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A random matrix model is introduced that probabilistically describes the spatial and temporal multipath propagation between a transmitting and receiving antenna array with a limited number of scatterers for mobile radio and indoor environments. The model characterizes the channel by its richness delay profile which gives the number of scattering objects as a function of the path delay. Each delay is assigned the eigenvalue distribution of a random matrix that depends on the number of scatterers, receiving antennas, and transmitting antennas. The model allows one to calculate signal-to-interference-and-noise ratios (SINRs) and channel capacities for large antenna arrays analytically and quantifies to what extent rich scattering improves performance.