The focus of this thesis is to mitigate the very large peak-to-average transmit power ratios (PAPRs) inherent to conventional orthogonal frequency division multiplexing (OFDM) systems, particularly in the context of transmission over multi-input multi-output (MIMO) wireless broadband channels. This problem is important as a large PAPR generally needs an expensive radio frequency (RF) power amplifier at the transmitter due to the requirement for linear operation over a wide amplitude range and such a cost would be compounded when multiple transmit antennas are used. Advanced signal processing techniques which can reduce PAPR whilst retain the integrity of digital transmission therefore have considerable potential for application in emergent MIMO-OFDM wireless systems and form the technical contributions of this study.