||Digital cellular systems which use TDMA techniques have recently became one of the most popular mobile communication systems. However, the propagation characteristics of a wireless communication channel make it difficult to achieve high speed data transmission at low error rates. In particular, intersymbol interference (ISI) and co-channel interference (CCI) are two main factors which may significantly degrade the system performance. To achieve a reliable high bit-rate transmission and high system capacity, methods to cancel such interference are thus necessary. Traditionally, equalization was used to mitigate the effect of ISI. Recently, various methods have been developed to extend equalization to cancel CCI as well. In the first part of this thesis, an adaptive equalization scheme which can cancel both ISI and CCI is proposed. The proposed algorithm is blind in the sense that we do not have knowledge of the training sequences of the interfering users. In particular, it is a maximum likelihood sequence estimation (MLSE) equalizer that is implemented by the generalized Viterbi algorithm (GVA) with an RLS-based channel estimator. To demonstrate the potential of the proposed method, various simulation results over a frequency selective Rayleigh fading environment in the presence of CCI are presented. As the complexity of the GVA can be quite large, a new sequential algorithm with adaptive thresholds is introduced to reduce the computational complexity of GVA. It is demonstrated that computational complexity reduction along with good system performance can be achieved as long as the adaptive thresholds are properly selected. In various situation, it may be difficult or inefficient to use training sequences for adjusting the equalizer parameters. Hence, in the second part of this thesis we investigate the use of GVA with the proposed sequential algorithm as a blind equalization method that is suitable for short-burst TDMA communication systems.