The objectives of this project are the synthesis of digitally implemented demodulator architectures which achieve near ideal coherent digital communication performance in the frequency nonselective slow fading channel. Coherent digital communication performance provides a 3 dB improvement over the most commonly utilized fading channel demodulation architecture, differentially coherent detection. Digitally implemented architectures are the best method of achieving this coherent performance since they possess many practical and theoretical advantages. The first stage of this project focuses on the development of generalized algorithms for carrier estimation and symbol demodulation. This work is developing phase estimation algorithms optimized for the fading channel and a carrier with frequency uncertainty. In the second phase symbol timing estimation and joint phase and symbol timing estimation on the fading channel is being investigated. The work will help produce modems with near optimal performance on the fading channel with many practical advantages.