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Optimal direction finding of broadband signals by an antenna array based on the application of superresolution techniques

Keywords:

A. N. Novikov – Ph.D. (Eng.), Lecturer of Military Academy of Strategic Rocket Troops after Peter the Great (Balashikha)
E-mail: band31@mail.ru


The saturation of modern megacities with radio-electronic means leads to problems in the transmission and reception of information, which is due to the poor electromagnetic compatibility of radio electronic equipment. One of the promising directions for solving this problem is use of superresolution methods for spatial selection of signals in antenna systems. This is due to the fact that these methods make it possible to obtain angular resolution for signal sources of higher degree than determined by the dimensions of the antenna aperture in accordance with the Rayleigh criterion. Thus, in addition to the frequency, time, and code separation of signals, it is possible for spatial separation with high density.
The analysis showed that at present the problem of spatial selection of signals based on the methods of superresolution is solved only for narrowband signals. However, modern conditions for radio-exchange dictate the need for signals with ultra-wide and wide bandwidth. The merits of these signals include high reliability of information transmission in conditions of multipath propagation of radio waves and the possibility of obtaining an ensemble of broadband signals occupying a common frequency band. If the mutually correlated functions of such signals have a negligible level, they can simultaneously be transmitted in the same band without significant mutual interference.
The article is devoted to the investigation of the possibilities of optimal spatial and frequency direction finding of broadband signals based on the Keipon superresolution methods and "thermal noise". For narrowband signals, this problem is solved by forming a direction-finding relief in the direction of arrival of the desired signals. Signals from other directions with the antenna array are not tracked. However, for broadband signals, it becomes necessary to form a direction-finding relief for all frequencies on which a broadband signal is transmitted. Thus, the difficulty of optimal spatial and frequency direction finding of broadband signals based on the methods of superresolution lies in the fact that it is necessary to form a direction-finding relief not only in the direction of the arrival of the useful signal but also for the entire frequency spectrum at which the spectral power of the signal is not zero.
Based on the known relationships describing the formation of the direction-finding relief in the case of direction-finding of narrow-band signals, analytical expressions describing the direction-finding relief based on the application of the Keipon method and "thermal noise" in the direction-finding of broadband signals were obtained.
The main difficulty in implementing these methods is the inversion of the covariance matrix of the signals. The article gives the rela-tionships that allow the matrix to be converted by a direct method.
Studies of the obtained regularities have shown that the direction-bearing relief is formed only at those frequencies and in those di-rections where the spectral density of broadband signals is not zero. However, it is necessary to form a direction-finding relief for an infinite spectrum of signal frequencies, which is associated with infinite computational costs. Therefore, the optimal direction finding of broadband signals based on the methods of superresolution is of a theoretical nature and has no practical implementation. In this regard, there is a need to develop practical quasi-optimal methods of directing broadband signals.

References:
  1. Ratynskij M.V. Adaptatsiya i sverkhrazreshenie v antennykh reshetkakh. M: Radio i svyaz'. 2003.
  2. Pistol'kors A.A., Litvinov O.S. Vvedenie v teoriyu adaptivnykh antenn. M.: Nauka. 1991.
  3. Litvinov O.S. Analiticheskie svojstva kovariatsionnoj matritsy pomekh v teorii priemnykh adaptivnykh reshetok // Antenny. 1982. № 30. S. 65–78.

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