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Synthesis and analysis of algorithm of radio-wave radiation direction evaluation in tracking system with a 2D few-element antenna array of optimal spatial structure


Yu.N. Parshin – Dr. Sc. (Eng.), Professor, Head of Department of Radio Technical Devices, Ryazan State Radio Engineering University. E-mail: P.A. Aleksandrov – Post-graduate Student, Ryazan State Radio Engineering University. E-mail:

Antenna arrays (AA) with a small number of elements, along with a relatively simple technical implementation are able to provide a digital beamforming algorithms and optimal spatial processing. Interference cancelation is an important part of optimal algorithms. Application of few element AA restricts spatial selection of signals and interference. One of the promising ways to empower linear spatial processing is to optimize the spatial structure of the system. The purpose of the paper is to improve the angular coordinate of the radio source evaluation efficiency when using a two-dimensional planar array antenna in case of spatially correlated noise in azimuth and elevation planes. The algorithm, optimal by the criterion of maximum likelihood ratio was investigated. Log-likelihood ratio expressions for deterministic, Quasideterministic and random Gaussian signal models were obtained. The accuracy of estimating the direction of the signal source is determined by the variance of the angular coordinate estimation error, the lower limit of which is defined by the Cramér Rao inequality. Dispersion matrix, which is obtained by substituting the partial derivatives of log-likelihood ratio in a matrix of Fisher Information from the Cramér Rao inequality, allow us to create error ellipses. Their semi-axes length characterize standard deviations of coordinates estimation. The major semi-axis of error ellipse could be considered as a measure of estimation efficiency. Estimation error calculations were performed for square AA with 2×2 and 3×3 elements with distance between elements is given by d = λ, where λ is a wavelength, depending on the position of single and multiple interference. The calculation results demonstrate the increase in efficiency evaluation of the angular coordinates of the desired signal source when a spatial difference between the desired signal and the noise is growing. It is shown that the number of elements and spatial structure of the AA have a significant impact on the efficiency of interference cancelation. There is an increase in angular coordinate estimation accuracy with the number of AA elements. Few-element AA application does not provide efficiency for a large number of interference sources, as well as extended interference. The required number of elements reduction or the amount of cancelable interference increase can be obtained by selecting the optimum position of AA elements. For example of the AA with 2×2 elements and four spaced interference it is shown that the optimum position for a particular interference environment reduces the estimation error several times. Angular coordinate estimation algorithms investigations revealed that the optimisation of the spatial structure of few-element AA is a significant factor in improving the accuracy of angular coordinate estimation.


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