Efficient Two-Dimensional Direction Finding via Auxiliary-Variable Manifold Separation Technique for Arbitrary Array Structure

A polynomial rooting direction of arrival (DOA) algorithm for multiple plane waves incident on an arbitrary array structure that combines the multipolynomial resultants and matrix computations is proposed in this paper. Firstly, a new auxiliary-variable manifold separation technique (AV-MST) is used to model the steering vector of arbitrary array structure as the product of a sampling matrix (dependent only on the array structure) and two Vandermonde-structured wavefield coefficient vectors (dependent on the wavefield). Then the propagator operator is calculated and used to form a system of bivariate polynomial equations. Finally, the automatically paired azimuth and elevation estimates are derived by polynomial rooting. The presented algorithm employs the concept of auxiliary-variable manifold separation technique which requires no sector by sector array interpolation and thus does not suffer from any mapping errors. In addition, the new algorithm does not need any eigenvalue decomposition of the covariance matrix and exhausted search over the two-dimensional parameter space. Moreover, the algorithm gives automatically paired estimates, thus avoiding the complex pairing procedure. Therefore, the proposed algorithm shows low computational complexity and high robustness performance. Simulation results are shown to validate the effectiveness of the proposed method

Wavefield modeling and signal processing for sensor arrays of arbitrary geometry

Sensor arrays and related signal processing methods are key technologies in many areas of engineering including wireless communication systems, radar and sonar as well as in biomedical applications. Sensor arrays are a collection of sensors that are placed at distinct locations in order to sense physical phenomena or synthesize wavefields. Spatial processing from the multichannel output of the sensor array is a typical task. Such processing is useful in areas including wireless communications, radar, surveillance and indoor positioning. In this dissertation, fundamental theory and practical methods of wavefield modeling for radio-frequency array processing applications are developed. Also, computationally-efficient high-resolution and optimal signal processing methods for sensor arrays of arbitrary geometry are proposed. Methods for taking into account array nonidealities are introduced as well. Numerical results illustrating the performance of the proposed methods are given using real-world antenna arrays. Wavefield modeling and manifold separation for vector-fields such as completely polarized electromagnetic wavefields and polarization sensitive arrays are proposed. Wavefield modeling is used for writing the array output in terms of two independent parts, namely the sampling matrix depending on the employed array including nonidealities and the coefficient vector depending on the wavefield. The superexponentially decaying property of the sampling matrix for polarization sensitive arrays is established. Two estimators of the sampling matrix from calibration measurements are proposed and their statistical properties are established. The array processing methods developed in this dissertation concentrate on polarimetric beamforming as well as on high-resolution and optimal azimuth, elevation and polarization parameter estimation. The proposed methods take into account array nonidealities such as mutual coupling, cross-polarization effects and mounting platform reflections. Computationally-efficient solutions based on polynomial rooting techniques and fast Fourier transform are achieved without restricting the proposed methods to regular array geometries. A novel expression for the Cramér-Rao bound in array processing that is tight for real-world arrays with nonidealities in the asymptotic regime is also proposed. A relationship between spherical harmonics and 2-D Fourier basis, called equivalence matrix, is established. A novel fast spherical harmonic transform is proposed, and a one-to-one mapping between spherical harmonic and 2-D Fourier spectra is found. Improvements to the minimum number of samples on the sphere that are needed in order to avoid aliasing are also proposed

Statistical Error Analysis of a DOA Estimator for a PCL System Using the Cramer-RAO Bound Theorem

Direction of Arrival (DOA) estimation of signals has been a popular research area in Signal Processing. DOA estimation also has a significant role in the object location process of Passive Coherent Location (PCL) systems. PCL systems have been in open literature since 1986 and their applications are not as clearly understood as the DOA estimation problem. However, they are the focus of many current research efforts and show much promise. The purpose of this research is to analyze the DOA estimation errors in a PCL system. The performance of DOA estimators is studied using the Cramer-Rao Bound (CRB) Theorem. The CRB provides a lower bound on the variance of unbiased DOA estimators. Since variance is a desirable property for measuring the accuracy of an estimator, the CRB gives a good indication about the performance of an estimator. Previous DOA estimators configured with array antennas used the array antenna manifold, or the properties of the array antenna structure, to estimate signal DOA. Conventional DOA estimators use arbitrary signal (AS) structures. Constant Modulus (CM) DOA estimators restrict the input signals to a family of constant envelope signals, and when there are multiple signals in the environment, CM DOA estimators are able to separate signals from each other using the CM signal property. CM estimators then estimate the DOA for each signal individually. This research compares the CRB for AS and CM DOA estimators for a selected system. The CRB is also computed for this system when single and multiple and moving objects are present. The CRBAS and CRBCM are found to be different for the multiple signal case and moving object cases

Model Order Estimation in the Presence of multipath Interference using Residual Convolutional Neural Networks

Model order estimation (MOE) is often a pre-requisite for Direction of Arrival (DoA) estimation. Due to limits imposed by array geometry, it is typically not possible to estimate spatial parameters for an arbitrary number of sources; an estimate of the signal model is usually required. MOE is the process of selecting the most likely signal model from several candidates. While classic methods fail at MOE in the presence of coherent multipath interference, data-driven supervised learning models can solve this problem. Instead of the classic MLP (Multiple Layer Perceptions) or CNN (Convolutional Neural Networks) architectures, we propose the application of Residual Convolutional Neural Networks (RCNN), with grouped symmetric kernel filters to deliver state-of-art estimation accuracy of up to 95.2\% in the presence of coherent multipath, and a weighted loss function to eliminate underestimation error of the model order. We show the benefit of the approach by demonstrating its impact on an overall signal processing flow that determines the number of total signals received by the array, the number of independent sources, and the association of each of the paths with those sources . Moreover, we show that the proposed estimator provides accurate performance over a variety of array types, can identify the overloaded scenario, and ultimately provides strong DoA estimation and signal association performance

Array communications in wireless sensor networks

Imperial Users onl

Ein Beitrag zur effizienten Richtungsschätzung mittels Antennenarrays

Sicherlich gibt es nicht den einen Algorithmus zur Schätzung der Einfallsrichtung elektromagnetischer Wellen. Statt dessen existieren Algorithmen, die darauf optimiert sind Hunderte Pfade zu finden, mit uniformen linearen oder kreisförmigen Antennen-Arrays genutzt zu werden oder möglichst schnell zu sein. Die vorliegende Dissertation befasst sich mit letzterer Art. Wir beschränken uns jedoch nicht auf den reinen Algorithmus zur Richtungsschätzung (RS), sondern gehen das Problem in verschiedener Hinsicht an. Die erste Herangehensweise befasst sich mit der Beschreibung der Array-Mannigfaltigkeit (AM). Bisherige Interpolationsverfahren der AM berücksichtigen nicht inhärent Polarisation. Daher wird separat für jede Polarisation einzeln interpoliert. Wir übernehmen den Ansatz, eine diskrete zweidimensionale Fouriertransformation (FT) zur Interpolation zu nutzen. Jedoch verschieben wir das Problem in den Raum der Quaternionen. Dort wenden wir eine zweidimensionale diskrete quaternionische FT an. Somit können beide Polarisationszustände als eine einzige Größe betrachtet werden. Das sich ergebende Signalmodell ist im Wesentlichen kompatibel mit dem herkömmlichen komplexwertigen Modell. Unsere zweite Herangehensweise zielt auf die fundamentale Eignung eines Antennen-Arrays für die RS ab. Zu diesem Zweck nutzen wir die deterministische Cramér-Rao-Schranke (Cramér-Rao Lower Bound, CRLB). Wir leiten drei verschiedene CRLBs ab, die Polarisationszustände entweder gar nicht oder als gewünschte oder störende Parameter betrachten. Darüber hinaus zeigen wir auf, wie Antennen-Arrays schon während der Design-Phase auf RS optimiert werden können. Der eigentliche Algorithmus zur RS stellt die letzte Herangehensweise dar. Mittels einer MUSIC-basierte Kostenfunktion leiten wir effiziente Schätzer ab. Hierfür kommt eine modifizierte Levenberg- bzw. Levenberg-Marquardt-Suche zum Einsatz. Da die eigentliche Kostenfunktion hier nicht angewendet werden kann, ersetzen wir diese durch vier verschiedene Funktionen, die sich lokal ähnlich verhalten. Diese Funktionen beruhen auf einer Linearisierung eines Kroneckerproduktes zweier polarimetrischer Array-Steering-Vektoren. Dabei stellt sich heraus, dass zumindest eine der Funktionen in der Regel zu sehr schneller Konvergenz führt, sodass ein echtzeitfähiger Algorithmus entsteht.It is save to say that there is no such thing as the direction finding (DF) algorithm. Rather, there are algorithms that are tuned to resolve hundreds of paths, algorithms that are designed for uniform linear arrays or uniform circular arrays, and algorithms that strive for efficiency. The doctoral thesis at hand deals with the latter type of algorithms. However, the approach taken does not only incorporate the actual DF algorithm but approaches the problem from different perspectives. The first perspective concerns the description of the array manifold. Current interpolation schemes have no notion of polarization. Hence, the array manifold interpolation is performed separately for each state of polarization. In this thesis, we adopted the idea of interpolation via a 2-D discrete Fourier transform. However, we transform the problem into the quaternionic domain. Here, a 2-D discrete quaternionic Fourier transform is applied. Hence, both states of polarization can be viewed as a single quantity. The resulting interpolation is applied to a signal model which is essentially compatible to conventional complex model. The second perspective in this thesis is to look at the fundamental DF capability of an antenna array. For that, we use the deterministic Cramér-Rao Lower Bound (CRLB). We point out the differences between not considering polarimetric parameters and taking them as desired parameters or nuisance parameters. Such differences lead to three different CRLBs. Moreover, insight is given how a CRLB can be used to optimize an antenna array already during the design process to improve its DF performance. The actual DF algorithm constitutes the third perspective that is considered in this thesis. A MUSIC-based cost function is used to derive efficient estimators. To this end, a modified Levenberg search and Levenberg-Marquardt search are employed. Since the original cost function is not eligible to be used in this framework, we replace it by four different functions that locally show the same behavior. These functions are based on a linearization of Kronecker products of two polarimetric array steering vectors. It turns out that at least one of these functions usually exhibits very fast convergence leading to real-time capable algorithms