A great interest in high rate communications has developed recently. InterSymbol Interference (ISI) is the main restricition in such systems. In order to circumvent ISI to reach high rate data transmission, application of the equalization methods seems unavoidable. The function of an equalizer is to improve the performance in retrieving the transmitted data symbols by compensating the ISI without excessive noise magnification in these systems. Equalizers are divided into two main groups: Linear and Nonlinear. Decision Feedback Equalizer (DFE) is nonlinear and uses previously detected symbols in order to estimate their interference and, consequently, reduce ISI in the current symbol. Regarding low realization complexity, it is appropriate to use such an equalizer in high rate applications. On the other hand, It is well known that the error propagation phenomenon is the main drawback of DFE, and it is not used very often in practice in severe channels (like wireless channels). The weighted DFE (WDFE) is proposed to limit this problem and is presented in this report. However, the design of an optimal equalizer is based upon a prior knowledge of the channel impulse response, as well as, some statistical characteristics of the noise and input signals, which are not available in most practical situations. So, common equalizers utilize training sequences which are known to the receiver. They can substantially solve the problem but decrease the effective bit rate, especially under substantial channel variations requiring frequent training sequences transmission. In some cases transmitting a training sequence is imopossible or difficult. So in recent decades, Blind Equalization (BE) (without training) has emerged significantly attractive and is addressed in this work. Furthermore, particularly in severely fading channels, Single-Inpute Multi-Output (SIMO) transmission is widely replacing Single-Input Single-Output (SISO) approach to enhance the performance via diversity combining. Hence, SIMO systems are also considered. In this report, some existing equalization methods with their main drawbacks for SISO and SIMO channels are presented. Then, a blind and adaptive DFE is proposed which has high speed convergence to desired Mean Square Error (MSE) and moreover, because of the adaptive structure can adapt to severe fast-varying channels. This method is comprised of two major steps. Channel information is blindly estimated over a short time period to be designed an optimal DFE. This design is used to initialize the second step. Next in this thesis, a new equalization Key Words : 1-Decision feedback equalizer (DFE), Supervised equalization, Blind equalization, ingle-Input Multi-Output (SIMO) channels, Multipath Rician fading channels