This paper presents idealized computer simulation results of an equalizer using two-ray and measurement-based channel impulse response models. A decision feedback equalizer (DFE) with a recursive least squares (RLS) algorithm is used as the equalization scheme. The results show that adaptive equalization can significantly improve the bit-error-rate (BER) of a mobile system if the channel does not change too rapidly. The simulation shows that in a two-ray Rayleigh fading channel, If the delay of the second ray Is too small, then adaptive equalization will degrade the BER performance. The value of the delay at which the adaptive equalizer can improve the BER depends on the normalized Doppler frequency. Also, a mobile channel simulator is used to show how much the equalizer can Improve the BER in real world urban channels. The performance of adaptive equalization for indoor high data rate systems is abo evaluated. Finally, an equalization structure for n/4 DQPSK modulation is developed and simulation results are presented.