The Cramer-Rao lower bound (CRLB) for calculating errors and accuracy of direction-of-arrival (DOA) estimation is discussed for a number of planar waves arriving on an antenna array. It is well known that the geometry of antenna arrays imposes restrictions on the performances of the direction-of-arrival estimation. In particular, the influence of the directivity factor of the individual antenna elements on the accuracy of the DOA estimation of the radio emission sources for circular (cylindrical), cubic and spherical antenna arrays consisting of the directional antenna elements is investigated. The directivity factor of antenna elements is changed within wide limits in order to determine the values at which the high accuracy of the direction-finding can be achieved. It is shown that further increasing the directivity factor of each antenna element makes the mean square error in the determination of the coordinates of the signals increase as well. The exact expression for the Cramer-Rao lower bound for the DOA-estimation variance calculation depending on the antenna directivity and the geometry is presented. The obtained exact equation shows the most important factors that the direction-of-arrival estimation accuracy is dependent on. A technique of obtaining antenna arrays with optimal directional elements locations is proposed. Those arrays allow increasing DOA estimation accuracy by several times.
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