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A correlation-based double-directional stochastic channel model for indoor multiple-input multiple-output (MIMO) ultra-wideband (UWB) propagation channels is proposed. The proposed model extends the IEEE 802.15.3a standard model to spatially correlated MIMO channels. Both angular and temporal statistics are taken into account in the modelling procedure. Spatial correlation is introduced into the multipath amplitude and time-of-arrival (ToA) matrices of the channel model. Each amplitude matrix consists of entries of correlated lognormal random variables, whereas each ToA matrix is obtained as the sum of a reference matrix and a difference matrix. The frequency-dependent spatial correlation function is derived to give an insight of model properties. Model parameters are determined based on well-known measurement campaigns. In addition, simulation-based analysis indicates that this model has desirable spatial correlation properties in both the time and frequency domains. The ToA correlation matrix was also found to have dominant effects on the correlation characteristics. This suggests that future research into spatial correlation properties of MIMO-UWB channels should focus on ToA correlation characteristics, rather than amplitude correlation characteristics, which are the current focus of narrowband and wideband MIMO channel research.