LABIANCA/HARPER: A THEORETICAL APPROACH TO THE PREDICTION OF SIGNAL 



FLUCTUATIONS DUE TO ROUGH-SURFACE SCATTERING 



Figure 7 illustrates the ray-theoretic interpretation from a 

 different point of view, that of the generation of the first-order 

 sidebands at the point of impact of the surface-reflected carrier ray. 

 Given the angle of incidence of the carrier, the angles of the side- 

 band rays can be determined. It is clear from this diagram that each 

 of the two sidebands which contributes to a given field point must 

 have been generated by separate carrier rays impinging on the surface 

 at different points. Energy conservation is illustrated in Figure 8. 

 We have, in fact, established that to second order, the energy which 

 impinges on the surface is conserved in a ray-tube sense. The energy 

 which traverses a cross section of the incident ray tube is equal to 

 the sum of the energies which traverse cross sections of the sideband 

 and carrier ray tubes. 



The field-point contribution to the time series for the sinusoidal 

 surface case is illustrated in Figure 9. The first term corresponds 

 to the direct field and R is the distance between source and receiver. 

 The second term is the specularly reflected carrier. Here R is the 

 distance between the image and receiver and the term involving Q is 

 the energy-conservation correction to the carrier. The remaining 

 terms are the up and down Doppler-shifted sidebands. It is clear 

 from this form of the time series that the surface-scattering process 

 can be regarded as a narrowband FM process, a fact of some significance 

 in signal-processing applications. 



NUMERICAL RESULTS 



A description of some numerical results for the sinusoidal 

 surface case is given below. Noteworthy features are the asymmetry 

 in the sideband structure and the planes of symmetry in which the 

 sidebands become equal. The results for the sinusoidal surface case 



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