Probabilistic Interval Analysis for the Analytic Prediction of the Pattern Tolerance Distribution in Linear Phased Arrays With Random Excitation Errors

Abstract

A statistical approach based on the Interval Analysis (IA) is proposed for the analysis of the effects, on the radiation patterns radiated by phased arrays, of random errors and tolerances in the amplitudes and phases of the array-elements excitations. Starting from the efficient, reliable, and inclusive computation of the bounds of the complex-valued interval array pattern function by means of IA, an analytic method is presented to yield closed-form expressions for the probability of occurrence of a user-chosen value of the power pattern or of its features within the corresponding IA-derived bounds. A set of numerical examples is reported and discussed to assess the reliability of the proposed probabilistic interval analysis (PIA) method with the results from Monte Carlo simulations as well as to point out its effectiveness and potentialities/advantages/efficiency in real applications of great industrial interest.

Impact Analysis and Calibration Methods of Excitation Errors for Phased Array Antennas

“…Generally speaking, the Polygonal IA method performs the best for most scenarios, while the Circular IA method performs the worst. An analytic method is also proposed to analyze and further dig the information from the shape of the convex polygon of the array pattern, and map it into the probability distribution of the bound interval [40].…”

“…Although well established, statistical methods have not always guaranteed reliable confidence bounds, some extreme cases can still fall outside the bounds. On the contrary, IA based methods introduce intervals to represent the possible values of the element excitation including both amplitude and phase, and predict the array performance by its upper and lower bounds [30][31][32][33][34][35][36][37][38][39][40]. Thanks to the inclusion property of IA to deal with uncertainties, the determined bounds of antenna array pattern are finite and inclusive thus reliable.…”

Closed‐loop controlled microwave beamformer

“…Closed‐form expressions are presented in Reference 45 to quantify these three deviations by assuming that the random errors in the amplitude and phase of the coefficients are normally distributed. More recently, in Reference 21, a new statistical approach is introduced to evaluate these radiation pattern distortions.…”

“…Phased arrays with microwave beamformer, 2 the focus of this paper, are composed of an array of antennas and high‐frequency circuitry (i.e., beamformer) that imposes complex weights (amplitudes and phases) on the signals at the terminals of each antenna. Random errors on these complex weights limit the accuracy of radiation pattern control, being an important issue related to this system 21 . Such errors are caused mainly by temporal variations of the parameters of active components (e.g., amplifiers, phase shifters, variable attenuators, and controllers) and by environmental changes (e.g., thermal, vibrations, and mechanical strains) 22,23 .…”

“…The analysis of the radiation pattern degradation caused by the random errors in the excitation coefficients imposed by the beamforming circuit is another important issue related to microwave beamformers 21,45–49 . In particular, special attention is given to the beam pointing deviation, directivity fluctuation, and side lobe level (SLL) variation.…”