# Sparse Array DFT Beamformers for Wideband Sources

## TL;DR

This paper introduces a DFT-based sparse array design for wideband beamforming that maximizes SINR, offering computational efficiency and improved performance in jamming environments.

## Contribution

It formulates the sparse array design as a QCQP in the DFT domain with a novel re-weighted SDR approach for wideband sources.

## Key findings

- DFT approach reduces computational cost significantly.
- Re-weighted SDR promotes sparse solutions effectively.
- Enhanced SINR performance in wideband jamming scenarios.

## Abstract

Sparse arrays are popular for performance optimization while keeping the hardware and computational costs down. In this paper, we consider sparse arrays design method for wideband source operating in a wideband jamming environment. Maximizing the signal-to-interference plus noise ratio (MaxSINR) is adopted as an optimization objective for wideband beamforming. Sparse array design problem is formulated in the DFT domain to process the source as parallel narrowband sources. The problem is formulated as quadratically constraint quadratic program (QCQP) alongside the weighted mixed $l_{1-\infty}$-norm squared penalization of the beamformer weight vector. The semidefinite relaxation (SDR) of QCQP promotes sparse solutions by iteratively re-weighting beamformer based on previous iteration. It is shown that the DFT approach reduces the computational cost considerably as compared to the delay line approach, while efficiently utilizing the degrees of freedom to harness the maximum output SINR offered by the given array aperture.