realizable equalizer are analyzed. Its relations with the conventional equalization methods are studied. We show that, although in general a Kalman filter has an infinite impulse response, the Kalman filter based decision-feedback equalizer (Kalman DFE) is a finite length filter. We also propose a novel successive interference cancellation (SIC) scheme to suppress the inter-channel interference encountered in multi-input multi-output systems. Based on spatial filtering theory, the SIC scheme is again converted to a Kalman filtering problem. Combining the Kalman DFE and the SIC scheme in series, the resultant two-stage receiver achieves optimal realizable interference suppression. Our results are the most general ever obtained, and can be applied to any linear channels that have a state-space realization, including time-invariant, time-varying, finite impulse response, and infinite impulse response channels. The second half of the dissertation devotes to the parameter estimation and tracking of single-input single-output time-varying multipath channels. We propose a novel method that can blindly estimate the channel second order statistics (SOS). We establish the channel SOS identifiability condition and propose novel precoder structures that guarantee the blind estimation of the channel SOS and achieve diversities. The estimated channel SOS can then be fit into a low order autoregressive (AR) model characterizing the time evolution of the channel impulse response. Based on this AR model, a new approach to time-varying multipath channel tracking is proposed
