Space-time-frequency coded Multiple-Input and Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) systems have recently attracted much attention for broadband wireless communications including recent IEEE standards 802.11n and 802.16e. Space-time/Frequency Coding (SFC) can achieve the spatial and multipath diversities for a MIMO-OFDM system by coding across multiple antennas and subcarriers. In this research, we focus on a family of space-time-frequency codes proposed by Zhang et al to achieve both full spatial and multipath diversities by using Orthogonal Space-Time Block Codes (OSTBC). In particular, we develop a precoding algorithm for Peak-to-Average Power Ratio (PAPR) reduction and a clipping noise model based Maximum Likelihood (ML) decoding algorithm for Space-Time-Frequency Block Codes (STFBC) coded MIMO-OFDM systems. An important issue for OFDM systems is their high PAPR and it is important to reduce the PAPR in a practical (power efficient) system. The first goal of this research is to modify the repeating process and adjust phases of coded symbols so that the PAPR of the OFDM system is reduced. In particular, we propose to use Chu sequences for phase adjustment and show that the discrete PAPR can be reduced by & Gamma; times where & Gamma; is the times of the repeating across subcarriers. Another efficient way to reduce the PAPR in OFDM systems is clipping. After the clipping in an MIMO-OFDM system, the overall additive noise, including the clipping distortion, may not be white. The second goal of this research is to develop fast ML decoding algorithms for Orthogonal Space-Time-Frequency Block Codes (OSTFBC) and Quasi Orthogonal Space-Time-Frequency Block Codes (QOSTFBC) in clipped MIMO-OFDM systems. By using a clipping noise model with Gaussian approximation, our newly proposed fast ML decoding algorithms improve the system performance without increasing the decoding complexity. Simulation results are presented to illustrate the improvement. In order to apply the clipping noise model based ML decoding, the clipping ratio needs to be known at the receiver. We also consider the case when the clipping ratio is not known at the receiver. So a decision-aided clipping ratio estimation for MIMO-OFDM systems is proposed in our research, too. Except for MIMO-OFDM systems, in this work, cooperative OFDM system is investigated too. OFDM transmission has been proposed for cooperative communications to combat the time delays from the relay nodes, where the paths from relay nodes to destination node are treated as multipaths and space-time (or frequency) coding is used to achieve the spatial (or multipath) diversity. With this approach, when the Cyclic Prefix (CP) length is less than the time delay length, inter-block interference occurs. In this research, we consider Alamouti coded OFDM systems in cooperative communications where the CP length may be less than the time delay length. By taking the advantage of the Alamouti code structure, we propose a time domain interference cancellation algorithm.