This proposal is set in the context of the ever increasing demand for high data rate transmission over wireless access, underpinned by the growth of increasingly sophisticated multimedia services. This is very challenging due to the quality of service requirements and tight constraints on available radio spectrum in practical systems. The ultimate aim of our work is therefore to enable wireless systems such as WLANs and WMANs to provide seamless data transmission beyond 100Mb/s, and possibly up to 1Gb/s, as a replacement for established wire-line technology such as cable modems and ADSL. We believe that it will only be possible to support such very high speed data transmission through the exploitation spatial diversity, i.e. exploiting the plurality of paths provided by having multiple antennas at the transmitter and most probably at the receiver too.We will in particular propose advanced transmit diversity and spatial multiplexing techniques and associated resource allocation algorithms for broadband wireless access systems. The proposed diversity techniques will be based on channel state information feedback. Since such channel state information requires considerable bandwidth in the reverse link for its transmission, we will investigate various novel feedback quantization techniques and will propose Grassmannian plane (subspace) packing based matrix quantization techniques to reduce feedback overhead significantly. We will also develop space-time-frequency based statistical mean and covariance feedback techniques to further reduce the feedback overhead. The performance of all of our methods will be evaluated using in depth mathematical analysis and simulation studies (on synthetic and field datasets, with guidance from Telecom Modus) based upon error statistics such as bit error rates and block error rates. Our work will be presented at the foremost international conferences and published within the leading IEEE technical journals, such as IEEE Trans. Wireless Communications.