# Theoretical Analysis for Extended Target Recovery in Randomized Stepped Frequency Radars

## TL;DR

This paper provides a theoretical analysis of block sparse recovery methods for extended target reconstruction in Randomized Stepped Frequency Radar, demonstrating conditions for guaranteed exact recovery and validating with simulations and experiments.

## Contribution

It introduces a theoretical framework analyzing block coherence and spectral norm in RSFR, establishing bounds for guaranteed extended target recovery.

## Key findings

- Block sparse recovery outperforms conventional sparse recovery in RSFR.
- Theoretical bounds ensure exact recovery of range-Doppler information.
- Simulation and field tests confirm the effectiveness of the proposed approach.

## Abstract

Randomized Stepped Frequency Radar (RSFR) is very attractive for tasks under complex electromagnetic environment. Due to the synthetic high range resolution in RSRFs, a target usually occupies a series of range cells and is called an extended target. To reconstruct the range-Doppler information in a RSFR, previous studies based on sparse recovery mainly exploit the sparsity of the target scene but do not adequately address the extended-target characteristics, which exist in many practical applications. Block sparsity, which combines the sparsity and the target extension, better characterizes a priori knowledge of the target scene in a wideband RSFR. This paper studies the RSFR range-Doppler reconstruction problem using block sparse recovery. Particularly, we theoretically analyze the block coherence and spectral norm of the observation matrix in RSFR and build a bound on the parameters of the radar, under which the exact recovery of the range-Doppler information is guaranteed. Both simulation and field experiment results demonstrate the superiority of the block sparse recovery over conventional sparse recovery in RSFRs.