V.Yu. Semenov – Ph.D.(Phys.-Math.), Senior Lecturer, 
Department of Radio Engineering, Lobachevsky State University of Nizhni Novgorod
E-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

The article is intended for specialists in the field of radar and electronic warfare. It considers one of the methods for solving the classical radar problem - the reception of a useful signal reflected from the target when exposed to noise interference. A rather complicated and important practice case is studied when the useful signal and active noise interference are broadband processes, while the interference is of a pulsed nature. To account for the broadband interference and the useful sounding signal, a multi-tap delay line is built into the filter, the length of which corresponds to the length of the sounding broadband signal (for example, the M-sequence). The signals in the taps of the delay line are multiplied by weights and summed, forming the output signal of the adaptive filter. The set of weights is combined into a weight vector, the dimension of which 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 correlation matrix of the input process in the taps of the delay line on the vector-phasor of the useful signal. 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 weight coefficients (weight vector).
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 dimension of the weight vector. In this case, the most plausible estimate of the correlation 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 restriction on the dimension of the power basis. The physical meaning of regularization is to evaluate the effective number of active interference, based on the criterion for the maximum ratio of the useful signal power to the total power of intrinsic noise and external interference at the output of the antenna array.
The main advantage of the proposed temporal signal processing is the ability to adaptively estimate the number of active pulsed broadband interference, the frequency band occupied by them, and suppress interference using the minimum number of samples per interference. In this case, the useful broadband signal is distorted minimally. It is believed that a time interval is allocated during the sensing period for calculating the correlation matrix of interference in the taps of the delay line. During this interval, the transmission and reception of the useful sounding signal is not performed.
The computational complexity of the proposed method has been estimated and it has been shown that this method involves performing a much smaller amount of calculations compared to 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 algorithm itself for calculating the weight vector.
The results of numerical modeling of the effectiveness of the proposed method are presented. An M-sequence was used as a useful signal, and each broadband interference was formed as the sum of closely spaced tonal interference in a certain frequency band with random amplitudes and phases and with given probability density functions. The pulsed nature of the interference was formed using the trigger circuit. The presented results show a higher efficiency of the power-law method compared to the method of direct inversion of the correlation interference matrix.

Semeno V.Yu.v, Podkopaev A.A. Suppression of pulse broadband interference by adaptive filter based on method of power vectors. Electromagnetic waves and electronic systems. 2020. V. 25. № 4. P. 46−55. DOI: 10.18127/j15604128-202004-06. (in Russian)

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