Taylor Expansion and Matrix-Based Interval Analysis of Linear Arrays With Patch Element Pattern Tolerance

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.