# Robust SAR Waveform Design for Extended Target in Spectrally Dense Environments

## TL;DR

This paper introduces a method to design robust SAR waveforms for better imaging of extended targets in crowded frequency environments.

## Contribution

A novel waveform design method that maximizes worst-case signal-to-clutter ratio under uncertainty and spectral constraints.

## Key findings

- The proposed method derives closed-form solutions for uncertain statistics in SAR imaging.
- The QCQP problem is transformed into solvable semidefinite programming using Dinkelbach’s algorithm and Lagrange duality.
- Numerical examples confirm the effectiveness of the proposed robust waveform design.

## Abstract

To enhance the signature of an extended target in a SAR image, a robust waveform design method is presented for spectrally dense environments. First, the problem is formulated by maximizing the worst-case signal-to-clutter ratio (SCR) over the uncertainty set of statistics for both target and background scattering characteristics, subject to energy, similarity, and spectrum constraints. Second, the closed-form solutions for the uncertain statistics are derived. The problem of maximizing worst-case SCR is boiled down to a nonconvex fractional quadratically constrained quadratic problem (QCQP). Resorting to the Dinkelbach’s algorithm and Lagrange duality, the QCQP is split into a series of solvable semidefinite programming problems. A convergence analysis is conducted, where a sufficient condition for global convergence is derived. Finally, numerical examples are presented to demonstrate the performance of the proposed scheme.