Document Details

Document Type : Thesis 
Document Title :
Covariance Matrix Estimation for Beamforming, Portfolio Optimization, and Linear Discriminant Analysis Applications
تقدير مصفوفة التغاير لتطبيقات تشكيل الحزمة وتحسين المحفظة وتحليل التمييز الخطي
 
Subject : Faculty of Engineering 
Document Language : Arabic 
Abstract : The thesis focuses on advanced techniques for estimating covariance matrices. Covariance matrix estimation problems undergo difficulties when the number of observations is insufficient or low compared to the dimension. As an essential theme throughout this thesis, sample covariance matrices are viewed in the context of linear models, where regularization techniques are introduced to balance the variance and bias of the estimator. Choosing a proper regularization parameter is crucial to improve the performance of the estimated covariance matrix. This research deals with two methods for selecting the regularization parameter properly. The first approach is based on the bounded perturbation regularization (BPR) method, which selects the parameter automatically given the sample covariance matrix. As an application, the linearly constrained minimum power beamformer is considered where it is shown that implementing the BPR has advantages over other competitive methods in limited-snapshot scenarios. The second approach is suitable for applications under a high-dimensional regime. In this case, the selection of the regularization parameter relies on a one-dimensional searching technique that leverages tools from RMT. In a high- dimensional regime, both the dimension and the number of observations grow essentially at a constant ratio. Two applications are presented in this work using RMT results to estimate the covariance matrix. In the portfolio optimization problem, a consistent estimator of the MSE of the noise vector is introduced to select the parameter effectively. The obtained results demonstrate superiority in limited observations as the uncertainty in estimating the mean is incorporated in the model. Finally, A nonlinear estimator of the covariance matrix is proposed for linear discriminant analysis. The misclassification error of this nonlinear estimator was derived using a consistent estimator, which reveals competitive performance. 
Supervisor : Prof. Muhammad Moinuddin 
Thesis Type : Doctorate Thesis 
Publishing Year : 1444 AH
2022 AD 
Co-Supervisor : Prof. Ubaid Al-Saggaf 
Added Date : Tuesday, February 28, 2023 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
معاذ الحاج مهديMahadi, Maaz ElhagResearcherDoctorate 

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