Subspace-Based Frequency Estimation of Sinusoidal Signals in Alpha-Stable Noise

Abstract

In the frequency estimation of sinusoidal signals observed in impulsive noise environments, techniques based on Gaussian noise assumption are unsuccessful. One possible way to find better estimates is to model the noise as an alpha-stable process and to use the fractional lower order statistics (FLOS) of the data to estimate the signal parameters. In this work, we propose a FLOS-based statistical average, the generalized covariation coefficient (GCC). The GCCs of multiple sinusoids for unity moment order in SαS noise attain the same form as the covariance expressions of multiple sinusoids in white Gaussian noise. The subspace-based frequency estimators FLOS-multiple signal classification (MUSIC) and FLOS-Bartlett are applied to the GCC matrix of the data. On the other hand, we show that the multiple sinusoids in SαS noise can also be modeled as a stable autoregressive moving average process approximated by a higher order stable autoregressive (AR) process. Using the GCCs of the data, we obtain FLOS versions of Tufts-Kumaresan (TK) and minimum norm (MN) estimators, which are based on the AR model. The simulation results show that techniques employing lower order statistics are superior to their second-order statistics (SOS)-based counterparts, especially when the noise exhibits a strong impulsive attitude. Among the estimators, FLOS-MUSIC shows a robust performance. It behaves comparably to MUSIC in non-impulsive noise environments, and both in impulsive and non-impulsive high-resolution scenarios. Furthermore, it offers a significant advantage at relatively high levels of impulsive noise contamination for distantly located sinusoidal frequencies.