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Mobile-to-mobile channels find increasing applications in futuristic intelligent transport systems, ad hoc mobile wireless networks, and relay-based cellular networks. Their statistical properties are quite different from typical cellular radio channels, thereby requiring new methods for their simulation. This paper proposes a "double-ring" model to simulate the mobile-to-mobile local scattering environment, and develops sum-of-sinusoids (SoS)-based models for simulating such channels. The proposed models produce waveforms having desired statistical properties with good accuracy, and also remove some drawbacks of an existing model derived by using the discrete line spectrum simulation method.