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Estimation of the elevation angle of the low altitude target: a mathematical model of the signal scattered by the rough surface at sliding propagation angles

DOI 10.18127/j20700784-201911-03


A.A. Monakov – Dr.Sc. (Eng.), Professor, Department «Radio Engineering System», Saint-Petersburg State University of Aerospace Instruments
N.V. Povarenkin – Ph.D. (Eng.), Associate Professor,  Department «Radio Engineering System», Saint-Petersburg State University of Aerospace Instruments

The greatest difficulty in estimating the angular coordinates of a low altitude target occurs when the signal source and its antipode cannot be resolved in any of the signal parameters: angle (direction of wave arrival at the receiving point), range (time delay), speed (Doppler frequency), polarization. However, this problem has a solution in the case of using multi-channel spatial radar systems and the use of adequate signal models for the synthesis of signal processing algorithms. This article proposes a mathematical model of a signal received when observing a low altitude target flying over a rough surface. When constructing the model, it was assumed that the rough surface is cylindrical. This assumption made it possible to carry out a complete computer simulation and to control the correctness of the applied approximations, as well as to suggest calculations that can be used to solve the problem of electromagnetic wave scattering on a two-dimensional rough surface. In addition, the use of a cylindrical surface permitted to use the obtained results to simulate the situation of the radar vehicle flying perpendicular to waves on a water surface. The basis of the proposed mathematical model is the equation for the signal scattered from the rough surface obtained in the Kirchhoff approximation. The use of the stationary phase method allowed to calculate the mean value and the mean power of the coherent (specular) and incoherent (diffusive) components of the scattered wave. Analysis of the equations for each of the components allowed to make the following conclusions: the amplitude of the coherent component of the scattered signal rapidly decreases with increasing the surface roughness parameter, and if its value is greater than or equal to 2, this component in the received signal can be neglected; the incoherent component is a weakly correlated in adjacent antenna elements vector random process. The testing of the proposed model was carried out via computer simulation. The applicability of the analytically received equations for calculating the characteristics of a scattered field was tested through comparing them with the simulation results. The simulation showed that for the dependences of the mean powers of the coherent and incoherent components of the scattered signal versus the surface roughness, there was a good agreement between the theoretical and experimental results, and during the observation time the incoherent component practically did not change during the observation interval over a wide range of the surface roughness parameter.

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June 24, 2020
May 29, 2020

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