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Shape Optimization of Low-Element Antenna Arrays Based on the Minimization of the Azimuthal or Elevation Angles According to the Lower Cramer-Rao Bound

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This study proposes a method for designing optimally shaped antenna arrays from the perspective of error reduction of azimuthal or elevation angles for the identification of the direction of detected radio signals. The accuracy is determined by the lower Cramer–Rao bound, which is a statistical estimate of the error dispersion. It is the level below which it is impossible to access the signal regardless of the direction identification algorithm used. Thus, the purpose of this study is to build an antenna array in which the locations of the elements allow the minimization of the dispersion errors pertaining to the directionality of the detected radio signals. The proposed method minimizes the generalized expression of the lower Cramer–Rao bound. It shows that the accuracy of the identification of the radio direction is inversely proportional to the sum-of-the-squared differences between the coordinates of all omnidirectional elements along the x–, y–, and z–axes. Based on the estimated location area of the signal source, the arrangement of the antenna array elements is optimized in accordance with the maximum likelihood function that constitutes the basis of the lower Cramer–Rao bound. The optimization is based on the maximization of the probability of estimation. Accordingly, a study on the Multiple Signal Classification method is conducted and it shows that the accuracy of the direction identification can be increased up to 10-fold in comparison with similar, conventional (uniform), circular arrays.
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Radio Direction Detection; Optimization; Lower Cramer-Rao Bound; Antenna; Super-Resolution

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