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Achieving accurate and effective modeling of the vehicle-to-vehicle (V2V) communication channel has proven to be a challenging task, particularly owing to the highly dynamic nature of vehicular environments. V2V channels generally may have contributions from the line-of-sight path, reflections from large stationary and moving objects such as bridges and other vehicles, and a diffuse base from large numbers of small stationary objects in the environment. We propose a new geometrical model for the diffuse component based on scattering objects distributed along the roadside, and use this model to predict the Doppler spectrum and angle-of-arrival distribution associated with this component for various V2V scenarios. In contrast with previous roadside scattering models that sum the contributions from large numbers of randomly-generated scattering objects, our model assumes a uniform linear distribution along the roadside. This permits a computationally efficient, closed-form model. Comparisons with on-road measurement data as well as the double ring model demonstrate the validity and effectiveness of the proposed model.