This dissertation details three approaches for direction-of-arrival (DOA) estimation or beamforming in array signal processing from the perspective of sparsity. In the first part of this dissertation, we consider sparse array beamformer design based on the alternating direction method of multipliers (ADMM); in the second part of this dissertation, the problem of joint DOA estimation and distorted sensor detection is investigated; and off-grid DOA estimation is studied in the last part of this dissertation. In the first part of this thesis, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes ADMM, and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, ...

Data acquisition is a necessary first step in digital signal processing applications such as radar, wireless communications and array processing. Traditionally, this process is performed by uniformly sampling signals at a frequency above the Nyquist rate and converting the resulting samples into digital numeric values through high-resolution amplitude quantization. While the traditional approach to data acquisition is straightforward and extremely well-proven, it may be either impractical or impossible in many modern applications due to the existing fundamental trade-off between sampling rate, amplitude quantization precision, implementation costs, and usage of physical resources, e.g. bandwidth and power consumption. Motivated by this fact, system designers have recently proposed exploiting sparse and few-bit quantized sampling instead of the traditional way of data acquisition in order to reduce implementation costs and usage of physical resources in such applications. However, before transition from the tradition data ...

In this thesis, advanced techniques for antenna array processing are addressed. The problem of autocalibration is considered and a novel method for a two-dimensional array is developed. Moreover, practicable methods for high-resolution direction-of-arrival (DOA) estimation and detection in automotive radar are proposed. A precise model of the array response is required to maintain the performance of DOA estimation. When the sensor environment is time-varying, this can only be achieved with autocalibration. The fundamental problem of autocalibration of an unknown phase response for uniform rectangular arrays is considered. For the case with a single source, a simple and robust least squares algorithm for joint two-dimensional DOA estimation and phase calibration is developed. An identification problem is determined and a suitable constraint is proposed. Simulation results show that the performance of the proposed estimator is close to the approximate CRB for both ...

The topic of this thesis is the enhancement of noisy, periodic signals with application to speech signals. Generally speaking, enhancement methods can be divided into signal- and noise-driven methods. In this thesis, we focus on the signal-driven approach by employing relevant signal parameters for the enhancement of periodic signals. The enhancement problem consists of two major subproblems: the estimation of relevant parameters or statistics, and the actual noise reduction of the observed signal. We consider both of these subproblems. First, we consider the problem of estimating signal parameters relevant to the enhancement of periodic signals. The fundamental frequency is one example of such a parameter. Furthermore, in multichannel scenarios, the direction-of-arrival of the periodic sources onto an array of sensors is another parameter of relevance. We propose methods for the estimation of the fundamental frequency that have benefits compared to ...

System designers across all disciplines of technology face the need to develop machines capable of independently processing and analyzing data and predicting future data. This is the fundamental problem of interest in “estimation theory,” wherein probabilistic analyses are used to isolate relationships between variables, and in “statistical inference,” wherein those variables are used to make inferences about real-world quantities. In practice, all estimators are designed based on limited statistical generalizations about the behavior of the observed and latent variables of interest; however, these models are rarely fully representative of reality. In such cases, there exists a “model misspecification,” and the resulting estimators will produce results that differ from those of the properly specified estimators. Evaluating the performance of a given estimator may sometimes be done by direct comparison of estimator outputs to known ground truth. However, in many cases, there ...

This thesis addresses a number of problems all related to parameter estimation in sensor array processing. The unifying theme is that some of these parameters are known before the measurements are acquired. We thus study how to improve the estimation of the unknown parameters by incorporating the knowledge of the known parameters; exploiting this knowledge successfully has the potential to dramatically improve the accuracy of the estimates. For covariance matrix estimation, we exploit that the true covariance matrix is Kronecker and Toeplitz structured. We then devise a method to ascertain that the estimates possess this structure. Additionally, we can show that our proposed estimator has better performance than the state-of-art when the number of samples is low, and that it is also efficient in the sense that the estimates have Cramér-Rao lower Bound (CRB) equivalent variance. In the direction of ...

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 ...

The advent of multi-microphone setups on a plethora of commercial devices in recent years has generated a newfound interest in the development of robust microphone array signal processing methods. These methods are generally used to either estimate parameters associated with acoustic scene or to extract signal(s) of interest. In most practical scenarios, the sources are located in the far-field of a microphone array where the main spatial information of interest is the direction-of-arrival (DOA) of the plane waves originating from the source positions. The focus of this thesis is to incorporate robustness against either lack of or imperfect/erroneous information regarding the DOAs of the sound sources within a microphone array signal processing framework. The DOAs of sound sources is by itself important information, however, it is most often used as a parameter for a subsequent processing method. One of the ...

This thesis deals with the efficient and flexible acquisition and processing of spatial sound using multiple microphones. In spatial sound acquisition and processing, we use multiple microphones to capture the sound of multiple sources being simultaneously active at a rever- berant recording side and process the sound depending on the application at the application side. Typical applications include source extraction, immersive spatial sound reproduction, or speech enhancement. A flexible sound acquisition and processing means that we can capture the sound with almost arbitrary microphone configurations without constraining the application at the ap- plication side. This means that we can realize and adjust the different applications indepen- dently of the microphone configuration used at the recording side. For example in spatial sound reproduction, where we aim at reproducing the sound such that the listener perceives the same impression as if he ...

Audio systems receive the speech signals of interest usually in the presence of noise. The noise has profound impacts on the quality and intelligibility of the speech signals, and it is therefore clear that the noisy signals must be cleaned up before being played back, stored, or analyzed. We can estimate the speech signal of interest from the noisy signals using a priori knowledge about it. A human speech signal is broadband and consists of both voiced and unvoiced parts. The voiced part is quasi-periodic with a time-varying fundamental frequency (or pitch as it is commonly referred to). We consider the periodic signals basically as the sum of harmonics. Therefore, we can pass the noisy signals through bandpass filters centered at the frequencies of the harmonics to enhance the signal. In addition, although the frequencies of the harmonics are the ...

This dissertation is the combination of three manuscripts –either published in or submitted to journals– on compressive sensing of propeller noise for detection, identification and localization of water crafts. Propeller noise, as a result of rotating blades, is broadband and radiates through water dominating underwater acoustic noise spectrum especially when cavitation develops. Propeller cavitation yields cyclostationary noise which can be modeled by amplitude modulation, i.e., the envelope-carrier product. The envelope consists of the so-called propeller tonals representing propeller characteristics which is used to identify water crafts whereas the carrier is a stationary broadband process. Sampling for propeller noise processing yields large data sizes due to Nyquist rate and multiple sensor deployment. A compressive sensing scheme is proposed for efficient sampling of second-order cyclostationary propeller noise since the spectral correlation function of the amplitude modulation model is sparse as shown in ...

The theory of statistical signal processing finds a wide variety of applications in the fields of data communications, such as in channel estimation, equalization and symbol detection, and sensor array processing, as in beamforming, and radar systems. Indeed, a large number of these applications can be interpreted in terms of a parametric estimation problem, typically approached by a linear filtering operation acting upon a set of multidimensional observations. Moreover, in many cases, the underlying structure of the observable signals is linear in the parameter to be inferred. This dissertation is devoted to the design and evaluation of statistical signal processing methods under realistic implementation conditions encountered in practice. Traditional statistical signal processing techniques intrinsically provide a good performance under the availability of a particularly high number of observations of fixed dimension. Indeed, the original optimality conditions cannot be theoretically guaranteed ...

Array processing is an area of study devoted to processing the signals received from an antenna array and extracting information of interest. It has played an important role in widespread applications like radar, sonar, and wireless communications. Numerous adaptive array processing algorithms have been reported in the literature in the last several decades. These algorithms, in a general view, exhibit a trade-off between performance and required computational complexity. In this thesis, we focus on the development of array processing algorithms in the application of beamforming and direction of arrival (DOA) estimation. In the beamformer design, we employ the constrained minimum variance (CMV) and the constrained constant modulus (CCM) criteria to propose full-rank and reduced-rank adaptive algorithms. Specifically, for the full-rank algorithms, we present two low-complexity adaptive step size mechanisms with the CCM criterion for the step size adaptation of the ...

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 ...

This thesis deals with the synchronization of one or several replicas of a known signal received in a scenario with multipath propagation and directional interference. A connecting theme along this work is the systematic application of the maximum likelihood (ML) principle together with a signal model in which the spatial signatures are unstructured and the noise term is Gaussian- distributed with an unknown correlation matrix. This last assumption is key in obtaining estimators that are capable of mitigating the disturbing signals that exhibit a certain structure, and this is achieved without resorting to the estimation of the parameters of those signals. On the other hand, the assumption of unstructured spatial signatures is interesting from a practical standpoint and facilitates the estimation problem since the estimates of these signatures can be obtained in closed form. This constitutes a first step towards ...