CFAR based NOMP for Line Spectral Estimation and Detection

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.