CFAR based NOMP for Line Spectral Estimation and Detection

TL;DR

This paper introduces NOMP-CFAR, a novel line spectral estimation method that maintains a constant false alarm rate without knowing noise variance, combining NOMP and CFAR techniques for improved detection accuracy.

Contribution

The paper proposes a CFAR-based NOMP method that preserves CFAR properties in spectral estimation, outperforming traditional NOMP in noise variance scenarios.

Findings

NOMP-CFAR achieves only 1 dB performance loss compared to NOMP in white Gaussian noise.

NOMP-CFAR maintains CFAR property across varied noise variances.

Real experiments validate the effectiveness of NOMP-CFAR in spectral detection.

Abstract

The line spectrum estimation problem is considered in this paper. We propose a CFAR-based Newtonized OMP (NOMP-CFAR) method which can maintain a desired false alarm rate without the knowledge of the noise variance. The NOMP-CFAR consists of two steps, namely, an initialization step and a detection step. In the initialization step, NOMP is employed to obtain candidate sinusoidal components. In the detection step, CFAR detector is applied to detect each candidate frequency, and remove the most unlikely frequency component. Then, the Newton refinements are used to refine the remaining parameters. The relationship between the false alarm rate and the required threshold is established. By comparing with the NOMP, NOMP-CFAR has only $1$ dB performance loss in additive white Gaussian noise scenario with false alarm probability $10^{-2}$ and detection probability $0.8$ without knowledge of noise variance. For varied noise variance scenario, NOMP-CFAR still preserves its CFAR property, while NOMP violates the CFAR. Besides, real experiments are also conducted to demonstrate the detection performance of NOMP-CFAR, compared to CFAR and NOMP.