In direction finding (DF) applications, there are several factors affecting the estimation accuracy of the direction-of-arrivals (DOA) of unknown source locations. The major distortions in the estimation process are due to the array imperfections, model mismatches and multipath. The array imperfections usually exist in practical applications due to the nonidealities in the antenna array such as mutual coupling (MC) and gain/phase uncertainties. The model mismatches usually occur when the model of the received signal differs from the signal model used in the processing stage of the DF system. Another distortion is due to multipath signals. In the multipath scenario, the antenna array receives the transmitted signal from more than one path with different directions and the array covariance matrix is rank-deficient. In this thesis, three new methods are proposed for the problems in DF applications in the presence of array ...

Resistivity distribution estimation, widely known as Electrical Impedance Tomography (EIT), is a non linear ill-posed inverse problem. However, the partial derivative equation ruling this experiment yields no analytical solution for arbitrary conductivity distribution. Thus, solving the forward problem requires an approximation. The Finite Element Method (FEM) provides us with a computationally cheap forward model which preserves the non linear image-data relation and also reveals sufficiently accurate for the inversion. Within the Bayesian approach, Markovian priors on the log-conductivity distribution are introduced for regularization. The neighborhood system is directly derived from the FEM triangular mesh structure. We first propose a maximum a posteriori (MAP) estimation with a Huber-Markov prior which favours smooth distributions while preserving locally discontinuous features. The resulting criterion is minimized with the pseudo-conjugate gradient method. Simulation results reveal significant improvements in terms of robustness to noise, computation rapidity ...

This dissertation presents the outcome of investigations which envisaged to develop improved state and ‘combined state and parameter’ estimation algorithms for nonlinear signal models (during the contingent situations) where the complete knowledge of process and/or measurement noise covariance are not available. Variants of “adaptive nonlinear estimators” capable of providing satisfactory estimation results in the face of unknown noise covariance have been proposed in this dissertation. The proposed adaptive nonlinear estimators incorporate adaptation algorithms with which they can implicitly or explicitly, estimate unknown noise covariances along with estimation of states and parameters. Adaptation algorithms have been mathematically derived following different methods of adaptation which include Maximum Likelihood Estimation (MLE), Covariance Matching method and Maximum a Posteriori (MAP) method. The adaptive nonlinear estimators which have been proposed in this dissertation are formulated with the help of a general framework for adaptive nonlinear ...

Radar backscatter from an ocean surface is commonly referred to as sea clutter. Any radar backscatter not due to the scattering from an ocean surface constitutes a potential target. This thesis is concerned with the study of target detection techniques in the presence of high resolution sea clutter. In this dissertation, the high resolution sea clutter is treated as a compound process, where a fast oscillating speckle component is modulated in power by a slowly varying modulating component. While the short term temporal correlations of the clutter are associated with the speckle, the spatial correlations are largely associated with the modulating component. Due to the disparate statistical and correlation properties of the two components, a piecemeal approach is adopted throughout this thesis, whereby the spatial and the temporal correlations of high resolution sea clutter are treated independently. As an extension ...

During the last decades, information is being gathered and processed at an explosive rate. This fact gives rise to a very important issue, that is, how to effectively and precisely describe the information content of a given source signal or an ensemble of source signals, such that it can be stored, processed or transmitted by taking into consideration the limitations and capabilities of the several digital devices. One of the fundamental principles of signal processing for decades is the Nyquist-Shannon sampling theorem, which states that the minimum number of samples needed to reconstruct a signal without error is dictated by its bandwidth. However, there are many cases in our everyday life in which sampling at the Nyquist rate results in too many data and thus, demanding an increased processing power, as well as storage requirements. A mathematical theory that emerged ...

In this thesis, advanced robust estimation methodologies for signal processing are developed and analyzed. The developed methodologies solve problems concerning multi-sensor data, robust model selection as well as robustness for dependent data. The work has been applied to solve practical signal processing problems in different areas of biomedical and array signal processing. In particular, for univariate independent data, a robust criterion is presented to select the model order with an application to corneal-height data modeling. The proposed criterion overcomes some limitations of existing robust criteria. For real-world data, it selects the radial model order of the Zernike polynomial of the corneal topography map in accordance with clinical expectations, even if the measurement conditions for the videokeratoscopy, which is the state-of-the-art method to collect corneal-height data, are poor. For multi-sensor data, robust model order selection selection criteria are proposed and applied ...

The wireless communication industry has experienced rapid growth in recent years, and digital cellular systems are currently designed to provide high data rates at high terminal speeds. High data rates give rise to intersymbol interference (ISI) due to so-called multipath fading. Such an ISI channel is called frequency selective. On the other hand, due to terminal mobility and/or receiver frequency offset the received signal is subject to frequency shifts (Doppler shifts). Doppler shift induces time-selectivity characteristics. The Doppler effect in conjunction with ISI gives rise to a so-called doubly selective channel (frequency- and time-selective). In addition to the channel effects, the analog front-end may suffer from an imbalance between the I and Q branch amplitudes and phases as well as from carrier frequency offset. These analog front-end imperfections then result in an additional and significant degradation in system performance, especially ...

Signal processing techniques for multiple-antenna transmission can exploit the spatial dimension of the wireless channel to serve multiple users simultaneously, achieving high spectral efficiencies. Realizing such gains; however, is strongly dependent on the availability of highly accurate and up-to-date Channel State Information at the Transmitter (CSIT). This stems from the necessity to deal with multiuser interference through preprocessing; as receivers cannot coordinate in general. In wireless systems, CSIT is subject to uncertainty due to estimation and quantization errors, delays and mismatches. This thesis proposes optimized preprocessing techniques for broadcasting scenarios where a multi-antenna transmitter communicates with single-antenna receivers under CSIT uncertainties. First, we consider a scenario where the transmitter communicates an independent message to each receiver. The most popular preprocessing techniques in this setup are based on linear precoding (or beamforming). Despite their near-optimum rate performances when highly accurate CSIT ...

The predominant game-theoretic solutions for distributed rate-maximization algorithms in Gaussian interference channels through optimal power control require perfect channel knowledge, which is not possible in practice due to various reasons, such as estimation errors, feedback quantization and latency between channel estimation and signal transmission. This thesis therefore aims at addressing this issue through the design and analysis of robust game-theoretic algorithms for rate-maximization in Gaussian interference channels in the presence of bounded channel uncertainty. A robust rate-maximization game is formulated for the single-antenna frequency-selective Gaussian interference channel under bounded channel uncertainty. The robust-optimization equilibrium solution for this game is independent of the probability distribution of the channel uncertainty. The existence and uniqueness of the equilibrium are studied and sufficient conditions for the uniqueness of the equilibrium are provided. Distributed algorithms to compute the equilibrium solution are presented and shown to ...

Code-division multiple-access (CDMA) systems with random spreading and channel uncertainty at the receiver are studied. Frequency selective single antenna, as well as, narrowband multiple antenna channels are considered. Rayleigh fading is assumed in all cases. General Bayesian approach is used to derive both iterative and non-iterative estimators whose performance is obtained in the large system limit via the replica method from statistical physics. The effect of spatial correlation on the performance of a multiple antenna CDMA system operating in a flat-fading channel is studied. Per-antenna spreading (PAS) with random signature sequences and spatial multiplexing is used at the transmitter. Non-iterative multiuser detectors (MUDs) using imperfect channel state information (CSI) are derived. Training symbol based channel estimators having mismatched a priori knowledge about the antenna correlation are considered. Both the channel estimator and the MUD are shown to admit a simple ...

This thesis deals with minimum mean square error (MMSE) speech enhancement schemes in the short-time Fourier transform (STFT) domain with a focus on statistical models for speech and corresponding estimators. MMSE speech enhancement approaches taking speech presence uncertainty (SPU) into account usually consist of a common MMSE estimator for speech and an a posteriori speech presence probability (SPP) estimator. It is shown that both estimators should be based on the same statistical speech model, as they are in the same estimation framework and assume the same a priori knowledge. In order to give a synopsis of consistent MMSE estimation under SPU, typical common MMSE estimators and a posteriori SPP estimators are recapitulated. Furthermore, a new specific a posteriori SPP estimator is derived based on a novel statistical model for speech. Then, a synopsis of approaches to consistent MMSE estimation under ...

Compressed sensing (CS) is a recently introduced signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with Gaussian-derived reconstruction algorithms, fail to recover a close approximation of the signal. This dissertation develops robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. To achieve this objective, we make use of robust statistics theory to develop appropriate methods addressing the problem of impulsive noise in CS systems. We develop a generalized Cauchy distribution (GCD) ...

In recent years, inertial sensors have undergone major developments. The quality of their measurements has improved while their cost has decreased, leading to an increase in availability. They can be found in stand-alone sensor units, so-called inertial measurement units, but are nowadays also present in for instance any modern smartphone, in Wii controllers and in virtual reality headsets. The term inertial sensor refers to the combination of accelerometers and gyroscopes. These measure the external specific force and the angular velocity, respectively. Integration of their measurements provides information about the sensor’s position and orientation. However, the position and orientation estimates obtained by simple integration suffer from drift and are therefore only accurate on a short time scale. In order to improve these estimates, we combine the inertial sensors with additional sensors and models. To combine these different sources of information, also ...

Spectral unmixing is one the major issues arising when analysing hyperspectral images. It consists of identifying the macroscopic materials present in a hyperspectral image and quantifying the proportions of these materials in the image pixels. Most unmixing techniques rely on a linear mixing model which is often considered as a first approximation of the actual mixtures. However, the linear model can be inaccurate for some specific images (for instance images of scenes involving multiple reflections) and more complex nonlinear models must then be considered to analyse such images. The aim of this thesis is to study new nonlinear mixing models and to propose associated algorithms to analyse hyperspectral images. First, a post-nonlinear model is investigated and efficient unmixing algorithms based on this model are proposed. The prior knowledge about the components present in the observed image, their proportions and the ...

Mobile communication networks of the third and future generations are designed to offer high-data rate services like video-telephony and data-transfer. The current Rake receiver architecture will create a shortage in available bandwidth offered to the users. This is not due to a shortage in spectrum but results from inefficient receiver architectures. Spectral efficiency can be increased considerably through multi-user detection techniques in the receiver algorithms. The present thesis investigates iterative re- ceivers for encoded CDMA transmission in the uplink. The iterative receiver is a suboptimal receiver algorithm with manageable complexity. It consists of an inter- ference mitigating multi-user detector, a bank of single-user decoders, and a channel estimator. Instead of deciding on the transmitted symbols right after the first decod- ing, the receiver feeds back tentative decision symbols to mitigate multiple-access interference in the next iteration. Similarly, soft decision symbols ...