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In this paper, we present a new method for the design of ergodic sum-of-sinusoids (SOS) simulation models for multiple uncorrelated Rayleigh fading channels. The method, which is intended for a special class of SOS models, known as sum-of-cisoids (SOC) models, can be used to generate an arbitrary number of uncorrelated Rayleigh fading waveforms with specified Doppler power spectral characteristics. This is in contrast to the SOS simulators currently available in the open literature that have been designed under the isotropic scattering assumption, which are limited to the simulation of uncorrelated channels characterized by Clarke's U-shaped Doppler power spectral density (DPSD). The excellent performance of the proposed method is exemplarily demonstrated by comparing the correlation and the spectral characteristics of a set of generated Rayleigh fading waveforms with those of a reference group of uncorrelated Rayleigh fading channels by considering different types of DPSDs. The simulation approach described in this paper can easily be applied to the laboratory performance analysis of mobile broadband communication systems using diversity, multicarrier, or multiple-input multiple-output (MIMO) techniques under generalized scattering conditions.