Fluctuations of the apparent center of radiation near their expectation during the irradiation of distributed objects with probing signals from radar stations have been observed by scientists for many decades. An expression describing the statistical nature of such fluctuations is known in the literature. These fluctuations are called angular noise. With all this, there is still no expression connecting the angular dimensions of the object and the distribution parameters of its angular noise. This expression is necessary to predict the angular size of distributed objects in problems of simulating reflections from them. In the article, the problem indicated above is solved in two ways. When using the first method, it is possible to obtain an unambiguous relationship between the angular size of the object and the distribution parameters of its angular noise, but for each new object it is necessary to re-derive this relationship, which is not always possible. When using the second method, the probability is used with which the fluctuating apparent center of radiation of a signal reflected from a distributed object falls within the boundaries of this object. This method has no disadvantage of the first one. The results presented in this article were confirmed by means of mathematical modeling.
In this article we consider a problem of reliable modeling of echo signals and angle noise of distributed objects using twodimensional geometric models with random statistically unrelated signals. The conditions that ensure the invariance of distribution parameters of the angle noise generated by an arbitrary N-point configuration of a two-dimensional geometric model are obtained. In the particular case of a model whose emitters are supplied with signals of equal power, the conditions of invariance are reduced to the location of the model points on the plane in the form of a regular polygon. These results can be used to synthesize mathematical models used for simulating reflections from distributed objects and for developing a hardware-software complex for the simulation of electromagnetic fields reflected from the Earth surface, atmospheric inhomogeneities, the sea surface, etc.
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