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Worst-case analysis of array beampatterns using interval arithmetic.

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Interval arithmetic (IA) now finds specific errors causing worst-case phased-array beampattern bounds using backtracking. This method enables analysis of array performance and extends IA to complex geometries and error types.

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Area of Science:

  • Electrical Engineering
  • Computational Electromagnetics
  • Numerical Analysis

Background:

  • Interval arithmetic (IA) has been utilized for determining tolerance bounds of phased-array beampatterns.
  • IA provides reliable bounds without statistical error models, requiring only bounded element errors.
  • Previous studies have not focused on identifying specific error realizations that lead to these bounds.

Purpose of the Study:

  • To extend interval arithmetic capabilities by introducing a backtracking concept.
  • To enable direct recovery of error realizations and corresponding beampatterns for specific bounds.
  • To analyze worst-case array performance, specifically the peak sidelobe level (PSLL).

Main Methods:

  • Introduction of a "backtracking" concept within interval arithmetic.
  • Extension of IA to support arbitrary array geometries, including directive elements and mutual coupling.
  • Inclusion of element amplitude, phase, and positioning errors within the IA framework.
  • Derivation and numerical verification of a formula for approximate bounds of uniformly bounded errors.

Main Results:

  • The backtracking method allows for the recovery of specific error realizations and their resulting beampatterns.
  • IA is enhanced to handle complex array configurations and various error types.
  • A new formula for approximate bounds of uniformly bounded errors was derived and validated.
  • Insights into the limits of array size and apodization for reducing worst-case PSLL were gained.

Conclusions:

  • The developed backtracking approach enhances interval arithmetic for analyzing phased-array beampatterns.
  • The extended IA framework offers broader applicability to diverse array designs and error conditions.
  • The derived formula provides a valuable tool for understanding fundamental limitations on worst-case PSLL reduction.