This work presents a study of the adaptive equalization techniques designed to improve the bit error rates of digital transmissions degraded by intersymbol interference in radio communication. This thesis considers the following structures: the linear transversal equalizer (LTE), the decision feedback equalizer (DFE), the lattice equalizer, and the maximum likelihood sequence estimation (MLSE) equalizer. Least mean square (LMS) and recursive least squares (RLS) algorithms are used as the adaptive algorithms for these equalizers. Lattice-DFE, DFE, and MLSE with an RLS algorithm are recommended to be implemented in mobile systems because of their better performances. A two-ray Rayleigh fading channel model is used to simulate the mobile channels. The results show that adaptive equalization can significantly improve the performance of mobile communications if the channel does not change too fast. The simulation shows that if the delay (T) of the second ray is too small, the adaptive equalization will degrade the BER performance, and the value of T at which the adaptive equalizer can improve the BER is determined by the speed of the mobile channel variation. Also, simulation results obtained by using SIRCIM, a real world indoor channel simulator, shows that adaptive equalization has good performance in slowly varying channels. An equalizer working in indoor high data rate systems has a BER less than 10-3 at 15 dB Eb/Noâ ¢ The SMRCIM urban channel model is also developed and implemented for equalization simulation. Finally, equalization structures for differential modulation techniques are proposed.