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.
