This thesis investigates multiple-input-multiple-output (MIMO) channel modelling for a wideband indoor environment. Initially the theoretical basis of geometric modelling for a typical indoor environment is looked at, and a space-time model is formulated. The transmit and receive antenna correlation is then separated and is expressed in terms of antenna element spacing, the scattering parameter, mean angle of arrival and number of antenna elements employed. These parameters are used to analyze their effect on the capacity for this environment. Then the wideband indoor channel operating at center frequencies of 2.4 GHz and 5.2 GHz is investigated. The concept of MIMO frequency scaling is introduced and applied to the data obtained in the measurement campaign undertaken at the University of Pretoria. Issues of frequency scaling of capacity, spatial correlation and the joint RX/TX double direction channel response for this indoor environment are investigated. The maximum entropy (ME) approach to MIMO channel modelling is investigated and a new basis is developed for the determination of the covariance matrix when only the RX/TX covariance is known. Finally, results comparing this model with the established Kronecker model and its application for the joint RX/TX spatial power spectra, using a beamformer, are evaluated. Conclusions are then drawn and future research opportunities are highlighted.