PhD Thesis Seminar

Zoom link: https://caltech.zoom.us/j/87898684587
Line spectrum signals appear in diverse application areas ranging from molecular dynamics to astronomy. This thesis focuses on two specific applications involving line spectrum signals: 1) direction of arrival (DOA) estimation using sensor arrays and 2) denoising of discrete-time periodic signals. The main contribution of the thesis on the topic of DOA estimation is to propose unconventional sensor array geometries and algorithms specifically designed to address practical challenges, such as limited available aperture and high mutual coupling between sensors. Two classes of arrays are proposed for this: 1) rational arrays and 2) weight-constrained arrays. By extending the number-theoretic notions of greatest common divisor (GCD) of coprimality to rational numbers, theoretical identifiability properties are derived for rational arrays. The suitability of proposed rational coprime arrays over integer arrays in adverse SNR and snapshot conditions is experimentally demonstrated by appropriately generalizing DOA estimation algorithms. For denoising discrete-time periodic signals, we propose a hybrid structure. Signal analysis is done using Ramanujan filter banks optimized according to Capon beamforming principles, and pruned Ramanujan dictionaries are used for reconstruction. Several multirate properties of the Ramanujan subspace signal are proved to reduce the required computations in the analysis stage.

The focus of the defense talk will be on weight-constrained arrays and improved DOA estimation algorithms. We highlight the drawbacks of some of the traditionally followed design criteria for sparse arrays and propose modifications to mitigate the impact of mutual coupling on DOA estimation and reduce the required aperture. With this, we construct multiple families of weight-constrained arrays that have strategically placed central holes in their difference coarrays. A general array construction is also proposed to reduce the weights at other coarray lags further. These families of arrays offer different tradeoffs in terms of array aperture and degrees of freedom. To effectively utilize such arrays, we propose using two improved algorithms for DOA estimation: augmented coarray MUSIC and covariance interpolation. Monte-Carlo simulations demonstrate the advantages of weight-constrained arrays over traditional sparse arrays in terms of improved DOA estimation accuracy, design flexibility, and robustness to mutual coupling.