Fluctuations in received signal amplitude occur during mobile communications because of the motion of the mobile station through the spatial standing‐wave pattern resulting from the interaction of direct and reflected signals. A model is presented which permits a theoretical calculation of the power spectrum of these fluctuations and satisfactorily predicts the features of spectra computed from experimental fading data except for an observed rise at low frequencies.
The model is based on the geometry of the reflections from nearby randomly placed vertical plane reflectors. Vertical polarization is assumed. Both the standing‐wave pattern and the Doppler shift view of fading are used to obtain nearly identical results. The detailed shape and in particular the sharp cutoff frequency of the spectrum are shown to depend crucially on the angle a between the direction of vehicle motion and the direction to the fixed station. Detailed comparisons are made of theoretical spectra with experimental spectra representing a range of the angle α.
The collection, digitization, calibration, plotting, and digital processing to obtain power spectra of actual recorded fading waveforms are described.
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The cepstrum (power spectrum of the log power spectrum) and the pseudo-autocovariance (Fourier cosine transform of the log power spectrum) were proposed as a method to detect an echo in a time series, and for possible application as a substitute for autocorrelation to determine the depth of a seismic or acoustic source. The cepstrum and pseudoautocovariance are much more tolerant of the shape of the power spectrum of the echoed signal than is the autocorrelation. Computer-generated examples of white and colored echoed Gaussian signals in Gaussian noise are given that exhibit this property. [Work supported in part by the U. S. Navy Bureau of Ships.]
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