V.Yu. Semenov – Ph.D.(Phys.-Math.), Senior Lecturer of the Department of Radio Engineering, 
Lobachevsky State University of Nizhni Novgorod
E-mail: vitali.semenov@gmail.com

A.A. Podkopaev – Post-graduate student of the Department of Radio Engineering, 
Lobachevsky State University of Nizhni Novgorod
E-mail: podkolpaev.anton@yandex.ru

An adaptive antenna array in MIMO radar, which simultaneously performs the suppression of narrowband spatial interference and receives a narrowband useful signal, is considered. The exact correlation matrix of thermal noise in the MIMO radar has been determined. An algorithm for processing the signal in the basis of power vectors is proposed, which provides the maximum ratio of the power of the useful signal to the total power of intrinsic noise and external interference (SNIR), as an expansion in the basis of power vectors. A regularized solution and analytic expressions are obtained for the weight vectors over a limited number of samples of the input process. The evaluation of the computational complexity of the proposed method was made. The results of numerical simulation, which show the high efficiency of the proposed method, are given.

Essay: The article is intended for specialists in the field of radar. It examines one of the methods for solving the problem that has arisen in modern automotive construction, namely, the suppression of active interference in the MIMO radar used to help the driver in a difficult road situation. Interference occurs, in particular, from oncoming cars on which radar is also installed. The main feature of the MIMO radar antenna array is that due to a specially selected topography of the transmitting and receiving emitters on the plane, as well as coding signals on the transmitting and decoding on the receiving side, in these systems, a virtual antenna array is formed on the receiving side of a much larger number of emitters, equal to the product of the number of transmitting and receiving emitters. In order to achieve such an increase in the antenna array aperture, a different orthogonal code is applied to each of the transmitting emitters, for example, the Walsh code. On the receiving side, reverse decoding occurs in each of the receiving radiators, as a result of which virtual receiving channels are formed. It is shown in the work that the exact correlation matrix of thermal noise in the MIMO radar continues to be single, and the noise in the virtual receiving channels is uncorrelated.

We propose a method for forming a weight vector, based on its representation in the form of a finite expansion in the basis of power vectors. Power vectors are formed by cyclic action of the correlation matrix of the input process in the antenna array on the vectorphasor of the useful signal. They have a physical meaning of correlational vectors, which allows us to use 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 papers, the main attention is paid to the case of a short sample of the input process in the reception channels of the lattice, when the number of sample vectors is smaller than the dimension of the weight vector. In this case, the maximally plausible estimation of the correlation matrix is degenerate and it is necessary to apply regularized methods for estimating the weight vector. A regularized solution for a weight vector is obtained in this paper, based on a statistically correct restriction of the dimension of a power basis. The physical meaning of regularization consists in estimating the effective number of operating interference, based on the criterion of the maximum ratio of the power of the useful signal to the total power of the intrinsic noise and external noise at the output of the antenna array.

The main advantage of the proposed space signal processing is the ability to adaptively estimate the number of active interference and suppress interference using the minimum number of interference samples. In this case, the useful broadband signal is distorted minimally. It is believed that a transmission period is allocated a time interval for calculating the interference correlation matrix. During this interval, the transmission and reception of a useful sounding signal is not performed.

The computational complexity of the proposed method is estimated and it is shown that this method assumes a much smaller volume of computations than the traditional method of direct inversion of the most plausible estimation of the correlation matrix of the input process. A practical approach to the introduction of the power method in the software is proposed due to the iterative structure of the weight vector calculation algorithm itself.

The results of numerical simulation of the effectiveness of the proposed method are presented. The method is able to suppress the number of interference not exceeding the number of physically existing receiving channels minus one. At the same time, the number of generated power vectors is the order of the product of the number of transmitting channels and the number of active ones. The presented results show a higher efficiency of the power method in comparison with the method of direct inversion of the correlation interference matrix.

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