||As a result of developments in hardware miniaturization and computer technology, portable computers nowadays are becoming cheaper and smaller. Together with the trend towards ever smaller telecommunications transceivers, there is a great demand for the mobility of portable computers with wireless connection to data communication networks. Wireless LAN applications would require high bit rates of up to l0-20 Mbit/s if they are to compete with wire-line LAN systems such as Ethernet. Higher bit rates may even be required if multimedia services are to be supported. Associated with these high transmission rates, however, is the problem of multipath ISI due to frequency selective fading. Antenna diversity and adaptive equalization are two common and practical techniques for combating multi-path ISI. The combination of diversity reception and equalization may provide even greater reductions in ISI and the ultimate system performance has been investigated in previous studies In this thesis, the trade-offs between diversity combining and decision feed-back equalization with respect to the computational complexity and bit error rate performance is studied. The capability for combating co-channel interference (CCI), which occurs when frequency reuse is applied to maximize the number of users supported, will also be investigated. Results are provided as average probabilities of bit error (Pe) and also outage probabilities. These results would be useful to determine the required number of diversity branches and feedforward and feedback equalization taps in the wireless LAN design. Another practical issue of adaptive equalization schemes with or without diversity combining; namely, the convergence rate, has also been addressed in the thesis. Adaptive algorithms with slow convergence rates usually require long training sequences and hence, the throughput will be reduced. A well-known fast channel estimation technique with low complexity based on channel sounding is available for fast initialization of equalization. However, to obtain optimal estimation performance in channels corrupted by noise, optimal sequences which satisfy a certain desired auto-correlation property are needed. In this thesis, we study a class of optimal sequences consisting of complex symbols with constant magnitude, which are constructed with minimum length and are suitable for transmitters using non-linear power amplifiers. A new indirect sequence construction method is proposed, which is not only simple but also provides insight into the nature and properties of sequences which are based on underlying consecutive roots-of-unity phase difference sequences. Our method includes periodic and aperiodic optimal sequences, and provides a unification of some previous methods.