High-speed and high-quality data transmission in wireless communication environments is a very important issue, which has recently received considerable attention in the research and development of wireless personal communications systems. However, the performance of wireless digital communications systems is severely impaired by multipath fading in wireless communication channels. In order to mitigate the effects of wireless channels, various methods such as equalization and coding have been studied to achieve better system performance. Specifically, we first investigate the effects of time delay spread on unequalized trellis-coded modulation (TCM) and find the limitation on the transmission rate without equalization over frequency-selective fading channels. In order to support high signaling rates, we then propose an equalization structure that combines decision feedback equalization (DFE), TCM, soft-decision Viterbi decoding, interleaving and antenna diversity together to mitigate both ISI and a single dominant cochannel interference which typically occur in cellular mobile environments due to frequency reuse in spatially separated cells. In the proposed structure, more reliable detected symbols can be fed back to the DFE, so as to provide better system performance than that of the conventional DFE with TCM systems. In addition to the DFE based equalization, optimum signal detection methods are studied based on a posteriori probability (MAP) algorithms which are optimum in the sense of minimizing symbol error probability. These algorithms are suitable for concatenated equalization and coding systems because they can provide soft-information about detected symbols to the decoder. We study this type of algorithms and apply some MAP algorithms such as Lee's MAP algorithm to perform signal detection which was used in convolutional decoding, and propose a modified MAP algorithm and some channel estimation strategies that are needed in the MAP algorithms. In addition to the proposed equalization methods, a lower bound for the pairwise average error probability of the equalized TCM schemes over frequency selective fading channels is derived. An equalizer generally needs a training sequence for initial adjustment of its parameters. In some situations, it is impractical or inefficient to send a training sequence. It is also desired to equalize a multipath channel without the aid of training sequences. Therefore, blind equalization is studied for improving the transmission efficiency. We propose a blind equalization strategy that is suitable for short burst TDMA systems along with a blind equalization algorithm. Finally, we conclude this thesis by reviewing key findings and outlining further work.