Advances and New Applications of Spectral Analysis

Research output: ThesisDoctoral ThesisCollection of Articles


Spectral analysis is a mathematical tool for modeling signals and extracting information from signals. Among the areas where it finds applications are radar, sonar, speech processing, and communication systems. One of applications of spectral analysis is to model random signals with the so-called rational models like autoregressive (AR) model. Spectral analysis is used for estimating direction-of-arrival (DOA) in array processing as well. In addition, spectral analysis is used for channel estimation in communication systems such as massive/mmWave MIMO systems. It is because channels in these systems can be modeled with multipaths' gains and angles. This thesis proposes methods for the problems of noisy AR parameter estimation, DOA estimation in unknown noise fields, and massive/mmWave MIMO channel estimation and data detection with one-bit ADCs. The AR model offers a flexible yet simple tool for modeling complex signals. In practical scenarios, the observation noise may contaminate the AR signal. In this thesis, five methods for estimating noisy AR parameter estimation are proposed. In developing the methods, the concepts such as eigendecomposition (ED) and constrained minimization are used. The most common assumption about the structure of the observation noise in DOA estimation problem is the uniform noise assumption. According to it, the noise covariance matrix is a scaled identity matrix. However, other noise covariance matrix structures such as nonuniform or block-diagonal are more accurate in some practical situations. A generalized least-squares (GLS)-based DOA estimator that takes into consideration the signal subspace perturbation and also enjoys a properly designed DOA selection strategy is proposed for the case of uniform sensor noise. For the case of nonuniform noise, a non-iterative subspace-based (NISB) method is developed which is computationally efficient compared to state-of-the-art competitors. Moreover, a unified approach to DOA estimation in uniform, nonuniform, and block-diagonal sensor noise is presented. The use of one-bit ADCs instead of high-resolution ADCs is considered as an elegant solution for reducing power consumption of large-scale systems such as massive/mmWave MIMO and radar systems. In this thesis, we use the analogy between binary classification problem and one-bit parameter estimation to develop algorithms for massive MIMO and mmWave systems. In this regard, a method called SE-TMR is developed for one-bit mmWave UL channel estimation. Another method called L1-RLR-TMR is also offered for one-bit mmWave UL channel estimation. At last, the concept of AdaBoost is combined with Gaussian discriminant analysis (GDA) for developing computationally very efficient channel estimators and data detectors. It is shown that the proposed methods which use approximate versions of GDA as weak classifiers in iterations of the AdaBoost-based algorithms are exceptionally efficient, specifically in large-scale systems.
Translated title of the contributionAdvances and New Applications of Spectral Analysis
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Vorobyov, Sergiy, Supervising Professor
Print ISBNs978-952-64-1420-1
Electronic ISBNs978-952-64-1421-8
Publication statusPublished - 2023
MoE publication typeG5 Doctoral dissertation (article)


  • autoregressive signals
  • noisy observation
  • DOA estimation
  • nonuniform and block-diagonal noise
  • one-bit ADC
  • channel estimation
  • data detection


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