This thesis proposed a new adaptive equalization scheme which is a combination of recursive least squares adaptive algorithm, maximum likelihood sequence estimation and frequency offset compensation algorithm. Performance of the scheme is demonstrated in frequency selective fast fading mobile radio channels. The RLS-MLSE employs a parallel estimation scheme in which the state of the channel is estimated by the Viterbi algorithm and parameters of the channel impulse response are estimated by RLS. Carrier offset is estimated by averaging during preamble period and the proposed equalizer compensates this frequency offset. This proposed equalizer scheme is applied to the IS-136 TDMA cellular system. Computer simulations show that the BER performance of the proposed equalization scheme is better than the conventional RLS-MLSE scheme in the existence of frequency offset.