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The Gaussian quadrature rules (GQRs) are used to construct a wireless fading simulator based on the popular sum of sinusoids (SoS) method. The general statistics of the proposed simulator are given. This simulator is also shown to perform well for important design parameters. An extension of the GQRs is employed to build uncorrelated simulators, which are important in frequency selective and MIMO simulators. These simulation techniques are then applied to the mobile-to-mobile (MtM) spectrum and are compared with the best known SoS techniques for the MtM spectrum. Although the proposed method is more complex, the efficiency and accuracy are significantly better than the previously proposed methods.