REITERATIVE MINIMUM MEAN SQUARE ERROR ESTIMATOR FOR DIRECTION OF ARRIVAL ESTIMATION AND BIOMEDICAL FUNCTIONAL BRAIN IMAGING

Two novel approaches are developed for direction-of-arrival (DOA) estimation and functional brain imaging estimation, which are denoted as ReIterative Super-Resolution (RISR) and Source AFFine Image REconstruction (SAFFIRE), respectively. Both recursive approaches are based on a minimum mean-square error (MMSE) framework. The RISR estimator recursively determines an optimal filter bank by updating an estimate of the spatial power distribution at each successive stage. Unlike previous non-parametric covariance-based approaches, which require numerous time snapshots of data, RISR is a parametric approach thus enabling operation on as few as one time snapshot, thereby yielding very high temporal resolution and robustness to the deleterious effects of temporal correlation. RISR has been found to resolve distinct spatial sources several times better than that afforded by the nominal array resolution even under conditions of temporally correlated sources and spatially colored noise. The SAFFIRE algorithm localizes the underlying neural activity in the brain based on the response of a patient under sensory stimuli, such as an auditory tone. The estimator processes electroencephalography (EEG) or magnetoencephalography (MEG) data simulated for sensors outside the patient's head in a recursive manner converging closer to the true solution at each consecutive stage. The algorithm requires a minimal number of time samples to localize active neural sources, thereby enabling the observation of the neural activity as it progresses over time. SAFFIRE has been applied to simulated MEG data and has shown to achieve unprecedented spatial and temporal resolution. The estimation approach has also demonstrated the capability to precisely isolate the primary and secondary auditory cortex responses, a challenging problem in the brain MEG imaging community

Angle of Arrival Estimation Utilising Frequency Diverse Radio Antenna Arrays

The purpose of this research is to investigate a novel way of combining carrier signals that are transmitted successively over Multiple Frequencies (MF) and traditional metrics to improve AoA estimation. Every signal contains three metrics, amplitude, phase, and frequency. To achieve localisation, current systems utilise the metrics of amplitude (also known as Received Signal Strength (RSS)) and phase that resolves the AoA. However, the metric of frequency is mostly used with Orthogonal Frequency-Division Multiplexing (OFDM) to increase the number of RSS and AoA metrics, which is not optimal. This research answers two questions. Can the use of MF improve AoA estimation? Also, how can MF and traditional metrics be combined for AoA estimation? The aim is to prove that the metric of frequency can be utilised more optimally. Therefore, measurements of RSS and AoA are performed in different environments for MF. To perform these measurements, ten frequency diverse Software Defined Radios (SDRs) are employed. A novel technique to time/frequency synchronise the SDRs is developed and presented. Moreover, a ten element Uniform Linear Array (ULA) is designed, simulated and manufactured. The outcomes of this research are two novel algorithms for the MF AoA estimation of a carrier transmitter. Findings of the first algorithm show that the use of MF with the RSS metric performs equally with current systems that have a higher cost and complexity. The second algorithm that utilises MF with the AoA metric demonstrates a significant reduction in the AoA estimation error, compared to current systems. Specifically, for 50\% of the measured cases the AoA estimation error is reduced by 3.7 degrees, while for 95\% of the measured cases the AoA estimation error is reduced by 27 degrees. Hence, this research proves that MF with traditional metrics can reduce system complexity and greatly improve AoA estimation

Sparse Array Signal Processing: New Array Geometries, Parameter Estimation, and Theoretical Analysis

Array signal processing focuses on an array of sensors receiving the incoming waveforms in the environment, from which source information, such as directions of arrival (DOA), signal power, amplitude, polarization, and velocity, can be estimated. This topic finds ubiquitous applications in radar, astronomy, tomography, imaging, and communications. In these applications, sparse arrays have recently attracted considerable attention, since they are capable of resolving O(N2) uncorrelated source directions with N physical sensors. This is unlike the uniform linear arrays (ULA), which identify at most N-1 uncorrelated sources with N sensors. These sparse arrays include minimum redundancy arrays (MRA), nested arrays, and coprime arrays. All these arrays have an O(N2)-long central ULA segment in the difference coarray, which is defined as the set of differences between sensor locations. This O(N2) property makes it possible to resolve O(N2) uncorrelated sources, using only N physical sensors. The main contribution of this thesis is to provide a new direction for array geometry and performance analysis of sparse arrays in the presence of nonidealities. The first part of this thesis focuses on designing novel array geometries that are robust to effects of mutual coupling. It is known that, mutual coupling between sensors has an adverse effect on the estimation of DOA. While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as MRA, nested arrays, and coprime arrays, have reduced mutual coupling compared to ULA, but all of these have their own disadvantages. This thesis introduces a new array called the super nested array, which has many of the good properties of the nested array, and at the same time achieves reduced mutual coupling. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of super nested arrays in the presence of mutual coupling. Two-dimensional planar sparse arrays with large difference coarrays have also been known for a long time. These include billboard arrays, open box arrays (OBA), and 2D nested arrays. However, all of them have considerable mutual coupling. This thesis proposes new planar sparse arrays with the same large difference coarrays as the OBA, but with reduced mutual coupling. The new arrays include half open box arrays (HOBA), half open box arrays with two layers (HOBA-2), and hourglass arrays. Among these, simulations show that hourglass arrays have the best estimation performance in presence of mutual coupling. The second part of this thesis analyzes the performance of sparse arrays from a theoretical perspective. We first study the Cramér-Rao bound (CRB) for sparse arrays, which poses a lower bound on the variances of unbiased DOA estimators. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not applicable in the context of sparse arrays for which the number of identifiable sources exceeds the number of sensors. This thesis derives a new expression for the CRB to fill this gap. Based on the proposed CRB expression, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity. It is also possible to precisely specify the relation between the number of sensors and the number of uncorrelated sources such that these sources could be resolved. Recently, it has been shown that correlation subspaces, which reveal the structure of the covariance matrix, help to improve some existing DOA estimators. However, the bases, the dimension, and other theoretical properties of correlation subspaces remain to be investigated. This thesis proposes generalized correlation subspaces in one and multiple dimensions. This leads to new insights into correlation subspaces and DOA estimation with prior knowledge. First, it is shown that the bases and the dimension of correlation subspaces are fundamentally related to difference coarrays, which were previously found to be important in the study of sparse arrays. Furthermore, generalized correlation subspaces can handle certain forms of prior knowledge about source directions. These results allow one to derive a broad class of DOA estimators with improved performance. It is empirically known that the coarray structure is susceptible to sensor failures, and the reliability of sparse arrays remains a significant but challenging topic for investigation. This thesis advances a general theory for quantifying such robustness, by studying the effect of sensor failure on the difference coarray. We first present the (k-)essentialness property, which characterizes the combinations of the faulty sensors that shrink the difference coarray. Based on this, the notion of (k-)fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. These novel concepts provide quite a few insights into the interplay between the array geometry and its robustness. For instance, for the same number of sensors, it can be proved that ULA is more robust than the coprime array, and the coprime array is more robust than the nested array. Rigorous development of these ideas leads to expressions for the probability of coarray failure, as a function of the probability of sensor failure. The thesis concludes with some remarks on future directions and open problems.</p