A power-spectral theory of propagation in the mobile-radio environment

The statistical properties of radio propagation between a mobile unit and a base-station terminal are derived. The power spectrum of the transmission coefficient in the multipath medium is used to determine probability distributions of amplitude and phase, correlations of fields versus time and space at mobile and base stations, level-crossing rates and durations of fades, and random frequency modulation. Duality between the power spectrum and density of time delays is shown. The correlations versus frequency and the coherence bandwidth then follow from the density of time delays. The performance of standard diversity systems is then predicted. There is a review of results previously presented by Clarke [1], however, the derivations given herein utilize expressions of the power spectrum rather than expressions of the component waves. The power-spectral approach, used throughout, allows direct application of previous statistical analyses, particularly those of Rice [2].