V.Yu. Semenov – Ph.D.(Phys.-Mat.), Senior Lecturer,  Department of Radioengineering, Lobachevsky State University of Nizhni Novgorod Е-mail: vitali.semenov@gmail.com

A.A. Podkopaev – Post-Graduate Student, 
Department of Radioengineering, Lobachevsky State University of Nizhni Novgorod Е-mail: podkolpaev.anton@yandex.ru

A single-channel automatic noise compensation based on an adaptive trans-versal filter is considered, which provides the minimum output power of the interference against the background of thermal noise. A method for suppressing interference is proposed, based on the representation of the weight vector in the form of an expansion in power-law vectors. An analytical solution is obtained for the optimal weight vector of the noise auto-compensator, on the basis of which an adaptive algorithm for generating the amplitudefrequency characteristics of the filter is built. The main advantage of the proposed transverse broadband interference filter is an adaptive estimate of the number of active interference, the frequency band occupied by them, and the small number of samples in the noise to find the weight coefficients. The computational complexity of the proposed method was estimated and it was shown that it has a significantly lower computational complexity compared to the direct inversion of the correlation matrix of interference.

The article is intended for specialists in the field of electronic warfare and radar. It considers one of the methods for solving the problem of suppressing the previously unknown number of noise interference operating at different frequencies in a single-channel receiving system. A rather complicated case is being investigated when active noise interference is stationary broadband processes. To account for the broadband interference, a multi-tap delay line is built into the receive channel. A so-called adaptive transversal filter is formed. The signals at the taps of the delay line are multiplied by weights and added up, forming the output signal of the adaptive transverse filter. The set of weights is combined into a weight vector whose dimension is equal to the number of taps of the delay lines.

A method for the formation of a weight vector based on its representation in the form of a finite expansion in the basis of power vectors is proposed. Power vectors are formed by cyclic action of the autocorrelation matrix of the input process in the taps of the delay line on the vector of mutual correlations between the input process and the delayed signals in the taps of the delay line. They have the physical meaning of correlation vectors, which allows the use of correlation devices for their formation. The paper presents a rigorous analytical derivation of the expression for weighting factors (weight vector).

The main advantage of the proposed signal processing is the ability to adaptively estimate the number of active interference in the frequency domain and suppress them using the minimum number of samples per interference. The formed adaptive transversal filter can be called a single-channel auto-compensator. In contrast to the known works, the main attention is paid to the case of a short sample of the input process, when the number of samples is less than the number of delay lines. In this case, the most plausible estimate of the autocorrelation matrix is degenerate, and it is necessary to apply regularized methods for estimating the weight vector. In the article, a regularized solution for the weight vector is obtained, based on a statistically correct limitation of the dimension of the power basis. The physical meaning of regularization is to evaluate the effective number of interferences based on the criterion for the maximum absolute value of the interference suppression coefficient.

The results of numerical modeling of the effectiveness of the proposed method are presented. The method is able to suppress the number of interference not exceeding the number of delay elements in the delay line. Moreover, the number of generated power vectors is of the order of the number of active interference. The presented results show a higher efficiency of the power-law method in comparison with the method of direct inversion of the correlation matrix of noise.

The computational complexity of the proposed method has been estimated and it has been shown that this method involves significantly less computation than the traditional method of direct inversion of the most probable estimate of the correlation matrix of the input process. A practical approach is proposed for introducing the power method in software due to the iterative structure of the weight vector calculation algorithm itself.

Semenov V.Yu., Podkopaev A.A. Broadband single-channel auto-compensator based on method of power vectors. Electromagnetic waves and electronic systems. 2020. V. 25. № 1–2. P. 33−42. DOI: 10.18127/j15604128-202001-2-04 (in Russian).

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