A Decision Feedback Equalizer (DFE) structure with a varying number of tap lengths was used with a recursive least squares (RLS) algorithm to determine tradeoffs between equalizer size and performance in mobile and portable digital radio systems. A mobile channel simulator, SMRCIM, was used to demonstrate how much an equalizer can improve the BER in real world urban channels. The results show that at 850MHz, the DFE is unable to improve the BER when the mobile terminal exceeds speeds of 115km/h for U.S. Digital Cellular systems. The performance of adaptive equalization for indoor high data rate systems was evaluated using the indoor channel simulator SIRCIM, and we found that DFEs have excellent performance for indoor radio channels. For simple structures, the BER is less than 10-3 at 15dB Eb/NO using coherent QPSK modulation. Finally, an equalizer structure for non-coherent π/4 DQPSK modulation was developed and simulation results are presented.