Maximum likelihood estimates of the angle-of-arrival of deterministic and random signals in multielement antenna arrays of various configurations

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. 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. 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. 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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