Минимизация нижней границы Крамера-Рао для построения антенных решеток с направленными излучателями для повышения точности оценок угловых координат радиосигналов

Abstract

The use of antenna arrays equipped with digital signal processing units is a promising way to increase the throughput, noise immunity of modern wireless information transmission systems. The spatial diversity of the antenna is the main advantage of this approach which makes it possible to estimate the spatial coordinates of radio signals with subsequent beamforming. It is well known that the insufficient knowledge of the influence of the array geometry together with various types of antenna elements (such as a dipole, a patch, etc.) may be a cause reducing the accuracy of such systems. The article describes an approach aiming at reducing direction-of-arrival estimation errors of radio signal sources by means of optimal antenna array geometries. In particular, the Cramer-Rao lower bound is used for the task. The quantity sets a limit below which one or another algorithm for estimating the spatial coordinates of signal sources cannot descend for a particular geometry of the antenna array. The expressions based on the Cramer-Rao lower bound are derived which describes the dependence of the variance of direction-of-arrival estimation errors on the location of the array elements in the Cartesian coordinate system, i.e. along the x, y, z axes. In addition, the function of the radiation patterns of individual antennas is taken into account in the obtained formulas. Additionally it is considered that the antenna elements are directional. Therefore, the proposed technique is aimed at reducing the variance of direction-of-arrival estimation errors of statistical algorithms with superresolution by minimizing the obtained new formulas. As a result, the optimal locations of antenna elements along the x, y, z axes are calculated. In the paper, new geometries of antenna arrays have been obtained according to the proposed approach. In particular, two- and six-element arrays are researched, which are compared with equally spaced cylindrical ones. Graphs of the error variance of the Cramer-Rao boundary are presented, as well as a statistical study of the MUSIC method. It is shown that the magnitude of errors is reduced by new antenna arrays in all the researching scenarios. Thus the antenna arrays geometries obtained in this paper allow improving the accuracy of algorithms for estimating the angular coordinates of radio signals with superresolution.