# Block- and Rank-Sparse Recovery for Direction Finding in Partly Calibrated Arrays

## TL;DR

This paper introduces a novel sparse recovery method for direction finding in partly calibrated arrays, leveraging block-sparsity and low-rank structures, with improved performance over existing methods in challenging scenarios.

## Contribution

The paper presents a new technique combining nuclear norm and 1 norm minimization for direction finding in partly calibrated arrays, including a reformulation for efficient implementation and a gridless extension.

## Key findings

- Outperforms the RARE method in low SNR scenarios
- Effective with low sample numbers and correlated signals
- Applicable to arbitrary subarray topologies

## Abstract

A sparse recovery approach for direction finding in partly calibrated arrays composed of subarrays with unknown displacements is introduced. The proposed method is based on mixed nuclear norm and 1 norm minimization and exploits block-sparsity and low-rank structure in the signal model. For efficient implementation a compact equivalent problem reformulation is presented. The new technique is applicable to subarrays of arbitrary topologies and grid-based sampling of the subarray manifolds. In the special case of subarrays with a common baseline our new technique admits extension to a gridless implementation. As shown by simulations, our new block- and rank-sparse direction finding technique for partly calibrated arrays outperforms the state of the art method RARE in difficult scenarios of low sample numbers, low signal-to-noise ratio or correlated signals.