On the influence of detection tests on deterministic parameters estimation

In non-linear estimation problems three distinct regions of operation can be observed. In the asymptotic region, the Mean Square Error (MSE) of Maximum Likelihood Estimators (MLE) is small and, in many cases,close to the Cramer-Rao bound (CRB). In the a priory performance region where the number of independent snapshots and/or the SNR are very low, the MSE is close to that obtained from the prior knowledge about the problem. Between these two extremes, there is an additional transition region where MSE of estimators deteriorates with respect to CRB. The present paper provides exemples of improvement of MSE prediction by CRB, not only in the transition region but also in the a priori region, resulting from introduction of a detection step, which proves that this renement in MSE lower bounds derivation is worth investigating

LMPIT-inspired Tests for Detecting a Cyclostationary Signal in Noise with Spatio-Temporal Structure

In spectrum sensing for cognitive radio, the presence of a primary user can be detected by making use of the cyclostationarity property of digital communication signals. For the general scenario of a cyclostationary signal in temporally colored and spatially correlated noise, it has previously been shown that an asymptotic generalized likelihood ratio test (GLRT) and locally most powerful invariant test (LMPIT) exist. In this paper, we derive detectors for the presence of a cyclostationary signal in various scenarios with structured noise. In particular, we consider noise that is temporally white and/or spatially uncorrelated. Detectors that make use of this additional information about the noise process have enhanced performance. We have previously derived GLRTs for these specific scenarios; here, we examine the existence of LMPITs. We show that these exist only for detecting the presence of a cyclostationary signal in spatially uncorrelated noise. For white noise, an LMPIT does not exist. Instead, we propose tests that approximate the LMPIT, and they are shown to perform well in simulations. Finally, if the noise structure is not known in advance, we also present hypothesis tests using our framework

Passive detection of correlated subspace signals in two MIMO channels

In this paper, we consider a two-channel multiple-input multiple-output passive detection problem, in which there is a surveillance array and a reference array. The reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension, but unknown basis. The question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension, but unknown basis, which is correlated with the subspace signal in the reference channel. We consider a second-order detection problem where these subspace signals are structured by an unknown, but common, p-dimensional random vector of symbols transmitted from sources of opportunity, and then received through unknown M × p matrices at each of the M-element arrays. The noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances. We provide a unified framework to derive the generalized likelihood ratio test for these different noise models. In the most general case of arbitrary noise covariance matrices, the test statistic is a monotone function of canonical correlations between the reference and surveillance channels.I. Santamaría and J. Vía have received funding from Ministerio de Economía y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U. under projects TEC2013-47141-C4-3-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN) and TEC2016-81900-REDT (KERMES). The research of Haonan Wang was partially supported by NSF grant DMS-1521746

Unit Circle Roots Based Sensor Array Signal Processing

As technology continues to rapidly evolve, the presence of sensor arrays and the algorithms processing the data they generate take an ever-increasing role in modern human life. From remote sensing to wireless communications, the importance of sensor signal processing cannot be understated. Capon\u27s pioneering work on minimum variance distortionless response (MVDR) beamforming forms the basis of many modern sensor array signal processing (SASP) algorithms. In 2004, Steinhardt and Guerci proved that the roots of the polynomial corresponding to the optimal MVDR beamformer must lie on the unit circle, but this result was limited to only the MVDR. This dissertation contains a new proof of the unit circle roots property which generalizes to other SASP algorithms. Motivated by this result, a unit circle roots constrained (UCRC) framework for SASP is established and includes MVDR as well as single-input single-output (SISO) and distributed multiple-input multiple-output (MIMO) radar moving target detection. Through extensive simulation examples, it will be shown that the UCRC-based SASP algorithms achieve higher output gains and detection probabilities than their non-UCRC counterparts. Additional robustness to signal contamination and limited secondary data will be shown for the UCRC-based beamforming and target detection applications, respectively

Adaptive Imaging with a Cylindrical, Time-Encoded Imaging System

Most imaging systems for terrestrial nuclear imaging are static in that the design of the system and the data acquisition protocol are defined prior to the experiment. Often, these systems are designed for general use and not optimized for any specific task. The core concept of adaptive imaging is to modify the imaging system during a measurement based on collected data. This enables scenario specific adaptation of the imaging system which leads to better performance for a given task. This dissertation presents the first adaptive, cylindrical, time-encoded imaging (c-TEI) system and evaluates its performance on tasks relevant to nuclear non-proliferation and international safeguards. We explore two methods of adaptation of a c-TEI system, adaptive detector movements and adaptive mask movements, and apply these methods to three tasks, improving angular resolution, detecting a weak source in the vicinity of a strong source, and reconstructing complex source scenes. The results indicate that adaptive imaging significantly improves performance in each case. For the MATADOR imager, we find that adaptive detector movements improve the angular resolution of a point source by 20% and improve the angular resolution of two point sources by up to 50%. For the problem of detecting a weak source in the vicinity of a strong source, we find that adaptive mask movements achieve the same detection performance as a similar, non-adaptive system in 20%-40% less time, depending on the relative position of the weak source. Additionally, we developed an adaptive detection algorithm that doubles the probability of detection of the weak source at a 5% false-alarm rate. Finally, we applied adaptive imaging concepts to reconstruct complex arrangements of special nuclear material at Idaho National Laboratory. We find that combining data from multiple detector positions improves image uniformity of extended sources by 38% and reduces the background noise by 50%. We also demonstrate 2D (azimuthal and radial) imaging in a crowded source scene. These promising experimental results highlight the potential for adaptive imaging using a c-TEI system and motivate further research toward specific, real-world applications.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163009/1/nirpshah_1.pd

Comparison of adaptive radar algorithms : transformed SMI, eigencanceler, and SMI

Advanced airborne radars must perform target detection in the presence of interference and heavy clutter. In many applications, the practical usefulness of adaptive arrays is limited by their convergence rate. In this paper, we first analyze the performance of the SMI method. Then, two other methods, the transformed SMI and the eigencanceler, both based on the principle component inversion (PCI) technique, are described and analyzed by simulation. It is shown by simulation based comparison that the transformed SMI and the Eigencanceler outperform the SMI method. It is also shown that the transformed SMI and the eigencanceler has higher convergence rate in terms of output signal-to-noise ratio than the SMI, specially for short data record sizes. It is concluded that the transformed SMI and the eigencanceler are good alternatives to the SMI method when data set available is small

GNSS array-based acquisition: theory and implementation

This Dissertation addresses the signal acquisition problem using antenna arrays in the general framework of Global Navigation Satellite Systems (GNSS) receivers. The term GNSS classi es those navigation systems based on a constellation of satellites, which emit ranging signals useful for positioning. Although the American GPS is already available, which coexists with the renewed Russian Glonass, the forthcoming European contribution (Galileo) along with the Chinese Compass will be operative soon. Therefore, a variety of satellite constellations and signals will be available in the next years. GNSSs provide the necessary infrastructures for a myriad of applications and services that demand a robust and accurate positioning service. The positioning availability must be guaranteed all the time, specially in safety-critical and mission-critical services. Examining the threats against the service availability, it is important to take into account that all the present and the forthcoming GNSSs make use of Code Division Multiple Access (CDMA) techniques. The ranging signals are received with very low precorrelation signal-to-noise ratio (in the order of ���22 dB for a receiver operating at the Earth surface). Despite that the GNSS CDMA processing gain o ers limited protection against Radio Frequency interferences (RFI), an interference with a interference-to-signal power ratio that exceeds the processing gain can easily degrade receivers' performance or even deny completely the GNSS service, specially conventional receivers equipped with minimal or basic level of protection towards RFIs. As a consequence, RFIs (either intentional or unintentional) remain as the most important cause of performance degradation. A growing concern of this problem has appeared in recent times. Focusing our attention on the GNSS receiver, it is known that signal acquisition has the lowest sensitivity of the whole receiver operation, and, consequently, it becomes the performance bottleneck in the presence of interfering signals. A single-antenna receiver can make use of time and frequency diversity to mitigate interferences, even though the performance of these techniques is compromised in low SNR scenarios or in the presence of wideband interferences. On the other hand, antenna arrays receivers can bene t from spatial-domain processing, and thus mitigate the e ects of interfering signals. Spatial diversity has been traditionally applied to the signal tracking operation of GNSS receivers. However, initial tracking conditions depend on signal acquisition, and there are a number of scenarios in which the acquisition process can fail as stated before. Surprisingly, to the best of our knowledge, the application of antenna arrays to GNSS signal acquisition has not received much attention. This Thesis pursues a twofold objective: on the one hand, it proposes novel arraybased acquisition algorithms using a well-established statistical detection theory framework, and on the other hand demonstrates both their real-time implementation feasibility and their performance in realistic scenarios. The Dissertation starts with a brief introduction to GNSS receivers fundamentals, providing some details about the navigation signals structure and the receiver's architecture of both GPS and Galileo systems. It follows with an analysis of GNSS signal acquisition as a detection problem, using the Neyman-Pearson (NP) detection theory framework and the single-antenna acquisition signal model. The NP approach is used here to derive both the optimum detector (known as clairvoyant detector ) and the sov called Generalized Likelihood Ratio Test (GLRT) detector, which is the basis of almost all of the current state-of-the-art acquisition algorithms. Going further, a novel detector test statistic intended to jointly acquire a set of GNSS satellites is obtained, thus reducing both the acquisition time and the required computational resources. The eff ects of the front-end bandwidth in the acquisition are also taken into account. Then, the GLRT is extended to the array signal model to obtain an original detector which is able to mitigate temporally uncorrelated interferences even if the array is unstructured and moderately uncalibrated, thus becoming one of the main contributions of this Dissertation. The key statistical feature is the assumption of an arbitrary and unknown covariance noise matrix, which attempts to capture the statistical behavior of the interferences and other non-desirable signals, while exploiting the spatial dimension provided by antenna arrays. Closed form expressions for the detection and false alarm probabilities are provided. Performance and interference rejection capability are modeled and compared both to their theoretical bound. The proposed array-based acquisition algorithm is also compared to conventional acquisition techniques performed after blind null-steering beamformer approaches, such as the power minimization algorithm. Furthermore, the detector is analyzed under realistic conditions, accounting for the presence of errors in the covariance matrix estimation, residual Doppler and delay errors, and signal quantization e ects. Theoretical results are supported by Monte Carlo simulations. As another main contribution of this Dissertation, the second part of the work deals with the design and the implementation of a novel Field Programmable Gate Array (FPGA)-based GNSS real-time antenna-array receiver platform. The platform is intended to be used as a research tool tightly coupled with software de ned GNSS receivers. A complete signal reception chain including the antenna array and the multichannel phase-coherent RF front-end for the GPS L1/ Galileo E1 was designed, implemented and tested. The details of the digital processing section of the platform, such as the array signal statistics extraction modules, are also provided. The design trade-o s and the implementation complexities were carefully analyzed and taken into account. As a proof-of-concept, the problem of GNSS vulnerability to interferences was addressed using the presented platform. The array-based acquisition algorithms introduced in this Dissertation were implemented and tested under realistic conditions. The performance of the algorithms were compared to single antenna acquisition techniques, measured under strong in-band interference scenarios, including narrow/wide band interferers and communication signals. The platform was designed to demonstrate the implementation feasibility of novel array-based acquisition algorithms, leaving the rest of the receiver operations (mainly, tracking, navigation message decoding, code and phase observables, and basic Position, Velocity and Time (PVT) solution) to a Software De ned Radio (SDR) receiver running in a personal computer, processing in real-time the spatially- ltered signal sample stream coming from the platform using a Gigabit Ethernet bus data link. In the last part of this Dissertation, we close the loop by designing and implementing such software receiver. The proposed software receiver targets multi-constellation/multi-frequency architectures, pursuing the goals of e ciency, modularity, interoperability, and exibility demanded by user domains that require non-standard features, such as intermediate signals or data extraction and algorithms interchangeability. In this context, we introduce an open-source, real-time GNSS software de ned receiver (so-named GNSS-SDR) that contributes with several novel features such as the use of software design patterns and shared memory techniques to manage e ciently the data ow between receiver blocks, the use of hardware-accelerated instructions for time-consuming vector operations like carrier wipe-o and code correlation, and the availability to compile and run on multiple software platforms and hardware architectures. At this time of writing (April 2012), the receiver enjoys of a 2-dimensional Distance Root Mean Square (DRMS) error lower than 2 meters for a GPS L1 C/A scenario with 8 satellites in lock and a Horizontal Dilution Of Precision (HDOP) of 1.2.Esta tesis aborda el problema de la adquisición de la señal usando arrays de antenas en el marco general de los receptores de Sistemas Globales de Navegación por Satélite (GNSS). El término GNSS engloba aquellos sistemas de navegación basados en una constelación de satélites que emiten señales útiles para el posicionamiento. Aunque el GPS americano ya está disponible, coexistiendo con el renovado sistema ruso GLONASS, actualmente se está realizando un gran esfuerzo para que la contribución europea (Galileo), junto con el nuevo sistema chino Compass, estén operativos en breve. Por lo tanto, una gran variedad de constelaciones de satélites y señales estarán disponibles en los próximos años. Estos sistemas proporcionan las infraestructuras necesarias para una multitud de aplicaciones y servicios que demandan un servicio de posicionamiento confiable y preciso. La disponibilidad de posicionamiento se debe garantizar en todo momento, especialmente en los servicios críticos para la seguridad de las personas y los bienes. Cuando examinamos las amenazas de la disponibilidad del servicio que ofrecen los GNSSs, es importante tener en cuenta que todos los sistemas presentes y los sistemas futuros ya planificados hacen uso de técnicas de multiplexación por división de código (CDMA). Las señales transmitidas por los satélites son recibidas con una relación señal-ruido (SNR) muy baja, medida antes de la correlación (del orden de -22 dB para un receptor ubicado en la superficie de la tierra). A pesar de que la ganancia de procesado CDMA ofrece una protección inherente contra las interferencias de radiofrecuencia (RFI), esta protección es limitada. Una interferencia con una relación de potencia de interferencia a potencia de la señal que excede la ganancia de procesado puede degradar el rendimiento de los receptores o incluso negar por completo el servicio GNSS. Este riesgo es especialmente importante en receptores convencionales equipados con un nivel mínimo o básico de protección frente las RFIs. Como consecuencia, las RFIs (ya sean intencionadas o no intencionadas), se identifican como la causa más importante de la degradación del rendimiento en GNSS. El problema esta causando una preocupación creciente en los últimos tiempos, ya que cada vez hay más servicios que dependen de los GNSSs Si centramos la atención en el receptor GNSS, es conocido que la adquisición de la señal tiene la menor sensibilidad de todas las operaciones del receptor, y, en consecuencia, se convierte en el factor limitador en la presencia de señales interferentes. Un receptor de una sola antena puede hacer uso de la diversidad en tiempo y frecuencia para mitigar las interferencias, aunque el rendimiento de estas técnicas se ve comprometido en escenarios con baja SNR o en presencia de interferencias de banda ancha. Por otro lado, los receptores basados en múltiples antenas se pueden beneficiar del procesado espacial, y por lo tanto mitigar los efectos de las señales interferentes. La diversidad espacial se ha aplicado tradicionalmente a la operación de tracking de la señal en receptores GNSS. Sin embargo, las condiciones iniciales del tracking dependen del resultado de la adquisición de la señal, y como hemos visto antes, hay un número de situaciones en las que el proceso de adquisición puede fallar. En base a nuestro grado de conocimiento, la aplicación de los arrays de antenas a la adquisición de la señal GNSS no ha recibido mucha atención, sorprendentemente. El objetivo de esta tesis doctoral es doble: por un lado, proponer nuevos algoritmos para la adquisición basados en arrays de antenas, usando como marco la teoría de la detección de señal estadística, y por otro lado, demostrar la viabilidad de su implementación y ejecución en tiempo real, así como su medir su rendimiento en escenarios realistas. La tesis comienza con una breve introducción a los fundamentos de los receptores GNSS, proporcionando algunos detalles sobre la estructura de las señales de navegación y la arquitectura del receptor aplicada a los sistemas GPS y Galileo. Continua con el análisis de la adquisición GNSS como un problema de detección, aplicando la teoría del detector Neyman-Pearson (NP) y el modelo de señal de una única antena. El marco teórico del detector NP se utiliza aquí para derivar tanto el detector óptimo (conocido como detector clarividente) como la denominada Prueba Generalizada de la Razón de Verosimilitud (en inglés, Generalized Likelihood Ratio Test (GLRT)), que forma la base de prácticamente todos los algoritmos de adquisición del estado del arte actual. Yendo más lejos, proponemos un nuevo detector diseñado para adquirir simultáneamente un conjunto de satélites, por lo tanto, obtiene una reducción del tiempo de adquisición y de los recursos computacionales necesarios en el proceso, respecto a las técnicas convencionales. El efecto del ancho de banda del receptor también se ha tenido en cuenta en los análisis. A continuación, el detector GLRT se extiende al modelo de señal de array de antenas para obtener un detector nuevo que es capaz de mitigar interferencias no correladas temporalmente, incluso utilizando arrays no estructurados y moderadamente descalibrados, convirtiéndose así en una de las principales aportaciones de esta tesis. La clave del detector es asumir una matriz de covarianza de ruido arbitraria y desconocida en el modelo de señal, que trata de captar el comportamiento estadístico de las interferencias y otras señales no deseadas, mientras que utiliza la dimensión espacial proporcionada por los arrays de antenas. Se han derivado las expresiones que modelan las probabilidades teóricas de detección y falsa alarma. El rendimiento del detector y su capacidad de rechazo a interferencias se han modelado y comparado con su límite teórico. El algoritmo propuesto también ha sido comparado con técnicas de adquisición convencionales, ejecutadas utilizando la salida de conformadores de haz que utilizan algoritmos de filtrado de interferencias, como el algoritmo de minimización de la potencia. Además, el detector se ha analizado bajo condiciones realistas, representadas con la presencia de errores en la estimación de covarianzas, errores residuales en la estimación del Doppler y el retardo de señal, y los efectos de la cuantificación. Los resultados teóricos se apoyan en simulaciones de Monte Carlo. Como otra contribución principal de esta tesis, la segunda parte del trabajo trata sobre el diseño y la implementación de una nueva plataforma para receptores GNSS en tiempo real basados en array de antenas que utiliza la tecnología de matriz programable de puertas lógicas (en ingles Field Programmable Gate Array (FPGA)). La plataforma está destinada a ser utilizada como una herramienta de investigación estrechamente acoplada con receptores GNSS definidos por software. Se ha diseñado, implementado y verificado la cadena completa de recepción, incluyendo el array de antenas y el front-end multi-canal para las señales GPS L1 y Galileo E1. El documento explica en detalle el procesado de señal que se realiza, como por ejemplo, la implementación del módulo de extracción de estadísticas de la señal. Los compromisos de diseño y las complejidades derivadas han sido cuidadosamente analizadas y tenidas en cuenta. La plataforma ha sido utilizada como prueba de concepto para solucionar el problema presentado de la vulnerabilidad del GNSS a las interferencias. Los algoritmos de adquisición introducidos en esta tesis se han implementado y probado en condiciones realistas. El rendimiento de los algoritmos se comparó con las técnicas de adquisición basadas en una sola antena. Se han realizado pruebas en escenarios que contienen interferencias dentro de la banda GNSS, incluyendo interferencias de banda estrecha y banda ancha y señales de comunicación. La plataforma fue diseñada para demostrar la viabilidad de la implementación de nuevos algoritmos de adquisición basados en array de antenas, dejando el resto de las operaciones del receptor (principalmente, los módulos de tracking, decodificación del mensaje de navegación, los observables de código y fase, y la solución básica de Posición, Velocidad y Tiempo (PVT)) a un receptor basado en el concepto de Radio Definida por Software (SDR), el cual se ejecuta en un ordenador personal. El receptor procesa en tiempo real las muestras de la señal filltradas espacialmente, transmitidas usando el bus de datos Gigabit Ethernet. En la última parte de esta Tesis, cerramos ciclo diseñando e implementando completamente este receptor basado en software. El receptor propuesto está dirigido a las arquitecturas de multi-constalación GNSS y multi-frecuencia, persiguiendo los objetivos de eficiencia, modularidad, interoperabilidad y flexibilidad demandada por los usuarios que requieren características no estándar, tales como la extracción de señales intermedias o de datos y intercambio de algoritmos. En este contexto, se presenta un receptor de código abierto que puede trabajar en tiempo real, llamado GNSS-SDR, que contribuye con varias características nuevas. Entre ellas destacan el uso de patrones de diseño de software y técnicas de memoria compartida para administrar de manera eficiente el uso de datos entre los bloques del receptor, el uso de la aceleración por hardware para las operaciones vectoriales más costosas, como la eliminación de la frecuencia Doppler y la correlación de código, y la disponibilidad para compilar y ejecutar el receptor en múltiples plataformas de software y arquitecturas de hardware. A fecha de la escritura de esta Tesis (abril de 2012), el receptor obtiene un rendimiento basado en la medida de la raíz cuadrada del error cuadrático medio en la distancia bidimensional (en inglés, 2-dimensional Distance Root Mean Square (DRMS) error) menor de 2 metros para un escenario GPS L1 C/A con 8 satélites visibles y una dilución de la precisión horizontal (en inglés, Horizontal Dilution Of Precision (HDOP)) de 1.2