Compressive sensing of cyclostationary propeller noise

Abstract

This dissertation is the combination of three manuscripts -either published in or submitted to journals- on compressive sensing of propeller noise for detection, identification and localization of water crafts. Propeller noise, as a result of rotating blades, is broadband and radiates through water dominating underwater acoustic noise spectrum especially when cavitation develops. Propeller cavitation yields cyclostationary noise which can be modeled by amplitude modulation, i.e., the envelope-carrier product. The envelope consists of the so-called propeller tonals representing propeller characteristics which is used to identify water crafts whereas the carrier is a stationary broadband process. Sampling for propeller noise processing yields large data sizes due to Nyquist rate and multiple sensor deployment. A compressive sensing scheme is proposed for efficient sampling of second-order cyclostationary propeller noise since the spectral correlation function of the amplitude modulation model is sparse as shown in this thesis. A linear relationship between the compressive and Nyquist-rate cyclic modulation spectra is derived to utilize matrix representations for the proposed method. Cyclic modulation coherence is employed to demonstrate the effect of compressive sensing in terms of statistical detection. Recovery and detection performances of sparse approximation algorithms based on greedy pursuits are compared. Results obtained with synthetic and real data show that compression is achievable without lowering the detection performance. Main challenges are weak modulation, low signal-to-noise ratio and nonstationarity of the additive ambient noise, all of which reduce the sparsity level causing degraded recovery and detection performance. Higher-order cyclostationary statistics is introduced to characterize propeller noise due to its non-Gaussian nature. The third-order cyclic cumulant spectrum, also known as the cyclic bispectrum, is derived and its sparsity is demonstrated for the amplitude modulated propeller noise model. Cyclic modulation bispectrum is proposed for feasible approximation of the cyclic bispectrum based solely on the discrete Fourier transform. Additionally, compressive sensing of the cyclic modulation bispectrum is suggested. Numerical results are presented for acquisition of the propeller tonals using real-world underwater acoustic data. Tonals estimated by third-order cyclic modulation bicoherence are more notable than the ones obtained by second-order cyclic modulation coherence due to latter's higher noise floor. Sparse recovery results show that frequencies of the prominent tonals can be obtained with sampling significantly below the Nyquist rate. The accurate estimation of tonal magnitudes, on the other hand, is challenging even with large number of compressive samples. Compressive sensing can be extended to solve underdetermined system of equations which appears in direction-of-arrival estimation with uniform linear arrays. An estimator is proposed based on the compressive beamformer for cyclostationary propeller noise. Its asymptotic bias is derived, which is inherited from the conventional beamformer when there are multiple sources. Squared asymptotic bias and the finite-sample variance, also derived explicitly, constitute the mean-squared error. Spectral averaging is suggested to mitigate this error by decreasing the adverse effect of the spatial Dirichlet kernel. For low signal-to-noise ratios, averaging enables the proposed estimator to outperform the methods that assume stationarity. This is achieved even under weak cyclostationarity, numerous closely-spaced sources and few sensors. The proposed methods are not only suitable for compressive sensing of propeller cavitation noise but also for general class of cyclostationary signals. Relevant research areas include but are not limited to communication, radar, acoustics and mechanical systems with applications such as spectrum sensing, modulation recognition, time difference of arrival estimation, time-frequency distributions, compressive detection and rolling element bearing fault diagnosis.