Equalization of Numerically Calculated Element Patterns for Root-Based Direction Finding Algorithms

Abstract

Root-based direction finding algorithms (DF) have several advantages over search-based DF algorithms. A key advantage is the fact that they do not require the array steering vector; this is because these algorithms presume equalized element radiation patterns. In this paper the WIPL-D code is used in designing an array of rectangular probe-fed patch antennas with equalized radiation patterns for measuring the range and bearing of RF emitters in the PCS band (1900-1920 MHz). Direction of arrival (DoA) estimation results based on simulations and measured data are presented and used as a measure of element patterns deviation from equality. Direction finding (DF) algorithms for DoA estimation is a topic that has been studied thoroughly in the past few decades mainly by researchers in the signal processing and antenna theory communities. From signal processing point of view the focus has been on maximizing the number of DoAs that can be accurately estimated and at the same time reducing the computational cost involved in this work. Several algorithms exist and can be used to estimate the DoA of incident signal on an antenna structure (1)-(3). DF algorithms are classified as either search-based or root-based. We refer to the former class as S-DF algorithms and to the later class as R-DF algorithms. R-DF algorithms have several advantages over S-DF algorithms. In addition to their less computation cost where DoAs are calculated by finding the roots of a polynomial of certain order rather than going through intensive search in the whole angular domain, a key advantage from using R-DF algorithms is the fact that they do not require the array steering vector. This is because these algorithms presume equalized element patterns and their accuracy depends on how much the element patterns deviate from equality. This paper investigates the design and performance analysis of antenna structures with equalized element patterns for R-DF algorithms. Adding a number of passive elements around the center active elements and terminating them using a suitable set of loads minimize the deviation of the element patterns of the center elements from equality (4). Return loss and element patterns of two antenna structures comprised of a number of rectangular probe-fed patch antennas are calculated using the WIPL-D code (5). The first structure consists of four elements and no passive elements. In the second structure three passive elements are added on both sides of the four active elements and were terminated in 50Ω. DoA estimation results using the two antenna structures are compared with DoA estimated using measured data. The DoA accuracy is used as a measure of how much element patterns deviate from equality. The paper is organized into four sections. Following this introductory section, in section two return loss and element patterns calculated using WIPL-D are presented for the two antenna structures mentioned before. DoA estimation results using either WIPL calculated patterns or measured data are compared and presented in section three. Finally conclusions are provided in section four.