This work deals with the further development of a method for Direction of Arrival (DOA) estimation based on the Discrete Fourier Transform (DFT) of the sensor array output. In the existing DFT-based algorithm, relatively high SNR is considered, and it is assumed that a large number of sensors are available. In this study an overview of some of the most commonly used DOA estimation techniques will be presented. Then the performance of the DFT method will be analyzed and compared with the performance of existing techniques. Two main objectives will be studied, firstly the reduction of the number of sensors and secondly the performance of the DFT based technique in the presence of noise. Experimental simulations will be presented to illustrate that in absence of noise, the proposed method is very fast and using just one snapshot is sufficient to accurately estimate DOAs. Also, in presence of noise, the method is still relatively fast and using a small number of snapshots, it can accurately estimate DOAs. The above mentioned properties are the result of taking an average of the peaks of the DFTs, X_n (k), obtained from a sequence of N_s snapshots. With N_s sufficiently large, the average over N_s snapshots approaches expected value. Also, the conditions that should be satisfied to avoid overlapping of main-lobes, and thus loosing the DOA of some signals, in the DFT spectrum are examined. This study further analyzes the performance of the proposed method as well as two other commonly used algorithms, MUSIC and conventional beamformer. An extensive simulation was conducted and different features of the spatial DFT technique, such as accuracy, resolution, sensitivity to noise, effect of multiple snapshots and the number of sensors were evaluated and compared with those of existing techniques. The simulations indicate that in most aspects the proposed spatial DFT algorithm outperforms the other techniques. / Graduate

Cette thèse porte sur la localisation de sources spatialement distribuées. Premièrement, des résultats théoriques ont été établis concernant les performances des méthodes à haute résolution en présence d'erreurs de modèle dues à la distribution angulaire de source. Ainsi, le biais d'estimation et l'erreur quadratique moyenne sont exprimées en fonction des paramètres liés à l'erreur de modèle. De plus, les performances ont été étudiées en fonction de la géométrie de l'antenne afin de déterminer les configurations les plus robustes aux sources dispersées.Les résultats théoriques ont été validés par des simulations numériques. Dans un deuxième temps, une nouvelle approche non paramétrique a été proposée pour la localisation de sources distribuées : cette approche exploite les propriétés de parcimonie et de rang-faible de la matrice de covariance spatiale des sources. Cette méthode permet en outre d'estimer la forme de la distribution spatiale des sources. Les résultats de simulations ont permis de mettre en avant l'intérêt de l'hypothèse rang faible par rapport aux critères exploitant uniquement la parcimonie / This thesis focuses on the distributed source localization problem. In a first step, performance of high resolution methods in the presence of model errors due to the angular distribution of source has been studied. Theoretical expressions of the estimation bias and the mean square error of the direction of arrival of sources have been established in terms of model error. The impacts of the array geometry on the performances have studied in order to optimize the robustness of the array to the model error due to distributed sources.Theoretical results have been validated by numerical simulations.In a second step, a new approach for the localization of spatially distributed source has been proposed: the approach is based on the sparsity and low-rank property of the spatial covariance matrix of the sources. The proposed method provides also an estimation of the distribution shapes of the sources. Simulation results exhibit the advantages of exploiting the sparsity and the low rank properties.

As human settlement expands into the natural habitats of wild animals, the conflict between humans and wildlife increases. The human-elephant conflict is one that causes a tremendous amount of damage, often to poor villages close to the savannah. In this master's thesis, a system is developed, that is intended to detect, localise and track elephants from seismic vibrations generated from footsteps. The system consists of multiple devices, with three geophones, and a microprocessor each. To detect the footsteps, two different methods are evaluated. One that analyses features consistion of the normalised standard deviation, frequency peak, spectral centroid and low compared to high frequency content of a signal. These features of the signal are then compared to those of an elephant footstep. The other one compares the frequency content of the seismic wave from a footstep to an computed average of known elephant footsteps. The signal feature method performed the best with an accuracy of 89 %, and detecting 54 % of the footsteps. The detected footstep is sent to a backend where further calculations are done. With one device, estimations of the direction of arrival (DOA) angle can be made. This is done using a delay and sum algorithm. By using a Kalman filter on the DOA estimates, the bearing to the elephant can be tracked over time. From the detected elephant footsteps it has been shown that it is possible to estimate the direction of an elephant with quite high performance and by applying a Kalman filter to track the elephant, it has been shown that the filter gives better and more reasonable estimates. With two devices, a location can be estimated with triangulation and also an elephant's position can be tracked. With triangulation, where the easting position estimated to some extent, but the northing position did not give good results. By using these localisations estimates in a Kalman filter the elephant could be tracked in most of the cases with high enough performance and especially when there weren't too many high northing estimates. By using separate DOA estimations in an extended Kalman filter the easting position could be tracked fairly well, while the northing updates had some strange behaviours, most probably because of implementation error. / Project Ngulia

Signal acquisition, signal reconstruction and analysis of spectrum of the signal are the three most important steps in signal processing and they are found in almost all of the modern day hardware. In most of the signal processing hardware, the signal of interest is sampled at uniform intervals satisfying some conditions like Nyquist rate. However, in some cases the privilege of having uniformly sampled data is lost due to some constraints on the hardware resources. In this thesis an important problem of signal reconstruction and spectral analysis from nonuniformly sampled data is addressed and a variety of methods are presented. The proposed methods are tested via numerical experiments on both artificial and real-life data sets. The thesis starts with a brief review of methods available in the literature for signal reconstruction and spectral analysis from non uniformly sampled data. The methods discussed in the thesis are classified into two broad categories - dense and sparse methods, the classification is based on the kind of spectra for which they are applicable. Under dense spectral methods the main contribution of the thesis is a non-parametric approach named LIMES, which recovers the smooth spectrum from non uniformly sampled data. Apart from recovering the spectrum, LIMES also gives an estimate of the covariance matrix. Under sparse methods the two main contributions are methods named SPICE and LIKES - both of them are user parameter free sparse estimation methods applicable for line spectral estimation. The other important contributions are extensions of SPICE and LIKES to multivariate time series and array processing models, and a solution to the grid selection problem in sparse estimation of spectral-line parameters. The third and final part of the thesis contains applications of the methods discussed in the thesis to the problem of radial velocity data analysis for exoplanet detection. Apart from the exoplanet application, an application based on Sudoku, which is related to sparse parameter estimation, is also discussed.

Abstract In this doctoral thesis, initial code synchronization (i.e., code acquisition) of a direct sequence spread spectrum (DS/SS) system is studied when a smart antenna is used in a receiver. Code synchronization means time synchronization of the used spreading code in the receiver. After an introduction to the topic, a literature review of code acquisition is presented. In addition, a review of the results in the literature under fading, data modulation, Doppler, intentional interference, multiple-access interference, other system interference, and multiple antennas is given. After that, an overview of the smart antennas, especially focusing on digital beamforming and direction-of-arrival (DOA) estimation algorithms is presented. The end part of the thesis concentrates on the author’s own research of the topic. Original articles of this article dissertation have been classified according to their contents into two groups. The first group covers DS/SS code acquisition performance in intentional interference by exploiting how well different beamforming algorithms can eliminate narrowband and wideband interfering signals in the case, where the DOA of the desired signal is known. The obtained results show that most spatial beamforming algorithms are capable of cancelling multiple different types of interfering signals if they are not arriving from the same direction as the desired signal. If angle separation between desired and interfering signals is not sufficient, then more complex methods have to be used. The second group of articles focuses on a theoretical analysis of synchronization probabilities and mean acquisition times. If the DOA of the desired signal is unknown, the whole angular uncertainty region can be divided into small angular cells using beamforming techniques, as is proposed in the literature. Then there is a two-dimensional (delay-angle) acquisition problem. In this thesis, the research work of that area is expanded to cover also advanced beamforming techniques, since they offer increased interference suppression capability. It is shown that the code acquisition performance of the delay-angle method can be improved in some cases by adding a DOA estimator into the system, because it may reduce the number of required angular cells. In addition, such a minimum mean square error (MMSE) beamforming structure is proposed, where only one period of the known pseudo noise spreading code is used as a reference signal. The method was shown to have better acquisition performance than the delay-angle method has, since MMSE beamforming does not need DOA information. However, in this thesis, such a method was not found which outperforms the rest of the methods in all scenarios. / Tiivistelmä Tässä väitöstyössä tutkitaan suorahajotushajaspektrijärjestelmän (DS/SS, direct sequence spread spectrum) koodisynkronoinnin etsintävaihetta, kun vastaanottimessa käytetään älyantennia. Koodisynkronoinnilla tarkoitetaan järjestelmän käyttämän hajotuskoodin ajastuksen synkronointia vastaanottimessa. Johdannon jälkeen esitetään kirjallisuuskatsaus koodisynkronointiin sekä tuodaan esille kirjallisuudesta löytyviä tutkimustuloksia aihepiiristä seuraavissa tilanteissa: häipyvä kanava, Doppler-ilmiö, tahallinen häirintä, monikäyttöhäiriö, muiden järjestelmien aiheuttama häiriö sekä moniantennijärjestelmät. Tämän jälkeen esitetään yleiskatsaus älyantenneihin kohdistuen erityisesti digitaalisiin keilanmuodostus- sekä suuntaestimointialgoritmeihin. Työn loppuosa keskittyy kirjoittajan omaan tutkimukseen aiheesta. Tämän nippuväitöskirjan alkuperäiset artikkelit on luokiteltu kahteen ryhmään niiden sisältöön perustuen. Ensimmäinen ryhmä käsittelee DS/SS-järjestelmän koodisynkronoinnin etsintävaiheen suorituskykyä tahallisessa häirinnässä tutkimalla, miten hyvin erilaiset keilanmuodostusalgoritmit kykenevät poistamaan kapea- ja leveäkaistaisia häirintäsignaaleja tilanteessa, jossa hyötysignaalin tulosuunta tiedetään. Tutkimustulokset osoittavat, että monet tilatason keilanmuodostusalgoritmit kykenevät poistamaan useita erityyppisiä häirintäsignaaleita, jos ne eivät saavu hyötysignaalin kanssa samasta suunnasta. Mikäli kulmaero hyöty- ja häirintäsignaalien välillä ei ole riittävä, joudutaan käyttämään rakenteeltaan monimutkaisempia menetelmiä. Toinen ryhmä artikkeleita keskittyy synkronointiin liittyvien todennäköisyyksien ja keskimääräisen etsintäajan teoreettiseen analyysiin. Jos hyötysignaalin tulosuunta on tuntematon, voidaan kulmaepävarmuusalue jakaa pieniin kulmasoluihin käyttäen keilanmuodostustekniikoita, kuten kirjallisuudessa esitetään. Tällöin kyseessä on kaksiulotteinen (viive-kulma) etsintäongelma. Tässä työssä kyseistä tutkimusaihetta laajennetaan koskemaan myös edistyneet keilanmuodostusmenetelmät, koska ne tarjoavat parantuneen häiriönvaimennuskyvyn. Työssä osoitetaan, että viive-kulma menetelmän suorituskykyä voidaan parantaa joissakin tilanteissa lisäämällä järjestelmään suuntaestimaattori, koska se saattaa vähentää tarvittavien kulmasolujen lukumäärää. Lisäksi tutkitaan sellaista pienimmän keskineliövirheen (MMSE, minimum mean square error) keilanmuodostusmenetelmää, jossa ainoastaan yhtä hajotuskoodin koodijaksoa käytetään opetukseen. Kyseisellä menetelmällä todettiin olevan parempi suorituskyky kuin viive-kulma etsinnällä, koska MMSE-menetelmä ei tarvitse suuntainformaatiota. Tässä työssä ei kuitenkaan löydetty yhtä sellaista menetelmää, jonka suorituskyky on muita parempi kaikissa tilanteissa.

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Un radar MIMO (Multiple Input Multiple Output) est un système radar qui utilise plusieurs antennes émettrices et réceptrices, dans lequel les formes d'ondes émises peuvent être indépendantes. Par rapport aux radars utilisant des antennes en réseaux phasés, les radars MIMO offrent davantage de degrés de liberté, ce qui permet d'améliorer les performances du système en termes de détection et localisation. La technique MIMO offre également la possibilité de synthétiser un diagramme de rayonnement désiré par une définition judicieuse des formes d'ondes émises. Dans la mesure où les paramètres des cibles (positions, vitesses, directions d'arrivée (DOA), ...) sont estimés à partir des échos des signaux émis, on comprend aisément que les formes d'ondes employées jouent un rôle clé dans les performances du système. Cette thèse porte sur l'estimation de DOA et sur la conception des formes d'ondes pour un radar MIMO. Le cadre d'étude est restreint au cas où les antennes sont colocalisées et les cibles sont immobiles et supposées ponctuelles. La plupart des travaux antérieurs (au commencement de la thèse) portaient sur le radar MIMO bande étroite et faisaient l'hypothèse d'émetteurs-récepteurs idéaux et indépendants. Cette thèse contribue à élargir le cadre d'étude en s'intéressant d'une part au passage en large bande et d'autre part à la modélisation et à la prise en compte de la non-indépendance des émetteurs-récepteurs et autres imperfections. Dans la mesure où le recours à des signaux large bande est nécessaire lorsqu'une résolution importante est souhaitée, nous nous sommes attachés dans cette thèse à adapter le modèle d'un système de radar MIMO au cas large bande et à proposer de nouvelles techniques visant à améliorer les performances d'estimation de DOA dans le cas de signaux large bande. Cette thèse analyse également l'influence de conditions non idéales comme l'impact des phénomènes de couplage électromagnétique sur les diagrammes de rayonnement dans un réseau d'antennes. Cette étude est menée dans le cas bande étroite. En particulier, nous étudions l'influence du couplage direct entre les réseaux d'antennes d'émission et de réception (appelé « crosstalk ») sur les performances des techniques proposées. Nous établissons un modèle du signal permettant de prendre en compte ce phénomène et proposons une technique de réduction du « crosstalk » qui permet une estimation efficace des DOA des cibles. Nous montrons par ailleurs comment améliorer les performances d'estimation de DOA en présence de diagrammes de rayonnement incluant le couplage entre antennes. Le dernier apport principal de cette thèse est la conception et réalisation d'une plateforme expérimentale comportant une seule architecture d'émetteur-récepteur, qui permet de simuler un système MIMO utilisant des antennes colocalisées en appliquant le principe de superposition. Cette plateforme nous a permis d'évaluer les performances des techniques proposées dans des conditions plus réalistes / A Multiple-Input Multiple-Output (MIMO) radar is a system employing multiple transmitters and receivers in which the waveforms to be transmitted can be totally independent. Compared to standard phased-array radar systems, MIMO radars offer more degrees of freedom which leads to improved angular resolution and parameter identifiability, and provides more flexibility for transmit beampattern design. The main issues of interest in the context of MIMO radar are the estimation of several target parameters (which include range, Doppler, and Direction-of-Arrival (DOA), among others). Since the information on the targets is obtained from the echoes of the transmitted signals, it is straightforward that the design of the waveforms plays an important role in the system accuracy. This document addresses the investigation of DOA estimation of non-moving targets and waveform design techniques for MIMO radar with colocated antennas. Although narrowband MIMO radars have been deeply studied in the literature, the existing DOA estimation techniques have been usually proposed and analyzed from a theoretical point of view, often assuming ideal conditions. This thesis analyzes existing signal processing algorithms and proposes new ones in order to improve the DOA estimation performance in the case of narrowband and wideband signals. The proposed techniques are studied under ideal and non-ideal conditions considering punctual targets. Additionally, we study the influence of mutual coupling on the performance of the proposed techniques and we establish a more realistic signal model which takes this phenomenon into account. We then show how to improve the DOA estimation performance in the presence of distorted radiation patterns and we propose a crosstalk reduction technique, which makes possible an efficient estimation of the target DOAs. Finally, we present an experimental platform for MIMO radar with colocated antennas which has been developed in order to evaluate the performance of the proposed techniques under more realistic conditions. The proposed platform, which employs only one transmitter and one receiver architectures, relies on the superposition principle to simulate a real MIMO system

In this dissertation, sparse processing of signals for directions-of-arrival (DoAs) estimation is addressed in the framework of Compressive Sensing (CS). In particular, DoAs estimation problem for different types of sources, systems, and applications are formulated in the CS paradigm. In addition, the fundamental conditions related to the ``Sparsity'' and ``Linearity'' are carefully exploited in order to apply confidently the CS-based methodologies. Moreover, innovative strategies for various systems and applications are developed, validated numerically, and analyzed extensively for different scenarios including signal to noise ratio (SNR), mutual coupling, and polarization loss. The more realistic data from electromagnetic (EM) simulators are often considered for various analysis to validate the potentialities of the proposed approaches. The performances of the proposed estimators are analyzed in terms of standard root-mean-square error (RMSE) with respect to different degrees-of-freedom (DoFs) of DoAs estimation problem including number of elements, number of signals, and signal properties. The outcomes reported in this thesis suggest that the proposed estimators are computationally efficient (i.e., appropriate for real time estimations), robust (i.e., appropriate for different heterogeneous scenarios), and versatile (i.e., easily adaptable for different systems).

Cette thèse porte sur l’étude du positionnement optimale des réseaux de capteurs pour la localisation de sources. Nous avons étudié deux approches: l’approche basée sur les performances de l’estimation en termes d’erreur quadratique moyenne et l’approche basée sur le seuil statistique de résolution (SSR).Pour le première approche, nous avons considéré les bornes inférieures de l’erreur quadratique moyenne qui sont utilisés généralement pour évaluer la performance d’estimation indépendamment du type d’estimateur considéré. Nous avons étudié deux types de bornes: la borne Cramér-Rao (BCR) pour le modèle où les paramètres sont supposés déterministes et la borne Weiss-Weinstein (BWW) pour le modèle où les paramètres sont supposés aléatoires. Nous avons dérivé les expressions analytiques de ces bornes pour développer des outils statistiques afin d’optimiser la géométrie des réseaux de capteurs. Par rapport à la BCR, la borne BWW peut capturer le décrochement de l’EQM des estimateurs dans la zone non-asymptotique. De plus, les expressions analytiques de la BWW pour un modèle Gaussien général à moyenne paramétré ou à covariance matrice paramétré sont donnés explicitement. Basé sur ces expressions analytiques, nous avons étudié l’impact de la géométrie des réseaux de capteurs sur les performances d’estimation en utilisant les réseaux de capteurs 3D et 2D pour deux modèles des observations concernant les signaux sources: (i) le modèle déterministe et (ii) le modèle stochastique. Nous en avons ensuite déduit des conditions concernant les propriétés d’isotropie et de découplage.Pour la deuxième approche, nous avons considéré le seuil statistique de résolution qui caractérise la séparation minimale entre les deux sources. Dans cette thèse, nous avons étudié le SSR pour le contexte Bayésien moins étudié dans la littérature. Nous avons introduit un modèle des observations linéarisé basé sur le critère de probabilité d’erreur minimale. Ensuite, nous avons présenté deux approches Bayésiennes pour le SSR, l’une basée sur la théorie de l’information et l’autre basée sur la théorie de la détection. Ces approches pourront être utilisée pour améliorer la capacité de résolution des systèmes. / This thesis deals with the array geometry optimization problem in the context of sources localization. We have considered two approaches for the array geometry optimization: the performance estimation in terms of mean square error approach and the statistical resolution limit (SRL) approach. In the first approach, the lower bounds on the mean square error which are usually used in array processing to evaluate the estimation performance independently of the considered estimator have been considered. We have investigated two kinds of lower bounds: the well-known Cramér-Rao bound (CRB) for the deterministic model in which the parameters are assumed to be deterministic, and the Weiss-Weinstein bound (WWB) which is less studied, for the Bayesian model, in which, the parameters are assumed to be random with some prior distributions. We have proposed closed-form expressions of these bounds, which can be used as a statistical tool for array geometry design. Compared to the CRB, the WWB can predict the threshold effect of the MSE in the non-asymptotic area. Moreover, the closed-form expressions of the WWB proposed for a general Gaussian model with parameterized mean or parameterized covariance matrix can also be useful for other problems. Based on these closed-form expressions, the 3D array geometry and the classical planar array geometry have been investigated under (i) the conditional observation model in which the source signal is modeled as a deterministic sequence and under (ii) the unconditional observation model in which the source signal is modeled as a Gaussian random process. Conditions concerning the isotropic and uncoupling properties were then derived.In the second approach, we have considered the statistical resolution limit which characterizes the minimal separation between the two closed spaced sources which still allows to determine correctly the number of sources. In this thesis, we are interested in the SRL in the Bayesian context which is less studied in the literature. Based on the linearized observation model with the minimum probability of error, we have introduced the two Bayesian approaches of the SRL based on the detection and information theories which could lead to some interesting tools for the system design.

A new broadband beamformer composed of nested arrays (NAs), multi-dimensional (MD) filters, and multirate techniques is proposed for both linear and planar arrays. It is shown that this combination results in frequency-invariant response. For a given number of sensors, the advantage of using NAs is that the effective aperture for low temporal frequencies is larger than in the case of using uniform arrays. This leads to high spatial selectivity for low frequencies. For a given aperture size, the proposed beamformer can be implemented with significantly fewer sensors and less computation than uniform arrays with a slight deterioration in performance. Taking advantage of the Noble identity and polyphase structures, the proposed method can be efficiently implemented. Simulation results demonstrate the good performance of the proposed beamformer in terms of frequency-invariant response and computational requirements. The broadband beamformer requires a filter bank with a non-compatible set of sampling rates which is challenging to be designed. To address this issue, a filter bank design approach is presented. The approach is based on formulating the design problem as an optimization problem with a performance index which consists of a term depending on perfect reconstruction (PR) and a term depending on the magnitude specifications of the analysis filters. The design objectives are to achieve almost perfect reconstruction (PR) and have the analysis filters satisfying some prescribed frequency specifications. Several design examples are considered to show the satisfactory performance of the proposed method. A new blind multi-stage space-time equalizer (STE) is proposed which can separate narrowband sources from a mixed signal. Neither the direction of arrival (DOA) nor a training sequence is assumed to be available for the receiver. The beamformer and equalizer are jointly updated to combat both co-channel interference (CCI) and inter-symbol interference (ISI) effectively. Using subarray beamformers, the DOA, possibly time-varying, of the captured signal is estimated and tracked. The estimated DOA is used by the beamformer to provide strong CCI cancellation. In order to alleviate inter-stage error propagation significantly, a mean-square-error sorting algorithm is used which assigns detected sources to different stages according to the reconstruction error at different stages. Further, to speed up the convergence, a simple-yet-efficient DOA estimation algorithm is proposed which can provide good initial DOAs for the multi-stage STE. Simulation results illustrate the good performance of the proposed STE and show that it can effectively deal with changing DOAs and time variant channels. / Graduate / 0544 / imanmoaz@uvic.ca