WIDEBAND SCATTERING FROM RANDOMLY DISPERSED DISCONTINUITIES IN A TRANSMISSION LINE: STATISTICAL THEORY.
Physical sciences research papers no. 370,
AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
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In a theoretical treatment of the effects of signal bandwidth on the characteristics of electromagnetic waves reflected from randomly dispersed scatterers, a simplified one-dimensional model consisting of a transmission line with randomly spaced discontinuities is analyzed by methods of statistical communications and scattering theory. The probability density function PDF for the power reflection coefficient in this line is derived analytically for input signals composed of either discrete or continuous frequency spectra. The analysis shows that statistical fluctuations in the reflected power decrease with increasing bandwidth. An algorithm allows substituting a spectrum composed of equispaced, discrete frequencies for a continuous, band-limited spectrum in the analysis. The effects of interaction between the scatterers and of resistive attenuation in the transmission line are also considered quantitatively. The application of these results to three-dimensional scattering problems, such as microwave propagation in the troposphere or optical scattering from random particles, is discussed briefly. Techniques for extending the theory to physical situations that involve temporal and spatial, as well as spectral, variations of the scattered energy are included. Author
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