Abstract
In this study, a novel interval analysis (IA) approach for linear arrays with element pattern tolerance is proposed. This study differentiates itself from the classic interval analysis (CIA) method because it focuses on the effects of the array element (e.g., patch) pattern tolerance on the antenna array pattern; the tolerance may be caused by fabrication errors in the element. The closed-form pattern expressions of the element (e.g., patch) and array are deduced by the interval arithmetic method. To mitigate the interval extension (also referred to as the overestimation problem) caused by the dependency problem, Taylor expansion and matrix-based interval analysis (TMIA) methods are proposed and implemented in this study. A set of numerical examples is reported and analyzed to indicate the effectiveness of the proposed TMIA approach with the results of Monte Carlo (MC) and CIA methods, as well as to indicate its potential capabilities and advantages in the actual application of industrial antenna arrays.
Highlights
An antenna array is the most important radio frequency (RF) front-end element utilized for radar, wireless communication, and navigation systems
From [25], we can obtain the bounds of the patch antenna via classic interval analysis (CIA) as follows: feiPnfE/sup (θ )
Some conclusions can be drawn as follows: 1) for the significant overestimation problem of CIA, the Taylor expansion can apparently reduce the interval width effectively; 2) higher-order Taylor expansion leads to satisfactorily precise results, but the error between the higher order (7th-order) and lower order (5th-order) is tiny; 3) the effect of the element factor tolerance on the array power pattern varies with the lobes, and the same tolerance has a greater effect on further lobes than on the main and closer lobes
Summary
An antenna array is the most important radio frequency (RF) front-end element utilized for radar, wireless communication, and navigation systems. The interval arithmetic method can sufficiently address the problem of the interval parameter (i.e., tolerance); this method has been adapted for tolerance analysis of reflector antennas [18]–[20], arrays [3]–[7], reflector arrays [12], radomes [21], [22], and CLAS [23] Both the dimensions [12] and material errors [21] of an antenna resulting from the fabrication process are modeled as interval variables, and their effects on the radiation pattern are analyzed; no studies regarding tolerance analysis of an antenna array’s element factor (pattern) currently exist. We focus on the three geometric tolerances in this study
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