10 research outputs found
Advanced array processing techniques and systems
Research and development on smart antennas, which are recognized as a promising technique to improve the performance of mobile communications, have been extensive in the recent years. Smart antennas combine multiple antenna elements with a signal processing capability in both space and time to optimize its radiation and reception pattern automatically in response to the signal environment. This paper concentrates on the signal processing aspects of smart antenna systems. Smart antennas are often classified as either switched-beam or adaptive-array systems, for which a variety of algorithms have been developed to enhance the signal of interest and reject the interference. The antenna systems need to differentiate the desired signal from the interference, and normally requires either a priori knowledge or the signal direction to achieve its goal. There exists a variety of methods for direction of arrival (DOA) estimation with conflicting demands of accuracy and computation. Similarly, there are many algorithms to compute array weights to direct the maximum radiation of the array pattern toward the signal and place nulls toward the interference, each with its convergence property and computational complexity. This paper discusses some of the typical algorithms for DOA estimation and beamforming. The concept and details of each algorithm are provided. Smart antennas can significantly help in improving the performance of communication systems by increasing channel capacity and spectrum efficiency, extending range coverage, multiplexing channels with spatial division multiple access (SDMA), and compensating electronically for aperture distortion. They also reduce delay spread, multipath fading, co-channel interference, system complexity, bit error rates, and outage probability. In addition, smart antennas can locate mobile units or assist the location determination through DOA and range estimation. This capability can support and benefit many location-based services including emergency assistance, tracking services, safety services, billing services, and information services such as navigation, weather, traffic, and directory assistance
A flexible design strategy for three-element non-uniform linear arrays
This paper illustrates a flexible design strategy for a three-element non-uniform linear array (NULA) aimed at estimating the direction of arrival (DoA) of a source of interest. Thanks to the spatial diversity resulting from non-uniform sensor spacings, satisfactory DoA estimation accuracies can be achieved by employing a very limited number of receiving elements. This makes NULA configurations particularly attractive for low-cost passive location applications. To estimate the DoA of the source of interest, we resort to the maximum likelihood estimator, and the proposed design strategy is obtained by constraining the maximum pairwise error probability to control the errors occurring due to outliers. In fact, it is well known that the accuracy of the maximum likelihood estimator is often degraded by outliers, especially when the signal-to-noise power ratio does not belong to the so-called asymptotic region. The imposed constraint allows for the defining of an admissible region in which the array should be selected. This region can be further modified to incorporate practical design constraints concerning the antenna element size and the positioning accuracy. The best admissible array is then compared to the one obtained with a conventional NULA design approach, where only antenna spacings multiple of λ/2 are considered, showing improved performance, which is also confirmed by the experimental results
Estimation of Radio Channel Parameters
Kurzfassung
Diese Dissertation behandelt die SchÀtzung 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 ParameterschÀtzers
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)-
Ăbertragungssystemen, 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 vollstÀndige Erfassung der rÀumlichen 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 FunkkanalparameterschÀtzern, 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 GauĂschen 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 heiĂt der Messwerte, bestimmt. Als Grundlage fĂŒr die VarianzabschĂ€tzung wird
das aus der ParameterschÀtztheorie bekannte Konzept der Cramér-Rao-Schranke
angewandt. Im Rahmen der Ableitung der CramĂ©r-Rao-Schranke werden auĂerdem
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 Ăbersicht ĂŒber existierende Konzepte zur hochauflösenden
FunkkanalparameterschÀtzung wird die vorliegende SchÀtzaufgabe analysiert und in
Hinsicht ihres Typs klassifiziert. Unter der Voraussetzung, dass die Parameter
der verteilten Streuungen bekannt sind, lÀsst sich zeigen, daà sich die
SchÀtzung der Parameter der Ausbreitungspfade als ein nichtlineares gewichtetes
kleinstes Fehlerquadratproblem auffassen lÀsst. 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
KomplexitÀt des SchÀtzproblems zu reduzieren. Im folgenden Teil dieses
Abschnitts wird basierend auf aus der Literatur bekannten robusten numerischen
Algorithmen ein SchÀtzer zur genauen Bestimmung der Ausbreitungspfadparameter
abgeleitet. Im letzten Teil dieses Abschnitts wird die Anwendung
unterraumbasierter SchÀtzer zur Bestimmung der Ausbreitungspfadparameter
diskutiert. Es wird ein speichereffizienter Algorithmus zur SignalraumschÀtzung
entwickelt. Dieser Algorithmus ist eine Grundvoraussetzung fĂŒr die Anwendung von
mehrdimensionalen ParameterschÀtzern 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 SignalraumschÀtzung sind hier im Allgemeinen nicht anwendbar, da
sie einen zu groĂen Speicheraufwand erfordern. AuĂerdem wird in diesem Teil
gezeigt, dass ESPRIT-Algorithmen auch zur ParameterschÀtzung von Daten mit so
genannter versteckter Rotations-Invarianzstruktur eingesetzt werden können. Als
Beispiel wird ein ESPRIT-basierter Algorithmus zur RichtungsschÀtzung 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-SchÀtzers
wird ein Algorithmus entwickelt, der hinreichend geringe numerische KomplexitÀt
besitzt, so dass er praktisch anwendbar ist. In erster Linie wird dabei von der
Toeplitzstruktur der zu schÀtzenden 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-SchÀtzer
entwickelt (RIMAX), der alle Parameter des in Teil I entwickelten Modells der
Funkanalmessung im Verbund schÀtzt. Neben den geschÀtzten Parametern des
Datenmodells liefert der SchÀtzer zusÀtzlich ZuverlÀssigkeitsinformationen.
Diese werden unter anderem zur Bestimmung der Modellordnung, das heiĂt zur
Bestimmung der Anzahl der dominanten Ausbreitungspfade, herangezogen. AuĂerdem
stellen die ZuverlÀssigkeitsinformationen aber auch ein wichtiges SchÀtzergebnis
dar. Die ZuverlÀssigkeitsinformationen 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 Cramér-Rao lower bound is employed. On the way to
the Cramér-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
Topics in the accuracy and resolution of superresolution systems
Since their introduction in the 1970s and 1980s superresolution systems for point source
parameter estimation have received theoretical attention regarding their potential
performance. Two aspects of performance in particular are of interest, the accuracy of
the parameter estimation and the resolution achievable. Limitations on performance
may be considered to be due to noise affecting the data, or to errors in the system.
Superresolution methods divide roughly into two groups â âspectralâ methods and
maximum likelihood (ML) methods. MUSIC is perhaps the most effective example of a
spectral method and has been studied in considerable detail, in both performance
measures, but mainly only for the case of a single parameter. In this study the accuracy
of MUSIC in the application of two-dimensional direction finding (DF) has been
analysed, with and without system errors, using a general array. Theoretical results are
confirmed by simulations. An aim has been to produce simpler results for use in
estimating the potential performance of practical systems.
Little work has been reported on the resolution of ML methods and this is the second
main topic of this work, particularly for the two-dimensional DF case using a general
array, with a ML method (IMP) similar to the better known Alternating Projection.
Some results are obtained for resolution with and without errors for the case of noncoherent
signals. For coherent signals (including the standard radar case) the
performance is found to depend on the relative phase of the signals, varying from the
quadrature case, where the performance is as for the non-coherent case, to the in-phase
(or antiphase) case where only one signal peak is seen
Space-Time Parameter Estimation in Radar Array Processing
This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance
Space-Time Parameter Estimation in Radar Array Processing
This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance
Applications of Continuous Spatial Models in Multiple Antenna Signal Processing
This thesis covers the investigation and application of continuous spatial models for multiple antenna signal processing. The use of antenna arrays for advanced sensing and communications systems has been facilitated by the rapid increase in the capabilities of digital signal processing systems. The wireless communications channel will vary across space as different signal paths from the same source combine and interfere. This creates a level of spatial diversity that can be exploited to improve the robustness and overall capacity of the wireless channel. Conventional approaches to using spatial diversity have centered on smart, adaptive antennas and spatial beam forming. Recently, the more general theory of multiple input, multiple output (MIMO) systems has been developed to utilise the independent spatial communication modes offered in a scattering environment. ¶ ..