The Effect Upon Antenna Arrays of Variations of Element Orientation and Spacing in the Presence of Channel Noise, with an Application to Direction Finding

Date of Award


Degree Name

Ph.D in Electrical and Computer Engineering


Department of Electrical and Computer Engineering


Advisor: Robert Penno


This work introduces the developments of a modified Min-Norm method to determine the AoA of an unknown signal incident upon an arbitrarily spaced array of randomly oriented elements in conjunction with a linear phase interferometer to accommodate large element spacing. This method is then applied to arrays comprised of two distinct element types via the use of MATLAB code written expressly for this purpose. The CRLB for both the original Min-Norm AoA estimator and the modified Min-Norm AoA estimator is derived. This dissertation aims to design a direction finding system that uses a volumetric, arbitrarily oriented and spaced antenna array and examines the perturbation effects of the orientation and position of the antenna elements on the accuracy of the estimated Angle of Arrival (AoA). The perturbation of the antenna elements is represented by six parameters: three parameters for element position and three parameters for element orientation. The impact of the polarization mismatch between the incident signal and the antenna elements that occurs when the array contains many antennas with various orientations have been taken into consideration in this work. If not accounted for, these effects can severely affect the accuracy of the direction-finding systems.First, an expression for the electric field in the far-field zone was derived using a volumetric array of arbitrarily oriented and spaced short dipoles using the Integral Equation Method and a volumetric arbitrarily-oriented and spaced pyramidal horn array using the Euler Method. Then, the Min-Norm AoA estimation method is modified through the Standard Lagrange Optimization Method to accommodate variations in the array signal vectors caused by perturbation of the orientation and position of the antenna elements. This method is selected due to its ability to address the side effect of averaging the pseudo-spectrum in the MUSIC Method, in which the peaks corresponding to the direction of the actual incident signal decreased in amplitude, and some spurious peaks appeared in the pseudo-spectrum.A linear phase interferometer, using an array of diversely polarized, relatively wide inter-element spaced pyramidal horn antennas was combined with the proposed AoA estimation method to utilize the advantages of both approaches to minimize the Root Mean Square Error (RMSE) of the estimated AoA. The proposed AoA estimation method has the advantage of being robust against the effects on the received signal associated with the perturbation of the orientation and position of the antenna elements and the polarization mismatch between the antenna elements and the incident signals. The linear phase interferometer eliminates the ambiguous AoA solutions associated with the phase wrapping at the relatively large inter-element spacing. The proposed AoA estimation method is investigated using different antenna types and various array configurations at random perturbation of the antenna position and orientation.Elevation and azimuth AoA estimation are combined to establish a single figure of merit for the system. The RMSE of the estimated angle of arrival is calculated from 2000 iterations of a Monte-Carlo simulation. Simulations verify that the modified AoA estimation method provides improved performance compared with the standard Min-Norm Method in terms of RMSE of the estimated AoA. The effect of perturbation of antenna orientation and position on the elevation and azimuth AoA estimation were compared in terms of a range of incident elevation and azimuth directions.


Electrical Engineering, Angle of Arrival, Antenna Array, Orientation, Position, RMSE

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