Pattern Synthesis via Complex-Coefficient Weight Vector Orthogonal Decomposition--Part II: Robust Sidelobe Synthesis

TL;DR

This paper extends the C^2-WORD algorithm for robust sidelobe control in array processing, providing an analytical, iterative method to handle steering vector mismatches and achieve precise sidelobe synthesis.

Contribution

It introduces a robust C^2-WORD algorithm with analytical expression for sidelobe synthesis under steering vector mismatch, improving robustness and practicality.

Findings

Effective sidelobe control with steering vector mismatch considered

Analytical expression enables starting from arbitrary weight vectors

Simulation validates robustness and performance improvements

Abstract

In this paper, the complex-coefficient weight vector orthogonal decomposition ($ \textrm{C}^2\textrm{-WORD} $) algorithm proposed in Part I of this two paper series is extended to robust sidelobe control and synthesis with steering vector mismatch. Assuming that the steering vector uncertainty is norm-bounded, we obtain the worst-case upper and lower boundaries of array response. Then, we devise a robust $ \textrm{C}^2\textrm{-WORD} $ algorithm to control the response of a sidelobe point by precisely adjusting its upper-boundary response level as desired. To enhance the practicality of the proposed robust $ \textrm{C}^2\textrm{-WORD} $ algorithm, we also present detailed analyses on how to determine the upper norm boundary of steering vector uncertainty under various mismatch circumstances. By applying the robust $ \textrm{C}^2\textrm{-WORD} $ algorithm iteratively, a robust sidelobe synthesis approach is developed. In this approach, the upper-boundary response is adjusted in a point-by-point manner by successively updating the weight vector. Contrary to the existing approaches, the devised robust $ \textrm{C}^2\textrm{-WORD} $ algorithm has an analytical expression and can work starting from an arbitrarily-specified weight vector. Simulation results are presented to validate the effectiveness and good performance of the robust $ \textrm{C}^2\textrm{-WORD} $ algorithm.