Nowadays Orthogonal Frequency Division Multiplexing (OFDM) is used as a popular method for high data rate transmission in wireless systems. Dividing the wideband fading channel to several flat narrowband sub-channels, OFDM systems have a robust performance against destructive fading phenomenon of the channel. One of the topics discussed in this thesis is wireless channel estimation using Kalman filtering. Kalman filter can be used to estimate processes from a state space model. Channel estimation besides frequency and time synchronization are the two important and effective issues regarding OFDM systems performance. Not only the quality of the channel estimation algorithm affects the communication system’s overall performance, but also its computational complexity is of importance. In this thesis the transition matrix of the state space model is diagonalized by choosing a new basis for the model. Then by further simplifications we present a method named diagonalized Kalman filter based on the original Kalman filtering method. The method presented has lower computational complexity compared to the original method. The OFDM signal suffers from large peak variation which is usually represented by the Peak to Average Power Ratio (PAPR) parameter. Signals with large PAPR force the high power amplifiers to operate with low power efficiency in order to avoid signal clipping. In this thesis current PAPR reduction methods are introduced. These methods are divided into two groups of distortion and distortion less techniques. A new PAPR reduction method is also presented in this paper by modifying FFT and IFFT matrices.