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In this work we continue the analysis of a probabilistic approach and the corresponding stochastic multi-parametric model of wave propagation in built-up areas with randomly distributed buildings. Here we concentrate on the spectral properties of signal strength spatial variations and on Doppler spread spectrum distribution of signal power. The analysis is based on a unified stochastic approach of radio wave propagation above the built-up terrain with applications to mobile communications. We analyze the signal power spectrum of spatial frequencies and the signal power distribution in the Doppler domain for moving vehicles, taking into account Doppler shift proportional to the vehicle antenna speed with respect to the base station. The comparison between the theoretical prediction and experimental data was motivated by the proposed stochastic model and by other existing statistical models to verify the signal power distribution in the Doppler domain for various urban environments and terminal heights with respect to building rooftops. New effects of terrain features on signal power spectrum distribution are obtained and examined through the comparison with existing models and experimental data.