ESTIMATES OF THE NUMBER OF SPACE-TIME SIGNALS IN MULTI-CHANNEL RECEIVING

Abstract

The analysis of the first stage of ensuring the selectivity of multi-channel radio engineering systems under conditions of a parametrically uncertain interference environment, the detection of spatial signals with varying intensity and unknown angular parameters, is performed. Within the theory of multi-alternative solutions, using the likelihood ratio criterion, a method is proposed for solving the problem of estimating the number of space-time signals with unknown angular parameters in the indicated noise conditions, the starting point of which is the likelihood ratio criterion. On the basis of the theory of multi-alternative solutions, a decision rule was synthesized in favor of any of the proposed hypotheses on the number of orthogonal space-time signals with the above-mentioned model characteristics, which uses standard computational operations and allows to control the error probability of the first kind. It is proved that for an unknown character of the change in the intensity of orthogonal space-time signals, it is advisable to focus on performing analysis in an interference subspace. Distinctive feature of the synthesized decision rule: critical statistics are formed on the basis of the eigenvalues of the correlation matrix of observations under multichannel reception conditions. The analysis showed that the statistical distribution density is tabulated, which made it possible to "priori" set the required value of the error of the first kind. Attestation of the synthesized test − the decision rules in favor of the proposed hypothesis about the corresponding number of orthogonal space-time signals contained in multichannel observations, was carried out in two modes: the first - the change in the intensity of the signals was noise-like, the second - the envelope of each of the signals remained constant for a time interval. The significance level was set at 0.01. Based on the results of the simulation, a comparative analysis of the number of correct solutions (based on the implementation of the corresponding hypothesis on the number of space-time signals) on the signal-to-noise ratio in power for a given angular parameter spacing was carried out. Elements of selective correlation in the modeling process were estimated for 100 independent time samples. The results of the numerical simulation confirm the conclusions of the theoretical studies.

Keywords

• перевірка гіпотез, критерій відношення правдоподібності, багатоканальна система, сигнал