539 research outputs found

    Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

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    Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

    Generalized DOA and Source Number Estimation Techniques for Acoustics and Radar

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    The purpose of this thesis is to emphasize the lacking areas in the field of direction of arrival estimation and to propose building blocks for continued solution development in the area. A review of current methods are discussed and their pitfalls are emphasized. DOA estimators are compared to each other for usage on a conformal microphone array which receives impulsive, wideband signals. Further, many DOA estimators rely on the number of source signals prior to DOA estimation. Though techniques exist to achieve this, they lack robustness to estimate for certain signal types, particularly in the case where multiple radar targets exist in the same range bin. A deep neural network approach is proposed and evaluated for this particular case. The studies detailed in this thesis are specific to acoustic and radar applications for DOA estimation

    Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

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    A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques

    Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

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    A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques

    Estimation and Minimization of the Cramer-Rao lower bound for radio direction-finding on the azimuth and elevation of planar antenna arrays

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    In this paper an approach of obtaining optimal planar antenna arrays consisting of omnidirectional sensors is proposed. The novelty of the proposed approach is to apply an exact expression of the Cramer-Rao lower bound for an arbitrary planar antenna array consisting of a number of omnidirectional elements which has been presented in the further chapters of the paper. The obtained formula describes the influence of antenna elements locations on the direction-of-arrival estimation accuracy. It has been shown that the direction-of-arrival accuracy via planar antenna arrays is determined as the sum of squares of differences between all omnidirectional elements coordinates along x- and y-axis. Thus knowing an expected area or sector of signal source it is very easy to calculate optimal arrangement of antenna elements in order to reduce direction-finding errors, because obtained by that way positions gives the best match according to the maximum likelihood criterion. It is worth nothing that such antenna arrays are useful in the way that they allow estimating the coordinates of radio emission sources in the three-dimensional coordinate space, i.e. in azimuth and elevation. In order to confirm the proposed methodology optimal antenna arrays constructed after minimization of the new formulas are researched. It is found out that the new shapes of antenna arrays based on the analytical expressions have better direction-of-arrival accuracy in comparison with the circular ones

    A room acoustics measurement system using non-invasive microphone arrays

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    This thesis summarises research into adaptive room correction for small rooms and pre-recorded material, for example music of films. A measurement system to predict the sound at a remote location within a room, without a microphone at that location was investigated. This would allow the sound within a room to be adaptively manipulated to ensure that all listeners received optimum sound, therefore increasing their enjoyment. The solution presented used small microphone arrays, mounted on the room's walls. A unique geometry and processing system was designed, incorporating three processing stages, temporal, spatial and spectral. The temporal processing identifies individual reflection arrival times from the recorded data. Spatial processing estimates the angles of arrival of the reflections so that the three-dimensional coordinates of the reflections' origin can be calculated. The spectral processing then estimates the frequency response of the reflection. These estimates allow a mathematical model of the room to be calculated, based on the acoustic measurements made in the actual room. The model can then be used to predict the sound at different locations within the room. A simulated model of a room was produced to allow fast development of algorithms. Measurements in real rooms were then conducted and analysed to verify the theoretical models developed and to aid further development of the system. Results from these measurements and simulations, for each processing stage are presented

    Estimation of Radio Channel Parameters

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    Kurzfassung Diese Dissertation behandelt die SchĂ€tzung der Modellparameter einer Momentanaufnahme des Mobilfunkkanals. Das besondere Augenmerk liegt zum einen auf der Entwicklung eines generischen Datenmodells fĂŒr den gemessenen Funkkanal, welches fĂŒr die hochauflösende ParameterschĂ€tzung geeignet ist. Der zweite Schwerpunkt dieser Arbeit ist die Entwicklung eines robusten ParameterschĂ€tzers fĂŒr die Bestimmung der Parameter des entworfenen Modells aus Funkkanalmessdaten. Entsprechend dieser logischen Abfolge ist auch der Aufbau dieser Arbeit. Im ersten Teil wird ausgehend von einem aus der Literatur bekannten strahlenoptischen Modell eine algebraisch handhabbare Darstellung von beobachteten Wellenausbreitungspfaden entwickelt. Das mathematische Modell erlaubt die Beschreibung von SISO (single-input-single-output)- Übertragungssystemen, also von Systemen mit einer Sendeantenne und einer Empfangsantenne, als auch die Beschreibung von solchen Systemen mit mehreren Sende- und/oder Empfangsantennen. Diese Systeme werden im Allgemeinen auch als SIMO- (single-input-multiple-output), MISO- (multiple-input-single-output) oder MIMO-Systeme (multiple-input-multiple-output) bezeichnet. Im Gegensatz zu bekannten Konzepten enthĂ€lt das entwickelte Modell keine Restriktionen bezĂŒglich der modellierbaren Antennenarrayarchitekturen. Dies ist besonders wichtig in Hinblick auf die möglichst vollstĂ€ndige Erfassung der rĂ€umlichen Struktur des Funkkanals. Die FlexibilitĂ€t des Modells ist eine Grundvoraussetzung fĂŒr die optimale Anpassung der Antennenstruktur an die Messaufgabe. Eine solche angepasste Antennenarraystruktur ist zum Beispiel eine zylindrische Anordnung von Antennenelementen. Sie ist gut geeignet fĂŒr die Erfassung der rĂ€umlichen Struktur des Funkkanals (Azimut und Elevation) in so genannten Outdoor- Funkszenarien. Weiterhin wird im ersten Teil eine neue Komponente des Funkkanaldatenmodells eingefĂŒhrt, welche den Beitrag verteilter (diffuser) Streuungen zur FunkĂŒbertragung beschreibt. Die neue Modellkomponente spielt eine SchlĂŒsselrolle bei der Entwicklung eines robusten ParameterschĂ€tzers im Hauptteil dieser Arbeit. Die fehlende Modellierung der verteilten Streuungen ist eine der Hauptursachen fĂŒr die begrenzte Anwendbarkeit und die oft kritisierte fehlende Robustheit von hochauflösenden FunkkanalparameterschĂ€tzern, die in der Literatur etabliert sind. Das neue Datenmodell beschreibt die so genannten dominanten Ausbreitungspfade durch eine deterministische Abbildung der Pfadparameter auf den gemessenen Funkkanal. Der Beitrag der verteilten Streuungen wird mit Hilfe eines zirkularen mittelwertfreien Gaußschen Prozesses beschrieben. Die Modellparameter der verteilten Streuungen beschreiben dabei die Kovarianzmatrix dieses Prozesses. Basierend auf dem entwickelten Datenmodell wird im Anschluss kurz ĂŒber aktuelle Konzepte fĂŒr FunkkanalmessgerĂ€te, so genannte Channel-Sounder, diskutiert. Im zweiten Teil dieser Arbeit werden in erster Linie AusdrĂŒcke zur Bestimmung der erzielbaren Messgenauigkeit eines Channel-Sounders abgeleitet. Zu diesem Zweck wird die untere Schranke fĂŒr die Varianz der geschĂ€tzten Modellparameter, das heißt der Messwerte, bestimmt. Als Grundlage fĂŒr die VarianzabschĂ€tzung wird das aus der ParameterschĂ€tztheorie bekannte Konzept der CramĂ©r-Rao-Schranke angewandt. Im Rahmen der Ableitung der CramĂ©r-Rao-Schranke werden außerdem wichtige Gesichtspunkte fĂŒr die Entwicklung eines effizienten ParameterschĂ€tzers diskutiert. Im dritten Teil der Arbeit wird ein SchĂ€tzer fĂŒr die Bestimmung der Ausbreitungspfadparameter nach dem Maximum-Likelihood-Prinzip entworfen. Nach einer kurzen Übersicht ĂŒber existierende Konzepte zur hochauflösenden FunkkanalparameterschĂ€tzung wird die vorliegende SchĂ€tzaufgabe analysiert und in Hinsicht ihres Typs klassifiziert. Unter der Voraussetzung, dass die Parameter der verteilten Streuungen bekannt sind, lĂ€sst sich zeigen, daß sich die SchĂ€tzung der Parameter der Ausbreitungspfade als ein nichtlineares gewichtetes kleinstes Fehlerquadratproblem auffassen lĂ€sst. Basierend auf dieser Erkenntnis wird ein generischer Algorithmus zur Bestimmung einer globalen Startlösung fĂŒr die Parameter eines Ausbreitungspfades vorgeschlagen. Hierbei wird von dem Konzept der Structure-Least-Squares (SLS)-Probleme Gebrauch gemacht, um die KomplexitĂ€t des SchĂ€tzproblems zu reduzieren. Im folgenden Teil dieses Abschnitts wird basierend auf aus der Literatur bekannten robusten numerischen Algorithmen ein SchĂ€tzer zur genauen Bestimmung der Ausbreitungspfadparameter abgeleitet. Im letzten Teil dieses Abschnitts wird die Anwendung unterraumbasierter SchĂ€tzer zur Bestimmung der Ausbreitungspfadparameter diskutiert. Es wird ein speichereffizienter Algorithmus zur SignalraumschĂ€tzung entwickelt. Dieser Algorithmus ist eine Grundvoraussetzung fĂŒr die Anwendung von mehrdimensionalen ParameterschĂ€tzern wie zum Beispiel des R-D unitary ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) zur Bestimmung von Funkkanalparametern aus MIMO-Funkkanalmessungen. Traditionelle Verfahren zur SignalraumschĂ€tzung sind hier im Allgemeinen nicht anwendbar, da sie einen zu großen Speicheraufwand erfordern. Außerdem wird in diesem Teil gezeigt, dass ESPRIT-Algorithmen auch zur ParameterschĂ€tzung von Daten mit so genannter versteckter Rotations-Invarianzstruktur eingesetzt werden können. Als Beispiel wird ein ESPRIT-basierter Algorithmus zur RichtungsschĂ€tzung in Verbindung mit multibeam-Antennenarrays (CUBA) abgeleitet. Im letzten Teil dieser Arbeit wird ein Maximum-Likelihood-SchĂ€tzer fĂŒr die neue Komponente des Funkkanals, welche die verteilten Streuungen beschreibt, entworfen. Ausgehend vom Konzept des iterativen Maximum-Likelihood-SchĂ€tzers wird ein Algorithmus entwickelt, der hinreichend geringe numerische KomplexitĂ€t besitzt, so dass er praktisch anwendbar ist. In erster Linie wird dabei von der Toeplitzstruktur der zu schĂ€tzenden Kovarianzmatrix Gebrauch gemacht. Aufbauend auf dem SchĂ€tzer fĂŒr die Parameter der Ausbreitungspfade und dem SchĂ€tzer fĂŒr die Parameter der verteilten Streuungen wird ein Maximum-Likelihood-SchĂ€tzer entwickelt (RIMAX), der alle Parameter des in Teil I entwickelten Modells der Funkanalmessung im Verbund schĂ€tzt. Neben den geschĂ€tzten Parametern des Datenmodells liefert der SchĂ€tzer zusĂ€tzlich ZuverlĂ€ssigkeitsinformationen. Diese werden unter anderem zur Bestimmung der Modellordnung, das heißt zur Bestimmung der Anzahl der dominanten Ausbreitungspfade, herangezogen. Außerdem stellen die ZuverlĂ€ssigkeitsinformationen aber auch ein wichtiges SchĂ€tzergebnis dar. Die ZuverlĂ€ssigkeitsinformationen machen die weitere Verarbeitung und Wertung der Messergebnisse möglich.The theme of this thesis is the estimation of model parameters of a radio channel snapshot. The main focus was the development of a general data model for the measured radio channel, suitable for both high resolution channel parameter estimation on the one hand, and the development of a robust parameter estimator for the parameters of the designed parametric radio channel model, in line with this logical work flow is this thesis. In the first part of this work an algebraic representation of observed propagation paths is developed using a ray-optical model known from literature. The algebraic framework is suitable for the description of SISO (single-input-single-output) radio transmission systems. A SISO system uses one antenna as the transmitter (Tx) and one antenna as the receiver (Rx). The derived expression for the propagation paths is also suitable to describe SIMO (single-input-multiple-output), MISO (multiple-input-single-output), and MIMO (multiple-input-multiple-output) radio channel measurements. In contrast to other models used for high resolution channel parameter estimation the derived model makes no restriction regarding the structure of the antenna array used throughout the measurement. This is important since the ultimate goal in radio channel sounding is the complete description of the spatial (angular) structure of the radio channel at Tx and Rx. The flexibility of the data model is a prerequisite for the optimisation of the antenna array structure with respect to the measurement task. Such an optimised antenna structure is a stacked uniform circular beam array, i.e., a cylindrical arrangement of antenna elements. This antenna array configuration is well suited for the measurement of the spatial structure of the radio channel at Tx and/or Rx in outdoor-scenarios. Furthermore, a new component of the radio channel model is introduced in the first part of this work. It describes the contribution of distributed (diffuse) scattering to the radio transmission. The new component is key for the development of a robust radio channel parameter estimator, which is derived in the main part of this work. The ignorance of the contribution of distributed scattering to radio propagation is one of the main reasons why high-resolution radio channel parameter estimators fail in practice. Since the underlying data model is wrong the estimators produce erroneous results. The improved model describes the so called dominant propagation paths by a deterministic mapping of the propagation path parameters to the channel observation. The contribution of the distributed scattering is modelled as a zero-mean circular Gaussian process. The parameters of the distributed scattering process determine the structure of the covariance matrix of this process. Based on this data model current concepts for radio channel sounding devices are discussed. In the second part of this work expressions for the accuracy achievable by a radio channel sounder are derived. To this end the lower bound on the variance of the measurements i.e. the parameter estimates is derived. As a basis for this evaluation the concept of the CramĂ©r-Rao lower bound is employed. On the way to the CramĂ©r-Rao lower bound for all channel model parameters, important issues for the development of an appropriate parameter estimator are discussed. Among other things the coupling of model parameters is also discussed. In the third part of this thesis, an estimator, for the propagation path parameters is derived. For the estimator the 'maximum-likelihood' approach is employed. After a short overview of existing high-resolution channel parameter estimators the estimation problem is classified. It is shown, that the estimation of the parameters of the propagation paths can be understood as a nonlinear weighted least squares problem, provided the parameters of the distributed scattering process are known. Based on this observation a general algorithm for the estimation of raw parameters for the observed propagation paths is developed. The algorithm uses the concept of structured-least-squares (SLS) and compressed maximum likelihood to reduce the numerical complexity of the estimation problem. A robust estimator for the precise estimation of the propagation path parameters is derived. The estimator is based on concepts well known from nonlinear local optimisation theory. In the last part of this chapter the application of subspace based parameter estimation algorithms for path parameter estimation is discussed. A memory efficient estimator for the signal subspace needed by, e.g., R-D unitary ESPRIT is derived. This algorithm is a prerequisite for the application of signal subspace based algorithms to MIMO-channel sounding measurements. Standard algorithms for signal subspace estimation (economy size SVD, singular value decomposition) are not suitable since they require an amount of memory which is too large. Furthermore, it is shown that ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) based algorithms can also be employed for parameter estimation from data having hidden rotation invariance structure. As an example an ESPRIT algorithm for angle estimation using circular uniform beam arrays (circular multi-beam antennas) is derived. In the final part of this work a maximum likelihood estimator for the new component of the channel model is developed. Starting with the concept of iterative maximum likelihood estimation, an algorithm is developed having a low computational complexity. The low complexity of the algorithm is achieved by exploiting the Toeplitz-structure of the covariance matrix to estimate. Using the estimator for the (concentrated, dominant, specular-alike) propagation paths and the parametric estimator for the covariance matrix of the process describing the distributed diffuse scattering a joint estimator for all channel parameter is derived (RIMAX). The estimator is a 'maximum likelihood' estimator and uses the genuine SAGE concept to reduce the computational complexity. The estimator provides additional information about the reliability of the estimated channel parameters. This reliability information is used to determine an appropriate model for the observation. Furthermore, the reliability information i.e. the estimate of the covariance matrix of all parameter estimates is also an important parameter estimation result. This information is a prerequisite for further processing and evaluation of the measured channel parameters
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