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Estimating the Number and Coordinates of Closely Spaced Radiation Sources From a Space-Time Sampling


M.I. Sychev

Space-time radio signal processing for estimating of the number and coordinates radiation sources, which are located in the same resolution unit by Relay criterion, is discussed. We will consider the problem of estimating the number and coordinate of closely spaced radiation sources as a multi-alternative test of the complex hypotheses . The hypothesis corresponds to the presence of N radiation sources in resolution unit. A multistep statistical procedure was proposed. At the first step of the procedure the hypothesis is tested against alternative . If the resulting procedure supports a decision in favor of the main hypothesis, the testing of the hypotheses is finished. We assume that the number of radiation sources in investigated resolution unit is equal to zero. If a decision is made in favor of alternative we proceed to the second step of testing the hypotheses, in which the hypothesis is tested against the alternatives . The testing is undertaken analogously in this step. If a decision was made in favor of alternative hypothesis, then in (N + 1)-th step, the hypothesis is tested against the alternative . The generalized likelihood ratio criterion was used to synthesize a decision rule at (N + 1)-th step of the procedure. Generally it leads to necessity of the decision of a problem of nonlinear optimization. Ways of simplification of the offered procedure are considered. Space-time signal processing algorithms that synthesized according to the proposed approach for line antenna array are discussed. Regular character of an arrangement of elements of an antenna array has allowed to reduce a problem of the estimation of the number and angular coordinates of the radiation sources for analyzed model, to well studied problems of linear algebra and a finding of roots of polynoms. Thus, it was possible to avoid the direct decision of a problem of nonlinear optimization. The synthesized procedure is reduced to formation of an estimation of a spatial correlation matrix. Its averaging in view of dot character of the radiation sources and the subsequent averaging under the aperture of an antenna array. After that, minimal eigenvalue which is compared to a threshold is calculated. The corresponding eigenvector is used for estimation of angular coordinates of the radiation sources. The algorithm is investigated by a simulation. The simulation results are presented
May 29, 2020

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