mireabulletinRussian Technological JournalRussian Technological Journal2782-32102500-316XRTU MIREA10.32362/2500-316X-2025-13-6-47-62EYOGWGmireabulletin-1293Research ArticleСОВРЕМЕННЫЕ РАДИОТЕХНИЧЕСКИЕ И ТЕЛЕКОММУНИКАЦИОННЫЕ СИСТЕМЫMODERN RADIO ENGINEERING AND TELECOMMUNICATION SYSTEMSМаксимально правдоподобные оценки угла прихода детерминированных и случайных сигналов в многоэлементных антенных решетках различной конфигурацииMaximum likelihood estimates of the angle-of-arrival of deterministic and random signals in multielement antenna arrays of various configurationshttps://orcid.org/0000-0002-6679-9295БолховскаяО. В.BolkhovskayaO. V.

Болховская Олеся Викторовна, к.ф.-м.н., доцент, кафедра статистической радиофизики и мобильных систем связи, Радиофизический факультет 

603950, Нижний Новгород, пр-т Гагарина, д. 23 

Scopus Author ID 56373874700

ResearcherID AAQ-4264-2020 

Olesya V. Bolkhovskaya, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Statistical Radiophysics and Mobile Communication Systems, Faculty of Radiophysics 

23, Gagarina pr., Nizhny Novgorod, 603950 

Scopus Author ID 56373874700

ResearcherID AAQ-4264-2020 

obol@rf.unn.ruНациональный исследовательский Нижегородский государственный университет им. Н.И. ЛобачевскогоРоссияNational Research Lobachevsky State University of Nizhny NovgorodRussian Federation2025051220251364762Copyright © Болховская О.В., 20252025Болховская О.В.Bolkhovskaya O.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.rtj-mirea.ru/jour/article/view/1293Цели

Цели. Целью работы является исследование свойств максимально правдоподобных (МП) оценок углов прихода детерминированных и случайных сигналов в многоэлементных антенных решетках, разработка эффективных алгоритмов нахождения МП-оценок и определение точных значений пороговых отношений сигнал/шум, ниже которых возникают аномально большие ошибки, существенно превышающие теоретически минимальные значения, определяемые границами Крамера – Рао.

Методы

Методы. Теория оптимального приема сигналов, численное моделирование системы обработки сигналов в многоэлементных антенных решетках на основе разработанных алгоритмов нахождения МП-оценок, сравнение среднеквадратичных ошибок полученных оценок с теоретически минимальными границами Крамера – Рао, найденными аналитически.

Результаты

Результаты. В широком интервале значений отношений сигнал/шум выполнено численное исследование характеристик МП-оценок угла прихода детерминированных и случайных сигналов в многоэлементных линейных и круговых антенных решетках. Предложена методика определения с высокой точностью пороговых значений отношений сигнал/шум, ниже которых возникают аномально большие ошибки измерений. С помощью численного моделирования показано, что когерентная и некогерентная обработка сигналов дают одинаковые предельно достижимые точности при одинаковых отношениях сигнал/шум, превышающих пороговые значения. В то же время, на величину порога существенно влияют вид полезного сигнала и метод его обработки. Выявлены общие закономерности между этими пороговыми значениями, конфигурациями антенных решеток, типом обрабатываемого сигнала и используемым алгоритмом оценивания.

Выводы

Выводы. Полученные численные и аналитические результаты дают возможность выработать рекомендации по выбору конфигураций многоэлементных антенных решеток и основных параметров систем высокоточного пеленгования источников излучения различных сигналов, что позволит избежать возникновения аномально больших ошибок измерений. Результаты могут быть использованы непосредственно при расчете характеристик проектируемых систем. 

Objectives

Objectives. The purpose of this work is to study in detail the properties of maximum likelihood (ML) estimates of the angles-of-arrival of deterministic and random signals in multielement antenna arrays, to develop effective algorithms for finding ML estimates and to determine the exact values of threshold signal-to-noise ratios (SNR), below which abnormally large errors occur significantly in excess of the theoretically minimum values determined by the Cramér– Rao bounds.

Methods

Methods. The methods used include: the theory of optimal signal detection; intensive numerical simulation of the signal processing system in multielement antenna arrays based on the developed algorithms for finding ML estimates; and comparison of the standard errors of the estimates obtained by means of the theoretically minimal analytically established Cramér–Rao bounds.

Results

Results. Numerical study of the characteristics of ML estimates of the direction of arrival for deterministic and random signals was performed over a wide range of SNRs in multielement linear and circular antenna arrays. The study proposes a method for high-precision determination of threshold SNR values, below which anomalously large measurement errors occur. Numerical simulations demonstrate that coherent and incoherent signal processing yield the same ultimately achievable accuracy at the same SNR values above the threshold. At the same time, the threshold value is significantly influenced by the type of signal and the processing method. The general relationships between these threshold values, antenna array configurations, the type of signal processed, and the estimation algorithm used were identified.

Conclusions

Conclusions. The numerical and analytical results obtained allow recommendations to be developed relating to the choice of multielement antenna arrays configurations and the main parameters of systems for high-precision bearing of radiation sources of various signals. These enable abnormally large measurement errors to be avoided. The results can be directly utilized in the calculation of characteristics of systems under design. 

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The authors declare that there are no conflicts of interest present.