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Permanent link (DOI): https://doi.org/10.7939/R3J919

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Parameter Estimation in Low-Rank Models from Small Sample Size and Undersampled Data: DOA and Spectrum Estimation Open Access

Descriptions

Other title
Subject/Keyword
Compressed sensing
DOA estimation
Undersampled data
Sub-Nyquist sampling
Spectrum estimation
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Shaghaghi, Mahdi
Supervisor and department
Jiang, Hai (Electrical and Computer Engineering)
Vorobyov, Sergiy A (Electrical and Computer Engineering)
Examining committee member and department
Vorobyov, Sergiy A (Electrical and Computer Engineering)
Zhao, Vicky (Electrical and Computer Engineering)
Bajwa, Waheed U (Rutgers, The State University of New Jersey)
Kong, Linglong (Mathematical and Statistical Sciences)
Jiang, Hai (Electrical and Computer Engineering)
Li, Yunwei (Electrical and Computer Engineering)
Department
Department of Electrical and Computer Engineering
Specialization
Communications
Date accepted
2014-12-19T13:51:55Z
Graduation date
2015-06
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
In estimation theory, a set of parameters are estimated from a finite number of measurements (samples). In general, the quality of estimation degrades as the number of samples is reduced. In this thesis, the problem of parameter estimation in low-rank models from a small number of samples is studied. Specifically, we consider two related problems that fit in this system model: direction-of-arrival (DOA) and spectrum estimation. We focus on subspace based DOA estimation methods which present a good compromise between performance and complexity. However, these methods are exposed to performance breakdown for a small number of samples. The reason is identified to be the intersubspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. A two-step algorithm is proposed to reduce the amount of the subspace leakage. Theoretical derivations and simulation results are given to show the improvement achieved by the introduced method. Furthermore, the dynamics of the DOA estimation method in the breakdown region has been investigated, which led to identification of a problem named root-swap where a root associated with noise is mistakenly taken for a root associated with the signal. Then, an improved method is introduced to remedy this issue. Spectrum estimation from undersampled data (samples obtained at a rate lower than the Nyquist rate) is studied next. Specifically, the performance of the averaged correlogram for undersampled data is theoretically analyzed for the finite length sample size as well as asymptotically. This method partitions the spectrum into a number of segments and estimates the average power within each segment from samples obtained at a rate lower than the Nyquist rate. However, the frequency resolution of the estimator is restricted to the number of spectral segments, and the estimation made for each segment has also limited accuracy. Therefore, it is of significant importance to analyze the performance of this method especially in the case that only a finite number of samples is available. We derive the bias and variance of the averaged correlogram for undersampled data for finite-length signals, and we show the associated tradeoffs among the resolution, the accuracy, and the complexity of the method. Finally, spectrum estimation from compressive measurements is studied. The number of such measurements is much less than the number of Nyquist samples, and they are obtained by correlating the signal with a number of sensing waveforms. We specifically consider signals composed of linear combinations of sinusoids. Albeit these type of signals have a sparse model, their representation in the Fourier basis exhibits frequency leakage. This problem results in the poor performance of the conventional compressive sensing recovery algorithms that rely on the Fourier basis. We introduce an improved model-based reconstruction algorithm which has a performance close to the Cramer-Rao bound, which we also derive.
Language
English
DOI
doi:10.7939/R3J919
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
M. Shaghaghi and S. A. Vorobyov, “Subspace leakage analysis and improved DOA estimation with small sample size,” submitted to IEEE Trans. Signal Process., Jul. 2014.M. Shaghaghi and S. A. Vorobyov, “Iterative root-MUSIC algorithm for DOA estimation,” invited paper, in Proc. 5th Inter. Workshop Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, The Friendly Island, Saint Martin, Dec. 2013, pp. 53–56.M. Shaghaghi and S. A. Vorobyov, “Finite-length and asymptotic analysis of correlogram for undersampled Data,” preprint: arXiv:1305.5592.M. Shaghaghi and S. A. Vorobyov, “Correlogram for undersampled data: bias and variance analysis,” in Proc. 37th IEEE Inter. Conf. Acoustics, Speech, and Signal Processing, ICASSP 2012, Kyoto, Japan, Mar. 2012, pp. 3513–3516.M. Shaghaghi and S. A. Vorobyov, “Improved model-based spectral compressive sensing via nested least squares,” in Proc. 36th IEEE Inter. Conf. Acoustics, Speech, and Signal Processing, ICASSP 2011, Prague, Czech Republic, May 2011, pp. 3904–3907.

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