Interval analysis as analysis tool for Sub-Array Phase Architectures

Shamim, A. (2014) Interval analysis as analysis tool for Sub-Array Phase Architectures. Masters thesis, University of Trento.

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Abstract

Interval Analysis (IA) consists of a set of rules and tools for the analysis and optimization of functions where the variables at hand are intervals of numbers and not single values as in classical arithmetical/optimization problems. For example, an interval of real values (a real interval) can be defined as a one-dimensional compact set (a segment) between two extreme points, namely the minimum and maximum interval values. Interval Analysis has several attractive features that can be exploited to perform a deep and accurate analysis in different situations dealing with uncertain, error and tolerances. More in detail: 1. IA has an intrinsic capability to deal with uncertainties, always present when measurements are at hand. 2. Analytical equations and relationships can be easily reformulated and addressed by including intervals of numbers once the fundamentals of IA are known. 3. The bounds of a function when evaluated over an interval are determined in a straightforward manner without the need of evaluating the function on all (infinite) points of the interval. In this project, the IA will be exploited to analyze the effect of tolerance on the phases shifter of a linear antenna array taking into account different sub-array architectures and different kind of phase-shifter, introducing different value of quantization error. For a given linear array of N elements and Q sub-arrays: 1. Single Level Phase Shifter - Element Level - N phase shifters - one for each array elements 2. Single Level Phase Shifter - Sub-array Level - Q phase shifters - one for each sub-array 3. Double Level Phase Shifter - Element / Subarray Level - N + Q phase shifter - one for each sub-array + one for each array element

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