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This paper introduces a general concept for the design of efficient multi-input multi-output (MIMO) narrowband fading channel simulators. The proposed procedure is applied on a reference model for the geometrical one-ring scattering model consisting of an infinite number of local scatterers lying on a ring around the mobile station (MS). The statistical properties of both the reference model and the simulation model are studied. Closed-form solutions are presented, e.g., for the space-time cross-correlation function (CCF), the time autocorrelation function (ACF), and the two-dimensional (2D) space CCF. It is shown how the parameters of the MIMO channel simulator can be determined for any given space-time CCF describing the reference model. The excellent performance of the proposed space-time channel simulator is demonstrated by comparing its temporal and spatial correlation properties with those of the reference model. Moreover, it is demonstrated how the channel simulator can be used to analyse the capacity of MIMO channels from time-domain simulations.