FDR Control for Complex-Valued Data with Application in Single Snapshot Multi-Source Detection and DOA Estimation

TL;DR

This paper introduces a fast FDR-controlling variable selection method for complex-valued high-dimensional data, with applications in signal processing tasks like source detection and DOA estimation.

Contribution

It proposes the CT-Rex selector that fuses multiple early terminated experiments to control FDR in complex data, filling a gap in existing methods.

Findings

Benchmarking shows superior FDR control and variable selection performance.

Application to DOA estimation demonstrates practical effectiveness.

Method achieves high detection accuracy in simulated complex regression scenarios.

Abstract

False discovery rate (FDR) control is a popular approach for maintaining the integrity of statistical analyses, especially in high-dimensional data settings, where multiple comparisons increase the risk of false positives. FDR control has been extensively researched for real-valued data. However, the complex data case, which is relevant for many signal processing applications, remains widely unexplored. We therefore present a fast and FDR-controlling variable selector for complex-valued high-dimensional data. The proposed Complex-Valued Terminating-Random Experiments (CT-Rex) selector controls a user-defined target FDR while maximizing the number of selected variables. This is achieved by optimally fusing the solutions of multiple early terminated complex-valued random experiments. We benchmark the performance in sparse complex regression simulation studies and showcase an example of FDR-controlled compressed-sensing-based single snapshot multi-source detection and direction of arrival (DOA) estimation. The proposed work applies to a wide range of research areas, such as DOA estimation, communications, mechanical engineering, and magnetic resonance imaging, bridging a critical gap in signal processing for complex-valued data.