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Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es Proyecto Fin de Carrera Investigation of Variety of Non-Coherent Front end Detectors for Timing Estimation Autor Luis Lacasa Calvo Director/Supervisor Satyam Dwivedi Ponente Enrique Masgrau Gómez Escuela de Ingeniería y Arquitectura 2013 asdfaas 1 Investigation of Variety of Non-Coherent Front End Detectors For Timing Estimation Resumen La localización en interiores de usuarios móviles es actualmente un tema central para muchas aplicaciones y campos, incluidas las redes de sensores, gestión de activos, asistencia sanitaria y localización de personal de seguridad pública. Las soluciones existentes se basan a menudo en la fusión de la información de múltiples sensores. La posibilidad de utilizar un sistema de banda ultra ancha (UWB) para la medición inalámbrica de distancias basada en el tiempo de ida y vuelta (RTT) se ha investigado en este proyecto final de carrera. Los receptores UWB no coherentes se han analizado utilizando dos enfoques diferentes: la detección de la amplitud y la detección de la energía. Para el análisis, se desarrolla un estudio teórico y también se han realizado diversas simulaciones. Además, ambos receptores UWB no coherentes han sido diseñados e implementados. Por otra parte, un método ha sido propuesto para permitir la reconstrucción de un pulso UWB a partir del submuestreo de una ráfaga de pulsos UWB y tratar de aproximar el rendimiento óptimo del receptor UWB ideal. Las simulaciones producen resultados interesantes en cuanto al rendimiento de la estimación de RTT. Ambas técnicas de detección se comparan, describiendo las ventajas y desventajas de cada uno. 1 Tabla de Contenidos Tabla de Contenidos 2 1 Introducción 5 1.1. Contexto .............................. 6 1.2. Motivación y Trabajo Previo . . . . . . . . . . . . . . . . . . . 6 1.3. Planteamiento del Problema . . . . . . . . . . . . . . . . . . . . 7 1.3.1. Tipos de receptores UWB no coherentes . . . . . . . . . 7 1.3.2. Objetivo principal de este PFC . . . . . . . . . . . . . . 8 1.4. Organización de la Memoria . . . . . . . . . . . . . . . . . . . . 8 2 Señales UWB y Receptor Ideal 9 2.1. Formas de Pulsos UWB . . . . . . . . . . . . . . . . . . . . . . 9 2.2. Receptor UWB Ideal . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Receptores UWB no coherentes 13 3.1. Arquitectura del los receptores no coherentes . . . . . . . . . . 13 3.2. Procedimiento de medida de la distancia . . . . . . . . . . . . . 14 3.3. AnálisisTeórico........................... 15 3.4. Selección del Umbral . . . . . . . . . . . . . . . . . . . . . . . . 17 4 Diseño Frontal de receptores UWB no coherentes 19 4.1. Arquitectura del sensor . . . . . . . . . . . . . . . . . . . . . . 19 4.2. Hardware: Selección de los componentes . . . . . . . . . . . . . 21 4.3. Implementación........................... 23 5 Resultados de las Simulaciones 27 6 Estimación de distancia con UWB y submuestreo 31 6.1. Principio de funcionamiento . . . . . . . . . . . . . . . . . . . . 31 7 Conclusiones 35 7.1. Discusión .............................. 35 7.1.1. Detección de amplitud . . . . . . . . . . . . . . . . . . . 35 7.1.2. Detección de energía . . . . . . . . . . . . . . . . . . . . 36 7.1.3. Formas de onda de pulsos UWB . . . . . . . . . . . . . 36 2 TABLA DE CONTENIDOS 3 7.1.4. Detección de amplitud vs detección de energía . . . . . 36 7.1.5. Diseño de los receptores . . . . . . . . . . . . . . . . . . 36 7.1.6. Receptor UWB con submuestreo . . . . . . . . . . . . . 37 7.2. Trabajofuturo ........................... 37 Bibliografía 39 Apéndices 41 A Documento Original del Proyecto Fin de Carrera 41 Capítulo 1 Introducción En este Proyecto Final de Carrera se ha investigado el uso de sensores de banda ultra-ancha (UWB) para localización en interiores, basándose en la medida del tiempo de ida y vuelta (RTT) de pulsos UWB. Se analizan dos tipos diferentes de receptores no coherentes (detección de amplitud y detección de energía), para así averiguar las ventajas e inconvenientes de cada uno. Además, el receptor UWB ideal también es analizado para ser comparado con los receptores no coherentes. Los resultados que se presentan en esta memoria, podrían ser de gran ayuda en la implementación de sensores UWB para medida de distancias. Esta memoria ofrece tanto análisis teórico como los resultados de las simulaciones llevadas a cabo durante el trabajo correspondiente a este PFC. Dichos resultados revelan características interesantes acerca del funcionamiento de los receptores UWB no coherentes. El principal objetivo es averiguar cuál de los receptores no coherentes estudiados presenta mejor rendimiento en determinadas situaciones. Además, distintas formas de los pulsos UWB son consideradas en el análisis. En este PFC se han diseñado e implementado también los dos tipos de receptores mencionados anteriormente. Uno de los capítulos está orientado a la descripción de estos diseños. Los diseños están basados en una implementación anterior realizada en el laboratorio de procesado de señal de la universidad KTH de Estocolmo, la cual se detalla en [1]. Un método que trata de aproximar el rendimiento del receptor ideal se ha propuesto en este PFC. Se trata de reconstruir un pulso UWB usando submuestreo sobre un tren de pulsos. Este método no se ha diseñado ni simulado, simplemente es una idea que pudiera ser usada en futuras investigaciones. 5 6CAPÍTULO 1. INTRODUCCIÓN 1.1. Contexto Este Proyecto Fin de Carrera ha sido realizado durante estudios de intercambio en la universidad KTH (Kungliga Tekniska Högskolan) de Estocolmo, Suecia; específicamente en el Laboratorio de Procesado de Señal de la EES (Electrical Engineering School). En dicho laboratorio, se implementó anteriormente a este trabajo un sistema UWB para medida de distancias. Dicha implementación está descrita en [1]. 1.2. Motivación y Trabajo Previo La localización en interiores de usuarios móviles es actualmente un tema central para muchas aplicaciones y campos, incluidas las redes de sensores, gestión de activos, la asistencia sanitaria, y localización de personal de seguridad pública [2]. Existen soluciones basadas el uso de múltiples sensores. En particular, algunos de los tipos de sensores más utilizados son los sistemas de navegación inercial [3], sistemas de imagen como cámaras o sensores infrarrojos [4], y tecnologías de posicionamiento basados en las radiocomunicaciones. La medición de la posición de los usuarios con precisión y fiabilidad es de particular relevancia en escenarios de localización de organismos de respuesta inmediata (bomberos, paramédicos, etc.), donde el conocimiento de la ubicación en entornos de sistemas globales de navegación por satélite (GNSS) es una herramienta importante para la eficiencia y la seguridad [5]. En dichos escenarios, las soluciones se suelen basar en técnicas cooperativas y oportunistas, ya que el sistema proporcionado debe ser operativo incluso en la ausencia de una infraestructura de localización preinstalada. Para investigar experimentalmente la medición de distancia y posición en interiores por medio de radiocomunicaciones, numerosos métodos han sido propuestos en la literatura. Sistemas como el descrito en [6] se implementan utilizando sistemas de comunicación inalámbrica de corto alcance. Además, para aplicaciones en las que no son estrictamente necesarias medidas muy precisas, es posible utilizar detectores de proximidad, tal como la técnica de detección de proximidad casi omnidireccional, basada en ZigBee descrita en [7]. En este contexto, los sistemas de banda ultra ancha (UWB) son objeto de considerable interés en la investigación, debido principalmente a su alta resolución y al bajo consumo de energía [8]. En particular, [9] propuso un nuevo nodo híbrido inalámbrico basado en el estándar radio tradicional IEEE802.15.4 con el apoyo de un transceptor UWB para la medida precisa de tiempo. Típicamente, una motivación de la utilización del sistema UWB en un sistema de localización multisensor es prevenir el crecimiento del error inherente a los sistemas de navegación inercial, porque el error en las estimaciones de distancia con UWB está limitado [10]. 1.3. PLANTEAMIENTO DEL PROBLEMA 7 1.3. Planteamiento del Problema Varios estudios han analizado la estimación del tiempo de llegada (TOA) usando sistemas UWB y muestreo, por ejemplo [11, 12]. Tales métodos requieren sincronización, y además, el extremadamente amplio ancho de banda de los pulsos UWB hace muy complejo el muestreo utilizando la frecuencia de muestreo de Nyquist. Por lo tanto, en este PFC se investigan los receptores UWB no coherentes. El RTT se utiliza para la medición de la distancia en lugar del TOA, por lo tanto no se necesita sincronización entre sensores. El desarrollo del sensor descrito en esta tesis sigue un enfoque novedoso que combina varios aspectos clave: Medida de distancia basada en tiempo de ida y vuelta Énfasis en las capacidades del procesado digital de señal Funcionamiento asíncrono Alta tasa de actualización de la medición Diseño basado en conversor tiempo-digital Estas características hacen que el sensor sea especialmente adecuado para la investigación experimental para aplicaciones de localización de interiores para organismos de respuesta inmediata (bomberos, paramédicos, etc.), sobre todo porque el tiempo de ida y vuelta no necesita de una infraestructura preinstalada y el TDC permite lograr alta precisión en la medida con baja complejidad y bajo consumo. 1.3.1. Tipos de receptores UWB no coherentes En este PFC se han considerado para el estudio dos tipos de receptores UWB no coherentes: detección de energía y detección de amplitud. Detección de energía La técnica detección de energía (ED) es ampliamente estudiada en la literatura de UWB. La detección del pulso se realiza comparando la energía de la señal recibida con un umbral. Detección de amplitud En este caso, la propia amplitud se compara directamente con un umbral. La detección de amplitud no ha sido tan estudiada en la literatura, pero aunque su rendimiento es a priori peor que el de ED, es interesante su estudio y como se mostrará en las simulaciones presentadas en el capítulo 5, puede ser adecuado su uso en determinadas situaciones. 14 CAPÍTULO 3. RECEPTORES UWB NO COHERENTES LNA BPF r(t) < > H0 H1 Figura 3.1: Diagrama de bloques del receptor UWB no coherente con detección de amplitud. LNA BPF r(t) < > H0 H1 (.)2 Figura 3.2: Diagrama de bloques del receptor UWB no coherente con detección de energía. Los diagramas de bloques de estos receptores no coherentes se ilustran en las Figuras 3.1 (amplitud) y 3.2 (energía). El diseño del hardware se describirá en el capítulo 4. 3.2. Procedimiento de medida de la distancia El objetivo es estimar el tiempo de ida y vuelta (RTT) de un pulso UWB que se propaga entre dos sensores; denominados como maestro y esclavo. El maestro es el que realmente mide la distancia y controla el procedimiento de la medida, mientras que el esclavo se encuentra en modo de espera hasta que detecta la llegada de un pulso, y entonces le responde al maestro con otro pulso. Los dos sensores están diseñados con el mismo receptor no coherente. La distancia se mide repetidamente con una tasa de actualización denotada por Rf. En este contexto, una tasa de actualización de la medida de al menos 100 Hz es deseable para un seguimiento de la distancia con alto y preciso rango dinámico. El inverso de Rfse denota como Tfy representa la duración de una trama. En este documento una trama se define como el intervalo de tiempo en el cual el maestro realiza una medición de distancia. De esta forma, el procedimiento de medida se repite en cada trama y sigue los siguientes pasos: 1. El maestro inicia el procedimiento de medida mediante la transmisión de un pulso UWB. Se transmite un pulso al comienzo de cada trama. 2. Cuando el esclavo detecta el pulso, éste responde al maestro tras una latencia fijada (Tw) enviando otro pulso. 3.3. ANÁLISIS TEÓRICO 15 3. El maestro detecta la respuesta del esclavo y mide el RTT ( ˆ TRT T ) para estimar la distancia. El proceso descrito anteriormente se utiliza tanto con detección de amplitud como con detección de energía; únicamente la técnica de detección de los pulsos cambia. Podría pasar que el maestro no detecta ningún pulso en una trama, por lo que no sería posible realizar la estimación en dicha trama. La probabilidad de detección se define como la probabilidad de que la anterior situación no se produzca. Si denotamos tal probabilidad de detección con PT D, entonces la tasa efectiva de actualización de la medida sería Reff f=PT DRf. Idealmente, el RTT estimado sería ˆ TRT T = 2Tp+Tw, donde Tpes el tiempo de propagación del pulso, que se relaciona con la distancia como Tp=c d, siendo d la distancia y cla velocidad de la luz. Por lo tanto, la distancia es estimada a partir del RTT como ˆ d=cˆ TRT T −Tw 2(3.1) La expresión anterior es válida si la medida es no sesgada, es decir, si la media del error es nula. En caso contrario se debería realizar un proceso de calibración, tal y como se describe en [1]. El proceso de medición mediante el RTT se ilustra gráficamente en la Figura 3.3. Cabe destacar que la tasa de actualización de la medida está directamente relacionada con la máxima distancia que puede ser medida, tal y como se muestra en las siguientes expresiones Tmax RT T =Tf−Tb Tmax p=Tmax RT T −Tw 2 dmax =c·Tmax p (3.2) Para una descripción más detallada, véase esta misma sección en el documento original (Apéndice A). 3.3. Análisis Teórico Esta sección presenta un análisis teórico más elaborado del proceso de medida del tiempo de ida y vuelta de los pulsos UWB. Se analiza primero el proceso de medida del RTT de forma genérica, para luego detallar el análisis para cada una de las dos técnicas de detección estudiadas. Se analizan factores como la probabilidad de detección y la distribución estadística del error de estimación del RTT. Dicho análisis junto con las correspondientes expresiones matemáticas no se muestran en esta versión de la memoria, pero pueden encontrarse en esta misma sección del documento original (Apéndice A). 16 CAPÍTULO 3. RECEPTORES UWB NO COHERENTES iTf (i+1)Tf (i-1)Tf Tw TRTT(i-1) (correct) TRTT(i) (incorrect) Tp Trs(i-1), Tds(i-1) (correct detection) Tts(i-1) Trm(i-1) Tds(i) (wrong detection) Tts(i) Trs(i) Trm(i) Master Slave Figure 3.3: Diagrama temporal del proceso de estimación del RTT. Se muestran dos mediciones (tramas). En la trama (i-1) el pulso es detectado correctamente en el esclavo. Por otro lado, en la trama i el esclavo detecta el pulso cuando todavía no está presente, debido al efecto del ruido, y por lo tanto la estimación del RTT es errónea. 3.4. SELECCIÓN DEL UMBRAL 17 3.4. Selección del Umbral Dado que esta sección esta muy relacionada con la anterior, se recomienda consultar este capítulo en la versión original del Apéndice A para entender mejor las expresiones que se muestran a continuación. Existen dos opciones para calcular el umbral de detección. Una es fijar la probabilidad de detección que se desea para una cierta SNR, para lo cual se usan las aproximaciones teóricas de la probabilidad de detección que se muestran en la versión original del Apéndice A. Sería aconsejable establecer un margen de protección, es decir, si se espera tener un cierto valor de SNR, calcular el umbral con una SNR menor. La otra alternativa, es fijar una cierta probabilidad de falsa alarma “instantánea”1, la cual se denota por pd. En este caso sólo es necesario conocer la potencia de ruido. Las expresiones para esta alternativa se muestran a continuación para detección de amplitud y detección de energía. Detección de amplitud γA=σQ−1pA d(3.3) donde Q−1(·)es la función inversa del complemento de la función de distribución de la normal estándar. La potencia de ruido es σ2. Detección de energía γE=N0 2Q−1 χ2 2TIBpE d(3.4) siendo Q−1 χ2 ν(·)la función inversa del complemento de la función de distribución de una distribución chi-cuadrado con νgrados de libertad. N0representa la distribución espectral de potencia del ruido. 1Ya que el sistema es analógico, se habla de probabilidad de falsa alarma “instantánea”, es decir, la probabilidad de que la señal de ruido (sin presencia de pulso) supere el umbral en un instante de tiempo. Capítulo 4 Diseño Frontal de receptores UWB no coherentes Este capítulo describe el diseño frontal de los receptores no coherentes realizados durante este PFC. La arquitectura del sensor está basada en el diseño previo descrito en [1]. En este PFC, el diseño se ha centrado la parte del receptor. Dos diseños diferentes se han llevado a cabo, uno para detección de amplitud y otro para detección de energía, implementándose dos placas de cada diseño, ya que tanto el maestro como el esclavo utilizan el mismo diseño. El diseño de las placas se ha realizado utilizando el software Eagle. 4.1. Arquitectura del sensor La arquitectura del sensor se muestra en la Figura 4.1. Se compone de una sección analógica UWB de medida y una sección de procesamiento digital, basada en una FPGA. Conceptualmente, el interfaz entre la sección analógica UWB y la sección de procesamiento digital es proporcionada por medio de un conversor tiempo-digital (TDC), que proporciona medidas del RTT con una resolución de 65 ps. Además, un conversor digital-analógico (DAC) de 12 bits es usado para fijar el umbral para la detección en la sección del receptor UWB. Dicho DAC es programado por la FPGA. Lo único que cambia en los dos diseños (detección de amplitud y detección de energía) es el transceptor UWB. Dicho transceptor se ilustra en el diagrama de bloques de la Figura 4.2. En el caso de detección de amplitud se utiliza simplemente un comparador (véase la Figura 3.1), mientras que en el caso de detección de energía se utiliza un detector de energía (ED), el cual incluye un dispositivo cuadrático, un integrador y un comparador (véase la Figura 3.2). Además el diseño incluye dos amplificadores de bajo ruido (LNA) que no se incluye en la Figura 4.2. 19 20 CAPÍTULO 4. DISEÑO FRONTAL DE RECEPTORES UWB NO COHERENTES FPGA (digital control and processing) DAC TDC UWB Transceiver THRESHOLD STOP START SPI SPI CONTROL UWB measurement section Figura 4.1: Diagrama simplificado de la arquitectura del sensor UWB. La sección analógica UWB se conecta a la FPGA mediante conexiones de interfaz de periférico serie (SPI) al TDC y al DAC para su configuración. La conexión entre el TDC y la FPGA también se usa para leer las mediciones de RTT. La FPGA controla el transceptor directamente con señales digitales de control. La sección de procesamiento digital permite controlar los parámetros temporales y operacionales del sensor. En particular, tal y como se muestra en la Figura 4.1, la sección de medición requiere varias señales digitales de control. Las funciones de la sección digital se enumeran a continuación: Controlar el transmisor UWB: La medición se inicia cuando el maestro pregunta al esclavo mediante la transmisión de un pulso UWB. La señal de disparo del transmisor se genera digitalmente. Es posible ajustar dinámicamente la duración de trama, Tf(tasa de actualización de la medida). Configurar y controlar el TDC: El TDC se configura para realizar la medición. La medida en el TDC se inicia cuando el pulso es transmitido. El TDC se comunica a través de un interfaz SPI. Controlar el switch: El switch que selecciona la transmisión o recepción se controla digitalmente. 4.2. HARDWARE: SELECCIÓN DE LOS COMPONENTES 21 Tabla 4.1: Lista de Componentes Componente Referencia y proveedor TDC TDC-GP2, Acam Messelectronic DAC ADC5620, Analog Devices Diodo generador de pulsos 5082-0112, HP Switch RSW-2-25P, Mini Circuits LNA MBC13720, Freescale Semiconductor Comparador LT1720, Linear Technology Detector de energía (ED) LTC5536, Linear Technology Configurar el DAC para el umbral de detección: El valor del umbral para detectar el pulso a la salida del comparador/ED es fijado digitalmente. Se puede fijar a priori o se puede calcular adaptativamente dependiendo de la probabilidad de falsa alarma requerida. Estimación de la distancia: Una vez que el maestro recibe la respuesta del esclavo, se calcula la distancia a partir de la lectura del RTT del TDC. La FPGA proporciona flexibilidad en el desarrollo, implementación y ajustes de los algoritmos. El modelo de FPGA usado es el ML505 Virtex-5. La FPGA proporciona un control reconfigurable del sensor UWB. 4.2. Hardware: Selección de los componentes La sección UWB de medición se ha implementado con una placa de circuito impreso en sustrato FR4 con una grosor de 1.0 mm. En este PFC, el esfuerzo en el diseño de los sensores se ha centrado en la parte del receptor, especialmente en la selección del LNA, comparador y ED. En un principio se realizó una búsqueda de componentes adecuados para este diseño y fueron priorizados teniendo en cuenta distintas características en función de las necesidades. Por ejemplo, en el caso del LNA, se tuvo en cuenta el ancho de banda de operación, la figura de ruido, la ganancia y el consumo de corriente. Una descripción detallada del proceso de selección de los componentes se encuentra en la correspondiente sección de la versión original (apéndice A). La Tabla 4.1 muestra los componentes que han sido utilizados en el diseño final de los sensores UWB. 22 CAPÍTULO 4. DISEÑO FRONTAL DE RECEPTORES UWB NO COHERENTES ED/ Comparator Pulse generator (step-recovery diode) RX/TX switch UWB Transceiver WIDEBAND DICONE ANTENNA STOP THRESHOLD CONTROL START Figura 4.2: Arquitectura del transceptor UWB. El generador de pulsos está realizado usando un diodo de recuperación escalonada basado en el circuito caracterizado en [16] y se controla mediante la señal “start” de la FPGA. La salida del detector de energía/comparador proporciona la señal “stop” que controla la medición del TDC. El switch selecciona la posición RX o TX mediante una señal digital proporcionada por la FPGA. Para la transmisión y recepción de los pulsos UWB se utiliza una antena discono omnidireccional de banda ancha. 4.3. IMPLEMENTACIÓN 23 Figura 4.3: Esquemático del receptor no coherente utilizando detección de amplitud. 4.3. Implementación En el diseño final, se conectaron dos amplificadores LNA en cascada, para así incrementar la sensibilidad del detector. Los esquemáticos de los transceptores a partir de los cuales se realizaron los circuitos impresos se muestran en las Figuras 4.3 (detección de amplitud) y 4.4 (detección de energía). El esquemático para detección de amplitud es igual al de detección de energía, pero reemplazando el ED por un comparador. Además en las Figuras 4.5 (detección de amplitud) y 4.6 (detección de energía) se muestran fotografías de placas implementadas. Capítulo 6 Estimación de distancia con UWB y submuestreo Este capítulo presenta el método propuesto que permite reconstruir un pulso UWB a partir de un tren de pulsos utilizando submuestreo. El objetivo es intentar aproximar el rendimiento del receptor ideal, sin la complejidad impuesta por la alta tasa de muestreo necesaria. 6.1. Principio de funcionamiento Este método probablemente sea más adecuado para medir tiempos de llegada (TOA) que para tiempos de ida y vuelta (RTT), ya que el submuestreo sólo puede ser utilizado en uno de los sensores. De forma que para medir RTTs, en el esclavo habría que utilizar detección no coherente. De esta manera, se mejoraría la precisión del receptor no coherente, pero no se podría lograr el mismo rendimiento que con el receptor ideal. Si fuese posible la sincronización de los sensores, podrían medirse TOAs, evitando la necesidad de utilizar detección no coherente. A continuación se describe el funcionamiento utilizando medidas de RTTs. La señal recibida por el maestro sería un tren de pulsos rm(t) = Np−1 X i=0 pEbp(t−iTd−TRT T ) + n(t)(6.1) siendo Tdel retraso entre pulsos consecutivos y Npel número total de pulsos transmitidos por el esclavo. El retraso entre pulsos se fija como Td=ts−Tb/Ns(6.2) donde tses el tiempo entre muestras y Nses el número de muestras que se requieren en el pulso reconstruido, es decir, la resolución del pulso sería Tb Ns, 31 32 CAPÍTULO 6. ESTIMACIÓN DE DISTANCIA CON UWB Y SUBMUESTREO siendo Tbla duración del pulso. Dicha resolución es precisamente la diferencia que existe entre el tiempo de muestreo y el retraso entre pulsos, lo que permite la reconstrucción del pulso submuestreando el tren de pulsos. Para asegurar la reconstrucción del pulso, el número de pulsos transmitidos debe ser Np=(Tmax RT T +Tb)Ns Tb + 1 (6.3) siendo Tmax RT T el máximo RTT que se desea medir. En la Figura 6.1 se muestra un ejemplo sencillo de cómo se reconstruye el pulso a partir del tren de pulsos mediante el submuestreo. La Figura 6.2 muestra en un diagrama temporal el proceso de transmisión de los pulsos. Hay un compromiso entre el rango de medición (Tmax RT T =ts−Tb) y la tasa de actualización de la medida, siendo la duración de una medición (trama) Tf=ts·Np(6.4) Así, que para mantener el mismo rango de medida que en el receptor ideal (o no coherente), la tasa de actualización de la medida se debe reducir. El consumo de potencia para transmitir todos los pulsos es (Np+1)Eb Tf, bastante mayor que con el detector no coherente con la misma tasa de actualización. Básicamente, la señal recibida muestreada es la forma de pulso original, con un retraso que depende precisamente del RTT. Dicha señal recibida puede expresarse como rm[n] = pEbpnTb Ns−nk+v[n]; n= 0. . . Np−1(6.5) El retraso, nk, está relacionado con el RTT de la siguiente forma nk=TRT T Ns Tb (6.6) Una vez que el pulso es reconstruido, éste se detecta de la misma forma que en el detector ideal, es decir, calculando la correlación con una máscara del pulso original, obteniéndose así una estimación ˆnk. El RTT se calcula sencillamente despejando de 6.6: ˆ TRT T =ˆnkTb Ns (6.7) 6.1. PRINCIPIO DE FUNCIONAMIENTO 33 0 0.5 1 1.5 2 2.5 x 10−7 −0.5 0 0.5 1 Burst of pulses Sampling over the burst (a) TRT T = 0 ns 0 0.5 1 1.5 2 2.5 x 10−7 −0.5 0 0.5 1 Burst of pulses Sampling over the burst (b) TRT T = 4 ns Figura 6.1: Ejemplo sencillo de cómo el submuestreo del tren de pulsos permite reconstruir el pulso original. El pulso usado es el monociclo de Scholtz. La duración de pulso, tasa de muestreo, y número de muestras del pulso reconstruido toman los siguientes valores: Tb= 1 ns,ts= 5ns,Ns= 10. (a) TRT T = 0ns, (b) TRT T = 4ns. 34 CAPÍTULO 6. ESTIMACIÓN DE DISTANCIA CON UWB Y SUBMUESTREO Master Slave ts TpTw Twexpected RTT region first pulse actual RTT 02ts Td second pulse ... ... k-th pulse (k-1)ts t t Figura 6.2: Diagrama temporal del proceso de medida del RTT usando submuestreo sobre un tren de pulsos. Capítulo 7 Conclusiones A continuación se resumen brevemente en una lista las conclusiones que se extraen de este PFC. Los receptores UWB no cohrentes parecen ser adecuados para la medida de distancias basándose en tiempos de ida y vuelta. El rendimiento es peor que el del receptor ideal, pero la pérdida no es grande y se gana simplicidad. La detección de energía parece presentar mejor precisión, a costa de requerir mayor SNR para funcionar correctamente. La detección de amplitud puede ser útil en lugares donde no es posible conseguir una SNR alta. Sin embargo, para distancias y/o latencias del esclavo largar, la precisión puede empeorar considerablemente. Es deseable que la latencia del esclavo sea lo más corta posible para así reducir la tasa de falsa alarma y por lo tanto, mejorar la precisión; especialmente para detección de amplitud ya que la precisión se ve más afectada que para detección de energía. El receptor propuesto que se basa en el submuestreo podría mejorar el rendimiento de los receptores no coherentes, a costa de mayor complejidad del diseño. La tasa de muestreo debe ser muy precisa. En estos momentos, parece difícil implementar este método, pero podría ser usado como punto de partida en futuras investigaciones. 7.1. Discusión 7.1.1. Detección de amplitud El receptor UWB no coherente usando detección de amplitud es muy simple, sólo se necesita comparar la amplitud de la señal recibida con un umbral tras el 35 36 CAPÍTULO 7. CONCLUSIONES filtrado y la amplificación. La principal ventaja es la baja SNR que se necesita para alcanzar altas probabilidades de detección. Por otro lado, los RTTs largos empeoran considerablemente la precisión debido a las falsas alarmas. Por lo tanto, para bajas SNR y si la latencia del esclavo no es demasiado larga, puede ser una buena opción. 7.1.2. Detección de energía El receptor no coherente usando detección de energía es más robusto frente a falsas alarmar para RTTs largos. Necesita de una mayor SNR para alcanzar alta probabilidad de detección. La tasa de falsa alarma es menor debido a la integración que se realiza al calcular la energía, lo que es equivalente a que el ruido es promediado. 7.1.3. Formas de onda de pulsos UWB La principal diferencia entre los distintos pulsos es el rendimiento de detección, principalmente para detección de amplitud. Para detección de energía la diferencia entre los distintos pulsos es despreciable, mientras que en detección de amplitud el monociclo de Scholtz presenta el mejor comportamiento, por lo que en cuanto a probabilidad de detección es la mejor opción. 7.1.4. Detección de amplitud vs detección de energía El diseño de ambos receptores es muy similar, únicamente hay que intercambiar un componente. Por lo tanto, en cuanto complejidad de diseño, no hay ninguna ventaja en escoger uno u otro. Para RTTs cortos, la detección de amplitud parece presentar una mejor precisión (si se escogiese el umbral óptimo) que la detección de energía. Sin embargo, dado que la precisión en el caso de detección de amplitud se ve afectada en mayor medida conforme los tiempos de ida y vuelta aumentan, la detección de energía ofrecería una mejor precisión para RTTs más largos. Ya que en la práctica la latencia del esclavo suele ser muy larga comparada con el tiempo de propagación del pulso, la detección de energía es la mejor opción en general. La detección de amplitud podría ser más robusta en entornos hostiles donde la SNR suele empeorar, ya que la curva de detección es más suave con la detección de amplitud. 7.1.5. Diseño de los receptores El diseño que se proporciona en este PFC es flexible y de baja complejidad. Ambas técnicas de detección se han implementado. Debido a la falta de tiempo, no ha sido posible realizar experimentos con las placas implementadas para su comparación con las simulaciones. 7.2. TRABAJO FUTURO 37 7.1.6. Receptor UWB con submuestreo El método propuesto para reconstruir un pulso a partir de una ráfaga de pulsos mediante submuestreo es una idea que podría ser usada en el futuro. En estos momentos, parece complicada su implementación ya que requiere alta precisión de la tasa de muestreo y retraso de los pulsos. 7.2. Trabajo futuro Las simulaciones realizadas en este PFC son válidas y pueden ser útiles para extraer conclusiones. Sin embargo, probablemente no coincidiría con los resultados de las simulaciones. La razón es que la latencia del esclavo en la práctica es muy larga. En estas simulaciones dicha latencia se ha considerado cero o muy corta porque sino el tiempo de ejecución de las simulaciones se vería incrementado en gran medida. Una posible continuación de este trabajo sería realizar simulaciones similares, pero con valores más reales de la latencia del esclavo. Además, como se ha mencionado antes, no ha sido posible llevar a cabo experimentos debido a la restricción del tiempo y a que los último tres meses he trabajado desde España. De esta forma, el siguiente paso sería realizar experimentos con las placas implementadas. Otro posible trabajo podría ser el desarrollo de un algoritmo para el ajuste dinámico del umbral de detección. La probabilidad de detección deseada sería fijada, y mediante procesado de señal el umbral sería aumentado o reducido en función de la estimación de probabilidad de detección. De esta forma, se conseguiría un umbral óptimo. El receptor propuesto que utiliza submuestreo, podría ser usado en futuro como un punto de partida. El método podría ser mejorado para permitir el uso del submuestreo en ambos sensores (maestro y esclavo). Se podría considerar el uso de retrasos variables de los pulsos. La naturaleza dispersiva de los canales UWB, lo cual provoca multicamino [11], no se ha considerado en este PFC. Este es un tema que debería ser tratado en futuras investigaciones en el contexto de receptores UWB no coherentes. Bibliografía [1] A. De Angelis, S. Dwivedi and P. Händel, “Characterization of a Flexible UWB Sensor for Indoor Localization”. [2] H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of Wireless Indoor Positioning Techniques and Systems,” Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, vol. 37, no. 6, pp. 1067–1080, Nov. 2007. [3] I. Skog, P. Händel, J. Nilsson, and J. Rantakokko, “Zero-velocity detection – an algorithm evaluation,” IEEE Transactions on Biomedical Engineering, vol. 57, no. 11, pp. 2657–2666, Nov. 2010. [4] D. Zachariah and M. Jansson, “Camera-aided inertial navigation using epipolar points,” in Position Location and Navigation Symposium (PLANS), 2010 IEEE/ION, May 2010, pp. 303–309. [5] J. Rantakokko, J. Rydell, P. Strömbäck, P. Händel, J. Callmer, D. Törnqvist, F. Gustafsson, M. Jobs, and M. Gruden, “Accurate and reliable soldier and first responder indoor positioning: multisensor systems and cooperative localization,” IEEE Wireless Communications, vol. 18, no. 2, pp. 10–18, Apr. 2011. [6] G. Santinelli, R. Giglietti, and A. Moschitta, “Self-calibrating indoor positioning system based on ZigBee R devices,” in IEEE Instrumentation and Measurement Technology Conference, May 2009, pp. 1205–1210. [7] D. Macii, F. Trenti, and P. Pivato, “A robust wireless proximity detection technique based on RSS and ToF measurements,” in IEEE International Workshop on Measurements and Networking Proceedings (M&N), Oct. 2011, pp. 31–36. [8] S. Gezici and H. Poor, “Position estimation via ultra-wide-band signals”, Proceedings of the IEEE, vol. 97, no. 2, pp. 386-403, 2009. [9] C. De Dominicis, A. Flammini, S. Rinaldi, E. Sisinni, A. Cazzorla, A. Moschitta, and P. Carbone, “High-precision UWB-based timestamping,” in International IEEE Symposium on Precision Clock Synchronization for Measurement Control and Communication (ISPCS), Sept. 2011, pp. 50–55. 39 Acknowledgements I would like to thank to my supervisor of the thesis, Satyam Dwivedi, for giving me the opportunity to perform my master thesis in the department of Signal Processing, in the School of Electrical Engineering of the Royal Institute of Technology in Stockholm, and for his excellent guidance and advice during all the period I have worked in this project. I also want to thank to him his flexibility and availability, allowing me to work on my own, even in being in Spain during last months. I also want to express my biggest thanks to my mother for giving me all the necessary support to perform this master thesis in Sweden, although this entailed several diculties. Table of Contents Table of Contents iv List of Figures vi List of Tables viii Nomenclature ix 1 Introduction 1 1.1 Background............................. 2 1.2 Motivation ............................. 3 1.3 Problemstatement......................... 3 1.3.1 UWB Non-Coherent Receiver Types . . . . . . . . . . . 4 1.3.1.1 Energy Detection . . . . . . . . . . . . . . . . 4 1.3.1.2 Amplitude Detection . . . . . . . . . . . . . . 4 1.4 Thesisorganization......................... 4 2 UWB Signal and Ideal Receiver 7 2.1 UWBPulseShapes......................... 7 2.1.1 Gaussianpulse ....................... 8 2.1.2 Gaussian monocycle . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Scholtz’s monocycle . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Manchester Monocycle . . . . . . . . . . . . . . . . . . . 10 2.1.5 RZ-Manchester Monocycle . . . . . . . . . . . . . . . . . 10 2.1.6 SineMonocycle....................... 10 2.1.7 Rectangle Monocycle . . . . . . . . . . . . . . . . . . . . 10 2.2 Ideal UWB Receiver . . . . . . . . . . . . . . . . . . . . . . . . 10 3 UWB Non-Coherent Receivers 13 3.1 Non-coherent receiver architecture . . . . . . . . . . . . . . . . 13 3.2 Distance measurement procedure . . . . . . . . . . . . . . . . . 14 3.3 Theoretical analysis . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3.1 Amplitude Detection . . . . . . . . . . . . . . . . . . . . 20 3.3.2 Energy Detection . . . . . . . . . . . . . . . . . . . . . . 21 3.4 Computing the threshold . . . . . . . . . . . . . . . . . . . . . 22 iv TABLE OF CONTENTS v 3.4.1 Amplitude detection . . . . . . . . . . . . . . . . . . . . 22 3.4.2 Energy detection . . . . . . . . . . . . . . . . . . . . . . 23 4 UWB Non-Coherent Receiver Front End Design 25 4.1 Sensor architecture . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Hardware: Selection of the components . . . . . . . . . . . . . 28 4.2.1 LNA............................. 29 4.2.2 Comparator......................... 30 4.2.3 ED.............................. 30 4.3 Finaldesign............................. 30 5 Simulations Results 37 5.1 Ideal UWB Receiver . . . . . . . . . . . . . . . . . . . . . . . . 39 5.2 UWB Non-Coherent Receivers . . . . . . . . . . . . . . . . . . 39 5.2.1 Detection performance: amplitude vs energy vs pulse shapes............................ 41 5.2.2 Accuracy: amplitude vs energy . . . . . . . . . . . . . . 45 5.2.3 Influence of the propagation time and slave latency . . . 47 5.2.4 Influence of the integration interval for energy detection 49 6 UWB Ranging with Undersampling Receiver 51 6.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . 51 7 Conclusions 57 7.1 Discussion.............................. 58 7.1.1 Amplitude detection approach . . . . . . . . . . . . . . 58 7.1.2 Energy detection approach . . . . . . . . . . . . . . . . 58 7.1.3 UWB Pulse shapes . . . . . . . . . . . . . . . . . . . . . 58 7.1.4 Amplitude detection vs energy detection . . . . . . . . . 58 7.1.5 UWB front end design . . . . . . . . . . . . . . . . . . . 59 7.1.6 UWB receiver with undersampling . . . . . . . . . . . . 59 7.2 Futurework............................. 59 Bibliography 61 List of Figures 2.1 ShapeWaveforms............................ 9 2.2 Block diagram of ideal UWB receiver . . . . . . . . . . . . . . . . 11 3.1 Block diagram of non-coherent UWB receiver with amplitude detection.................................. 14 3.2 Block diagram of non-coherent UWB receiver with energy detection 14 3.3 RTT estimation procedure. . . . . . . . . . . . . . . . . . . . . . . 17 4.1 Architecture of the sensor unit . . . . . . . . . . . . . . . . . . . . 26 4.2 Architecture of the UWB transceiver . . . . . . . . . . . . . . . . . 27 4.3 Schematic of the receiver with amplitude detection. . . . . . . . . . 31 4.4 Schematic of the receiver with energy detection. . . . . . . . . . . 32 4.5 Frequency response of the filter . . . . . . . . . . . . . . . . . . . . 32 4.6 Board layout for amplitude detection. . . . . . . . . . . . . . . . . 33 4.7 Board layout for energy detection. . . . . . . . . . . . . . . . . . . 33 4.8 Implemented board for amplitude detection. . . . . . . . . . . . . . 34 4.9 Implemented board for energy detection. . . . . . . . . . . . . . . . 35 5.1 Detection performance of ideal UWB receiver . . . . . . . . . . . . 40 5.2 Accuracy performance of ideal UWB receiver . . . . . . . . . . . . 40 5.3 Detection performance of amplitude detection for different pulse shapes.................................. 41 5.4 Detection performance of energy detection for different pulse shapes 42 5.5 Probability of detection: theory vs simulations . . . . . . . . . . . 43 5.6 Probability of detection: amplitude detection vs energy detection . 43 5.7 Detection performance of amplitude detection in terms of the threshold.................................... 44 5.8 Detection performance of energy detection in terms of the threshold 45 5.9 Accuracy of amplitude detection in terms of the threshold . . . . . 46 5.10 Accuracy of energy detection in terms of the threshold . . . . . . . 46 5.11 Accuracy in terms of SNR: amplitude detection vs energy detection 47 5.12 Accuracy of amplitude detection in terms of the propagation time 48 5.13 Accuracy of energy detection in terms of the propagation time . . 48 5.14 Accuracy in terms of slave latency: amplitude detection vs energy detection ................................ 49 vi List of Figures vii 5.15 Accuracy of energy detection in terms of the integration interval . 50 6.1 Example of the reconstruction of a UWB pulse using undersampling overaburstofpulses.......................... 53 6.2 Timing diagram of the RTT measurement procedure using undersampling. ................................ 54 List of Tables 2.1 Energy and bandwidth of each pulse shape . . . . . . . . . . . . . 8 4.1 Considered LNA components . . . . . . . . . . . . . . . . . . . . . 29 4.2 Partslist ................................ 30 viii Nomenclature ADC Analog-to-Digital Converter AWGN Additive White Gaussian Noise CDF Cummulative Distribution Function DAC Digital-to-Analog Converter ED Energy Detector FPGA Field Programmable Gate Array LNA Low-Noise Amplifier NF Noise Figure PDF Probability Density Function PSD Power Spectral Density RTT Round-Trip Time SNR Signal-to-Noise Ratio SPI Serial Peripherical Interface TDC Time-to-Digital Converter TOA Time Of Arrival UWB Ultra-Wide Band ix Chapter 1 Introduction In this thesis the operation of ultra wideband (UWB) ranging sensors for personnel indoor localization based on the measurement of the pulse round trip time (RTT) is investigated. Two non-coherent receiver types are analyzed in order to find out the strengths of each one. The difference between such receivers is the employed method to detect the UWB pulses: amplitude detection and energy detection. The ideal UWB receiver is also analyzed to compare it with the non-coherent receivers. The utilization of the results given in this thesis could in the future have a broader help in the implementation of UWB ranging sensors. This report gives theoretical analysis as well as the results of the simulations carried out during this master thesis work. Such results yield interesting features of the non-coherent receivers performance. The aim of this thesis has been to find out which of such non-coherent receivers works better in which situation. Different UWB pulse shapes are also considered. The designs of both non-coherent receiver front ends have also been carried out in this thesis work and there is a chapter dedicated to describe such designs. The designs are based on the previous work done in the Signal Processing Lab at KTH [1]. A new method to try to approximate the performance of the ideal receiver using undersampling is proposed in this master thesis in chapter 6. This method could be in the future a start point to reconstruct a UWB pulse by sampling a burst of pulses without needing to use the Nyquist-rate. 1 2CHAPTER 1. INTRODUCTION 1.1 Background The indoor localization of mobile users is currently a central issue for many applications and fields, including sensor networks, asset management, healthcare, ambient-assisted living, and public safety personnel localization [2]. Existing solutions often rely on the fusion of information from multiple sensors. In particular, some of the most widely used sensor types are inertial navigation systems [3], imaging systems such as cameras or infrared sensors [4], ultrasonic ranging sensors [5], and radio-based positioning technologies. Measuring the position of users accurately and reliably is of particular relevance for first responder localization scenarios, where location awareness in global navigation satellite systems (GNSS-denied) environments is an important tool for efficiency and safety [6]. The main mission-specific requirements for various types of professional users can be found in [7]. In such scenarios, solutions are often based on cooperative and opportunistic techniques, because the system provided must be operational even in the absence of a preinstalled localization infrastructure. To experimentally investigate radio-based indoor distance and position measurement, numerous methods have been proposed in the literature. Systems such as that described in [8] are implemented using off-the-shelf, short-range wireless communication systems. Furthermore, for applications in which coarse distance information may be considered sufficient and accurate positioning is not a strict requirement, proximity detectors may be used, such as the nearly omnidirectional, ZigBee-based proximity detection technique described in [9]. On the other hand, the accurate ranging prototype described in [10] is an example of a dedicated stand-alone solution. Finally, experimental proof-ofconcept demonstrators such as that presented in [11] are used to validate the algorithms developed using external electronic instrumentation. In this context, ultra wideband (UWB) systems are the object of considerable research interest due primarily to their high ranging resolution and low power operation [12]. Recently, the potential benefits for time synchronization of wireless nodes derived from the use of UWB technology have also been investigated. In particular, [13] proposed a new hybrid wireless node consisting of a traditional IEEE802.15.4 radio supported by a UWB transceiver for precise timestamping. From a regulatory viewpoint, a UWB system is defined in [14] as any intentional radiator having a fractional bandwidth greater than 20% or an absolute bandwidth greater than 500 MHz. Moreover, spectral masks defining the upper limits on emissions are provided by regulatory agencies; see, e.g., [14, 15]. Typically, a motivation of the use of a UWB ranging system in a multisensor localization system is to prevent the growth of the error inherent in inertial navigation systems, because the error in UWB ranging estimates is bounded [16]. 2.1. UWB PULSE SHAPES 9 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (ns) Amplitude Gaussian Pulse Waveform Tc=1 ns A=1 Tau=0.2 ns (a) 0 0.5 1 1.5 2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time (ns) Amplitude Gaussian Monocycle Waveform Tc=1 ns A=1 Tau=0.25 ns (b) 0 0.5 1 1.5 2 −0.5 0 0.5 1 Time (ns) Amplitude Scholtz’s Monocycle Waveform Tc=1 ns A=1 Tau=0.4 ns (c) 0 0.5 1 1.5 2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time (ns) Amplitude Manchester Monocycle Waveform A=1 Tc=1 ns (d) 0 0.5 1 1.5 2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time (ns) Amplitude RZ−Manchester Monocycle Waveform Tc=1 ns A=1 k=0.75 (e) 0 0.5 1 1.5 2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Time (ns) Amplitude Sine Monocycle Waveform Tc=1 ns A=1 (f) 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (ns) Amplitude Rectangle Monocycle Waveform Tc=1 ns A=1 (g) 0 0.5 1 1.5 2 x 10−9 −6 −4 −2 0 2 4 6 8 10 x 104 Time (s) Amplitude gaussian pulse gaussian monocycle scholtz monocycle manchester monocycle rz manchester monocycle sine monocycle rectangle monocycle (h) Figure 2.1: Shape Waveforms with duration Tb= 1 ns: (a) Gaussian pulse, (b) Gaussian monocycle, (c) Scholtz’s monocycle, (d) Manchester monocycle, (e) RZ-Manchester monocycle, (f) sine monocycle, (g) rectangle monocycle, and (h) all the shapes with the same energy in the same plot. 10 CHAPTER 2. UWB SIGNAL AND IDEAL RECEIVER 2.1.3 Scholtz’s monocycle Scholtz’s monocycle is similar to the second derivative of the Gaussian and can be represented by [21] w(t) = "1−4πt−Tb Tau 2#e −2πt−Tb Tau 2 (2.4) Tau = 0.4·Tbis an adequate value in this case. 2.1.4 Manchester Monocycle The Manchester monocycle has amplitude 1during half of the monocycle width and has amplitude −1during the other half 2.1.5 RZ-Manchester Monocycle The return-to-zero Manchester monocycle (with unit amplitude) has amplitude 1and −1for only a portion of each half monocycle width. Such portion is represented by the parameter k(0< k ≤1). 2.1.6 Sine Monocycle The sine monocycle is one period of a sine wave. The period of the sine wave is the pulse duration, Tb. 2.1.7 Rectangle Monocycle The rectangle monocycle has uniform amplitude during the whole pulse width. 2.2 Ideal UWB Receiver Although the objective of this thesis is not to investigate the ideal UWB receiver, it is interesting to analyze such receiver in order to compare the performance of the non-coherent UWB receivers and the proposed receiver using undersampling with such ideal receiver. This ideal receiver is based on the assumption that the UWB pulse can be sampled with a higher sampling frequency than the Nyquist rate. Due to the wide band of such pulses, the required sampling rate is very high, which makes the design to be very complex or even unfeasible. 2.2. IDEAL UWB RECEIVER 11 LNA BPF ADC p[n] n-Mp+1 n > < r(t) r[n] z[n] Figure 2.2: Block diagram of ideal UWB receiver Thus, the ideal receiver is assumed to be able to over-sample the UWB pulse, thus allowing to correlate the received sampled signal with the known pulse shape. Let the UWB received signal after filtering and amplification be represented by r(t) = pEbp(t−td) + n(t)(2.5) where Ebis the received pulse energy after amplification and tdis a generic delay of the pulse. Additive white Gaussian noise (AWGN) with zero-mean, double-sided power spectral density N0 2and variance σ2is denoted by n(t). Since the received signal is filtered, the bandwidth of the noise is limited. The variance or power of the noise is σ2=N0·B. The SNR is defined by Eb N0. After the filtering, the signal is sampled by an analog-to-digital converter (ADC) with sampling rate fs, greater than the Nyquist rate, being the sampled signal r[n] = r(nts) = pEbp[n−nd] + v[n](2.6) where tsis the inverse of the sampling rate (fs), ndis the delay in number of samples (nd=td ts). The sampled noise is denoted by v[n]. Such signal is correlated with the known pulse shape and compare with a threshold in order to detect the pulse. The correlated signal can be expressed by z[n] = n X k=n−Mp+1 r[k]p[k−n+Mp−1] (2.7) where p[n]is the known pulse shape, which has Mpsamples (Mp=Tb ts), being Tbthe pulse duration. The block diagram of this ideal receiver is shown in Figure 2.2. Thus, when z[n]exceeds the threshold, γ, the receiver estimates that the pulse is present. Without considering the noise, the maximum of z[n]would be √Eb at index n=round (nd). Therefore, the threshold may be set as a percentage of √Eb γ=kpEb; 0 ≤k≤1(2.8) Chapter 3 UWB Non-Coherent Receivers Since the use of the ideal UWB receiver (described in section 2.2) is unfeasible and very complex, we are interested in designing a simpler receiver. Two non-coherent detection approaches are investigated: amplitude detection and energy detection. Such techniques are implemented in the analog domain, so it is not needed to sample the UWB signal, making the design much simpler. The non-coherent receivers do not require channel estimation and have lowcomplexity implementation at the expense of performance loss. The suboptimal non-coherent receivers are suitable for low power and low-cost scenarios. The non-coherent receivers do not require synchronization, therefore it enables infrastructure-free and anchor-less localization. The detection is simply carried out by comparing some feature of the received UWB signal (amplitude or energy in the case of this thesis) with a threshold in a fully analog implementation. 3.1 Non-coherent receiver architecture Two UWB non-coherent receivers are studied in this thesis. They are quite similar, only the technique to detect the UWB pulses changes. Both noncoherent receivers detect the pulses by comparing a feature of the received signal with a threshold. In both receivers the received signal is filtered and amplified. After that it is different in each one: •Amplitude detection approach: The actual amplitude of the received signal after filtering and amplification is compared with a threshold, i.e. it only needs a comparator. •Energy detection approach: In this case the received signal after filtering and amplification is passed through a square-law device and an integrator with integration time TIbefore comparing with the threshold. 13 14 CHAPTER 3. UWB NON-COHERENT RECEIVERS LNA BPF r(t) < > H0 H1 Figure 3.1: Simplified block diagram of non-coherent UWB receiver using amplitude detection approach. LNA BPF r(t) < > H0 H1 (.)2 Figure 3.2: Simplified block diagram of non-coherent UWB receiver using energy detection approach. Therefore, the energy of the signal within intervals of TIis used to detect the pulses. Simplified block diagrams of these UWB non-coherent receivers are illustrated in Figures 3.1 (amplitude detection approach) and 3.2 (energy detection approach). The hardware front end design of such receivers will be further described in chapter 4. 3.2 Distance measurement procedure The aim is to measure the distance between two UWB sensors by estimating the round-trip-time (RTT) of a UWB pulse which propagates between such sensors. One sensors is called master and the another is the slave. The is master is which actually measures the distance and controls the measurement procedure, while the slave is always waiting to receive pulses to respond to them. The same UWB non-coherent receiver (described in the previous section) is used in both sensors. The distance is measured repeatedly with an update rate denoted by Rf. In this context, an update measurement rate of 100 Hz is desirable for accurate high dynamic range tracking. Let us denote the inverse of Rfby Tf, which is called in this document as frame duration. A frame is the time interval in which the master performs one distance measurement. Thus, the measurement procedure is repeated in every frame and it follows the following steps: 1. The master initiates the measurement procedure by sending a UWB pulse. It transmits a pulse at the beginning of every frame. 3.2. DISTANCE MEASUREMENT PROCEDURE 15 2. When the slave detects the pulse and it responds to the master after a fixed latency (Tw) by sending another pulse. 3. The master detects the slave response and it measures the RTT ( ˆ TRT T ) in order to estimate the distance. It might happen that the master does not detect any pulse within a frame, so no distance estimation is given. In the next section, the probability of detection will be defined, which is the probability of having a distance estimation in a frame. The process described above is the same for both amplitude and energy detection, only the technique to detect the pulse changes. Let us denote the following timing parameters related to the measurement process. Without loss of generality we do the analysis only considering one frame, for simplicity it starts at t= 0. •Tf: Frame duration •Tp: Propagation time. It is the elapsed time in the propagation of a pulse between the master and the slave, or viceversa. It is related to the distance by Tp=d c, where the distance is denoted by dand cdenotes the speed of light (3·108m /s). •Tw: Slave latency. It is the elapsed time between the pulse reception at the slave and the response transmission. •Tds: Detection time at the slave. It is the time when the slave detects the pulse. Ideally, it would be Tp, but there may be an error. •TRT T : Round-trip time (RTT). It is the time when the pulse transmitted by the slave arrives to the master. TRT T =Tds +Tw+Tp, which ideally (considering that at the slave the pulse is detected without error, i.e. Tds =Tp) would be 2Tp+Tw. •ˆ TRT T : Estimated RTT. It is the time when the master detects the pulse and it is used to measure the distance. Ideally, it would be TRT T , but as in the detection at the slave there may be an error. The estimated RTT, ˆ TRT T , is used to measure the distance between the master and the slave sensors. Thus, ˆ d=cˆ TRT T −Tw 2(3.1) 16 CHAPTER 3. UWB NON-COHERENT RECEIVERS The above expression is valid if there is not an offset1in the error. To avoid that, a look-up table made with a previous calibration process can be used, as described in [1]. The RTT estimation may be any value within a frame due to the error at the slave or at the master. The measurement procedure and the timing parameters are illustrated in Figure 3.3. We can easily see that in this case the maximum distance which can be measured properly is bounded by the RTT. Therefore, Tmax RT T =Tf−Tb Tmax p=Tmax RT T −Tw 2 dmax =c·Tmax p (3.2) Furthermore, the average power consumption due to the pulses transmission in both sensors would be 2Eb Tf. Thus, there is a trade-off between the measurement update rate, the range covered and the power consumption. 3.3 Theoretical analysis In this section, more elaborated theoretical analysis of the RTT measurement process is provided. The signal received by the slave is rs(t) = ∞ X j=−∞pEbp(t−jTf−Tp) + n(t)(3.3) where the frame index is denoted by j,Ebis the received pulse energy after amplification. Additive white Gaussian noise (AWGN) with zero-mean, doublesided power spectral density N0 2and variance σ2is denoted by n(t). Since the received signal is filtered, the bandwidth of the noise is limited. The variance or power of the noise is σ2=N0·B. The signal-to-noise ratio SNR is defined by Eb N0. The UWB pulse of duration Tbis denoted by p(t). Let us now denote the generic signal (it will be different for amplitude detection and energy detection) which is compared with a threshold, γ, at the slave by ys(t) = ss(t) + vs(t) where ss(t)is the pulse component and vs(t)is the noise component. Then, when ys(t)exceeds such threshold, the pulse is detected and the slave responds with another pulse after the latency, Tw. 1The offset of the error is equivalent to the error mean. 3.3. THEORETICAL ANALYSIS 17 iTf (i+1)Tf (i-1)Tf Tw TRTT(i-1) (correct) TRTT(i) (incorrect) Tp Trs(i-1), Tds(i-1) (correct detection) Tts(i-1) Trm(i-1) Tds(i) (wrong detection) Tts(i) Trs(i) Trm(i) Master Slave Figure 3.3: Timing diagram of the RTT estimation procedure. Two measurements are shown. In the (i-1)-th frame the pulse is correctly detected at the slave (Trs =Tds), while in the i-th frame the slave detects the pulse when it is not present due to the noise and consequently the RTT is wrong. 18 CHAPTER 3. UWB NON-COHERENT RECEIVERS Without loss of generality we do the analysis within a single frame, for simplicity the one with index j= 0. Hence, the instant of the detection at the slave, Tds, is given by Tds = min ys(t)>γ (t∈[−Tw−Tp, Tf−Tw−Tp]) (3.4) what means that the first time instant when the signal crosses the threshold, producing a pulse which arrives to the master within the frame j= 0, is the slave detection instant. Thus, the signal received by the master is rm(t) = pEbp(t−TRT T ) + n(t)(3.5) and the generic signal compared with a threshold at the master is ym(t) = sm(t) + vm(t), so the estimated RTT is ˆ TRT T = min ym(t)>γ (t∈[0 , Tf]) (3.6) The correct time of detection is assumed to be when the pulse component, s(t), crosses the threshold, γ. Thus, if we denote such time instants for zero delay by t1and t2(with t1< t2), we have that ss(Tp+t1) = ss(Tp+t2) = sm(TRT T +t1) = sm(TRT T +t2) = γ(3.7) Therefore, the error at the master and at the slave, ξmand ξs, respectively, would be ξm=ˆ TRT T −TRT T −t1 ξs=Tds −Tp−t1 (3.8) and the total error ξt=ξm+ξs=ˆ TRT T −2Tp−Tw−2t1(3.9) Hence, we are interested in finding out the probability density function (PDF) of such error, fξt(ξ). Let us denote the PDF of the estimated RTT, ˆ TRT T , given the actual RTT, by fˆ TRT T (τ;TRT T ). The SNR, the shape and the threshold will also affect the distribution of such estimated RTT. Note that ˆTf 0 fˆ TRT T (τ;TRT T )dτ =PD(3.10) where PDis the probability of detection at the master (ym(t)crosses the threshold at least once within the frame) with 0≤PD≤1, so it is not exactly a proper PDF. With the remaining probability, PM= 1 −PD, the pulse is not detected. Then, the PDF of Tds given Tpis related to fˆ TRT T (τ;TRT T )by fTds (τs;Tp) = fˆ TRT T (τ+Tp+Tw; 2Tp+Tw)(3.11) Chapter 4 UWB Non-Coherent Receiver Front End Design This chapter describes the UWB front end design which has been performed in this thesis. The sensor architecture is based on the design from [1], and the focus has been made in the part of the receiver. Two designs were carried out, one for amplitude detection and another for energy detection and two boards were implemented for each design since the same design is used for both master and slave. The board design was made using the software Eagle. 4.1 Sensor architecture The architecture of the sensor unit is shown in Figure 4.1. It is composed of an analog UWB measurement section, which was designed in-house and implemented using elementary off-the shelf components, and a digital processing section, which is based on a field programmable gate array (FPGA). Conceptually, the interface between the analog UWB section and the digital processing section is provided by a time-to-digital converter (TDC) commercial integrated circuit, which provides RTT measurements with a resolution of 65 ps. Furthermore, a 12-bit digital-to-analog converter (DAC) is programmed by the FPGA and used to set the threshold of the energy detector/comparator in the UWB receiver section. This flexible configuration leads to the convenient design and implementation of fast adaptive threshold sitting algorithms, such as those presented in [23]. Overall, the modular nature of this architecture enables the testing of alternative solutions both for the radio front end and the digital processing algorithms. 25 26 CHAPTER 4. UWB NON-COHERENT RECEIVER FRONT END DESIGN FPGA (digital control and processing) DAC TDC UWB Transceiver THRESHOLD STOP START SPI SPI CONTROL UWB measurement section Figure 4.1: Simplified diagram of the architecture of the sensor unit. The analog UWB measurement section is connected to the FPGA using serial peripheral interface (SPI) connections to the TDC and the DAC for configuration. The connection between the TDC and the FPGA is also used to read the measured RTT values. The FPGA triggers and controls the UWB transceiver directly using digital control signals. Two different UWB transceiver were implemented, using the non-coherent energy detection and amplitude detection approaches. Its main advantages are low-complexity and low-power implementation, because it avoids Nyquist-rate sampling of the UWB signal, which is infeasible for many applications due to the high bandwidth. Such transceiver section is illustrated by the block diagram in Figure 4.2. In such block diagram, a switch is used in order to use a single antenna, but in the final board it is also possible to use one antenna for transmission and another one for reception. The receiver part is different for amplitude or energy detection; the amplitude detection receiver uses just a comparator, while the energy detection receiver uses and energy detector (ED) which includes the square-law device, integrator and comparator (see Figure 3.2) in the same chip. Moreover, the design includes a low-noise amplifier (LNA) which is not included in the block diagram of Figure 4.2. 4.1. SENSOR ARCHITECTURE 27 ED/ Comparator Pulse generator (step-recovery diode) RX/TX switch UWB Transceiver WIDEBAND DICONE ANTENNA STOP THRESHOLD CONTROL START Figure 4.2: Architecture of the UWB transceiver. The pulse generator is realized using a step-recovery diode based on the circuit characterized in [24] and is triggered by the start signal from the FPGA. The output of the energy detector (ED)/comparator, after being compared with the voltage threshold in the on-chip comparator, provides the stop signal for the TDC measurement. The single-pole-double-throw (SPDT) switch selects the RX or TX position controlled by digital signals from the FPGA. A wideband omnidirectional discone antenna is used for the transmission and reception of the UWB pulses. 28 CHAPTER 4. UWB NON-COHERENT RECEIVER FRONT END DESIGN The digital section allows for implementing the proper timing and operation of the sensor system. In particular, as shown in Figure 4.1, the UWB measurement section requires various digital control and setup signals. The functionalities of the digital section are listed below: •Controlling the UWB transmitter: The measurement is initiated when the master interrogates the slave by sending a UWB pulse. The trigger signal to the transmitter is generated digitally. It is possible to dynamically adjust the frame duration, Tf(update measurement rate). •Configuring and controlling the TDC: the TDC is configured to perform the measurement. The TDC measurement is initiated when the pulse is transmitted. The TDC communicates through a SPI interface. •Controlling the transmit/receive switch: The transmit and receive switch connection the antenna to the transceiver is controlled digitally. •Configuring the DAC for the detection threshold: the value of the threshold to detect the pulse at the output of the ED/comparator is set digitally. It can be set a priori or can be calculated adaptively depending on the false alarm requirements. •Post-processing for range estimation: Once the master receives the answer from the slave, it computes the range the RTT readings from the TDC. In the digital processing section, the FPGA provides flexibility in the development, implementation and tuning of algorithms. ML505 Virtex-5 FPGA boards are used to implement the digital functionalities listed above. The FPGA allows reconfigurable control of the UWB front end. 4.2 Hardware: Selection of the components The UWB measurement section was implemented as a printed circuit board on FR4 substrate with a thickness of 1.0 mm. A picture of the realized board is shown in Figure (include picture). As said before, in this thesis the effort in the design of the boards has been made in the receptor part, specially in the selection of the LNA, comparator and ED. First, a search of components suitable for the design was made and then they were prioritized taking into account different features. 4.2. HARDWARE: SELECTION OF THE COMPONENTS 29 Table 4.1: Suitable LNAs for the receiver front end. The first column indicates the priority taking into account all the features, f1and f2are the low and high frequency of the operation bandwidth, respectively. B denotes the bandwidth of operation (f2−f1), NF and G are the noise figure and the gain, respectively. The seventh columns indicates the supply current and the last two columns show the manufacturer and the device reference. The row in red is the LNA chosen for the design. Pr. f1f2B (GHz) NF (dB) G (dB) S.C. (mA) Manufact.Manufact.ref. 1 400 MHz 1.5 GHz 1.1 0.66 31.8 45 Avago MGA-13516 2 400 MHz 1.4 GHz 1 0.52 21.3 60 Freescale MML09211H 3 5 MHz 2 GHz 1.995 1.1 20 5.2 RFMD SGL0363 4 100 MHz 2.5 GHz 2.4 1.2 24 4.7 Freescale MBC13917 5 400 MHz 2.5 GHz 2.1 1.2 20 5 Freescale MBC13720 6 1 GHz 2.5 GHz 1.5 1.27 18.9 3.8 Freescale MC13851 7 100 MHz 1.5 GHz 1.4 1 19.7 10 Avago MGA-68563 8 500 MHz 1.7 GHz 1.2 0.4 17.7 50 Avago MGA-16516 9 45 MHz 2.5 GHz 2.455 1.5 15 6 RFMD RF2884 10 450 MHz 2 GHz 1.55 0.56 17.8 40 Avago MGA-683P8 11 100 MHz 1.3 GHz 1.2 1.2 15.5 12 RFMD SGL0163Z 12 400 MHz 4 GHz 3.6 0.8 21 30 Analog ADL5523ACPZ 13 500 MHz 2.5 GHz 2 1.5 19 12 RFMD RF2442 14 800 MHz 2.4 GHz 1.6 1.55 13.5 7.8 Freescale MC13853 15 150 MHz 2.5 GHz 2.35 1.4 12.9 5.7 RFMD RF2314 16 50 MHz 4 GHz 3.95 0.8 18.2 46 RFMD SPF5043Z 17 0 4 GHz 4 1.9 24 45 RFMD SGA4586Z 18 300 MHz 2.5 GHz 2.2 1.6 11.7 8 RFMD RF2304 4.2.1 LNA The LNA must operate in a wide band suitable for the used UWB pulse (see Table 2.1), but such bandwidth is also desirable to be as low as possible in order to reduce the noise. Furthermore, low noise figure (NF) and high gain are desired, as well as low current consumption. A noise figure of about 1 dB is considered good enough. Thus, some suitable LNAs are shown in Table 4.1 with some of its main features (bandwidth of operation, noise figure, gain and supply current), which are taken all into account in order to select the most adequate device. Since the pulse shape which will be used in the experiments is the Scholtz’s monocycle, the LNA must operate within the bandwidth of such shape (see Table 2.1). That is not the case of the three first components. The fourth one was not available by the supplier, so finally the LNA MBC13720 30 CHAPTER 4. UWB NON-COHERENT RECEIVER FRONT END DESIGN Table 4.2: Parts list Component Part number TDC TDC-GP2, Acam Messelectronic DAC ADC5620, Analog Devices Pulse generator diode 5082-0112, HP Switch RSW-2-25P, Mini Circuits LNA MBC13720, Freescale Semiconductor Comparator LT1720, Linear Technology Energy detector LTC5536, Linear Technology from Freescale was selected. This LNA has adequate noise figure, gain and operation bandwidth, and the supply current is extremely low. Furthermore, the IP3 is 10 dBm at 1.9 GHz, which is acceptable. 4.2.2 Comparator The comparator is used in the design of the non-coherent receiver for amplitude detection, but not in energy detection because one single integrated circuit includes the square-law device, the integrator and the comparator itself. We need a comparator as fast as possible (i.e. low response time) and with low supply current. Another requirement is the match between the logic output of the comparator and the input of the TDC. Such TDC requires a low level input voltage lower than 0.8 V and a high level input voltage higher than 2 V. Thus, some ultra-fast comparators with RSPECL outputs are not acceptable and we need a device with outputs which directly interface to TTL and CMOS inputs. Such comparators are slower, but they can be fast enough. Hence, the selected comparator was the LT1720 from Linear Technology, which has rail-to-rail outputs, 4.5 ns response time and 4 mA current consumption. 4.2.3 ED The energy detector is equivalent to the comparator for the energy-detection receiver. The LTC5536 from Linear Technologies, which was also used in the previous design described in [1], was selected. This device rail-to-rail outputs, 25 ns response time and low operating current (2 mA). 4.3 Final design A list of the main parts used in the UWB measurement boards is provided in Table 4.2. Two LNAs were connected in cascade in the receiver in order to increase the sensitivity of the receiver. The schematics of both detectors are shown in Figures 4.3 and 4.4. Note that at the input and output of the LNAs there are networks 4.3. FINAL DESIGN 31 Figure 4.3: Schematic of the receiver with amplitude detection. with passive components. Such networks were taken from the datasheet of the MBC13720 component [25] for a typical 900 MHz LNA application. Such networks implement a band-pass filter. The total transfer function of the filter (input and output of the LNA) is illustrated in Figure 4.5. The insertion loss is about 6 dB and the bandwidth is suitable for the design (considering Scholtz’s monocycle shape). Furthermore, the layouts of the whole boards of the measurement sections for both non-coherent receivers are illustrated in Figures 4.6 and 4.7. The final implemented boards are shown in Figures (4.8) and (4.9), for amplitude and energy detection, respectively. 32 CHAPTER 4. UWB NON-COHERENT RECEIVER FRONT END DESIGN Figure 4.4: Schematic of the receiver with energy detection. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −10 −9.5 −9 −8.5 −8 −7.5 −7 −6.5 −6 Frequency (GHz) Filter Transfer Function (dB) Figure 4.5: Frequency response of the filter 4.3. FINAL DESIGN 33 Figure 4.6: Board layout for amplitude detection. Figure 4.7: Board layout for energy detection. 34 CHAPTER 4. UWB NON-COHERENT RECEIVER FRONT END DESIGN Figure 4.8: Implemented board for amplitude detection. 5.2. UWB NON-COHERENT RECEIVERS 41 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR (dB) Probability of Detection gaussian pulse gaussian monocycle scholtz monocycle manchester monocycle rz manchester monocycle sine monocycle rectangle monocycle Figure 5.3: Probability of detection for amplitude detection with pA d= 10−3, Tf= 50 ns and random Tp, in terms of the SNR. Each curve corresponds to a UWB pulse shape. 5.2.1 Detection performance: amplitude vs energy vs pulse shapes Figure 5.3 shows the curves detection performance for amplitude detection for the all the considered UWB pulse shapes in terms of the SNR. The frame duration is 50 ns and the threshold is computed with pA d= 10−3. The curves of the detection performance are different for the different shapes . Such difference is due to the fact that the different pulse shapes have different amplitude for the same energy and pulse duration (see Table 2.1), i.e. the higher the energy is for the same amplitude, the better the detection performance is. Hence, Scholtz’s monocycle presents the best detection performance using amplitude detection. On the other hand, the detection performance for energy detection is quite similar for all the pulse shapes (see Figure 5.4) because in this case what is compared with a threshold is the energy and for it is the same for the same SNR in all the pulses. The same parameters as the last simulations for amplitude detection are used in these simulations with energy detection. 42 CHAPTER 5. SIMULATIONS RESULTS 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR (dB) Probability of Detection gaussian pulse gaussian monocycle scholtz monocycle manchester monocycle rz manchester monocycle sine monocycle rectangle monocycle Figure 5.4: Probability of detection for energy detection with pE d= 10−3, Tf= 50 ns and random Tp, in terms of the SNR. Each curve corresponds to a UWB pulse shape. Moreover, we can check the validity of the approximations of the probability of detection presented in chapter 3 in expressions 3.22 and 3.28. Figure 5.5 shows the curves of the probability of detection of the simulations together with the theoretical curves. The theoretical approximations fit quite well the simulations, specially for amplitude detection. For energy detection, the matching between the approximation and the simulation is not so accurate, but is still a good approximation. We desire a high probability of detection, nearly 1 if it is possible. Thus, from the detection performance curves, we can measure such performance as the required SNR to achieve a certain value for the probability of detection. Comparing both receivers (with the thresholds computed with the same pd), we can see that Manchester monocycle, RZ-Manchester monocycle, rectangular monocycle and sine monocycle present similar detection performance with both receivers (the SNR required to achieve probability of detection nearly 1 is similar), while Gaussian pulse, Gaussian monocycle and Scholtz’s monocycle work better with amplitude detection regarding the detection performance. Figure 5.6 shows the detection performance curves of amplitude detection and energy detection (only Scholtz’s monocycle for energy detection) together. Scholtz’s monocycle requires lower SNR (for amplitude detection) to achieve probability of detection nearly 1 than the others pulse shapes. 5.2. UWB NON-COHERENT RECEIVERS 43 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR (dB) Probability of Detection scholtz monocycle amplitude simulation scholtz monocycle amplitude theory sine monocycle amplitude simulation sine monocycle amplitude theory scholtz monocycle energy theory scholtz monocycle energy simulation Figure 5.5: Comparison of the theoretical probability of detection and the probability of detection given by the simulations with pd= 10−3. 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR (dB) Probability of Detection gaussian pulse (amplitude) gaussian monocycle (amplitude) scholtz monocycle (amplitude) manchester monocycle (amplitude) rz manchester monocycle (amplitude) sine monocycle (amplitude) rectangle monocycle (amplitude) scholtz monocycle (energy) Figure 5.6: Probability of detection for amplitude detection (all shapes) and energy detection (only Scholtz’s monocycle) with pd= 10−3,Tf= 50 ns and random Tp, in terms of the SNR. Each curve corresponds to a UWB pulse shape. 44 CHAPTER 5. SIMULATIONS RESULTS 10−8 10−6 10−4 10−2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 pd A Probability of detection SNR=0 dB SNR=1.5 dB SNR=3 dB SNR=4.5 dB SNR=6 dB SNR=7.5 dB SNR=9 dB SNR=10.5 dB Figure 5.7: Probability of detection for amplitude detection using Scholtz’s monocycle, Tf= 50 ns and random Tp, in terms of the threshold (pA d). Each curve corresponds to a certain SNR. It is also worth to note that the detection performance of sine monocycle and rectangle monocycle is very similar with amplitude detection although sine monocycle has higher amplitude than rectangle monocycle for the same energy and pulse duration. The reason is that rectangle monocycle has the same amplitude during the whole pulse width while the amplitude in the sine monocycle varies over the pulse width and it is also negative within the half of the pulse width. The same behavior yields with another thresholds, but more SNR is needed if the threshold is increased in order to achieve the same probability of detection. Figures 5.7 and 5.8 show the detection performance in terms of the threshold (pd) for amplitude and energy detection, respectively, using Scholtz’s monocycle. These curves are useful to see which threshold we can use with a certain value of SNR, yielding a good probability of detection. We will see in the following subsection that the accuracy is also related to the threshold and that higher threshold yields higher accuracy. Therefore, from Figures 5.7 and 5.8 we can see the highest threshold (or lowest pd) which can be used for a certain SNR to provide a good probability of detection. 5.2. UWB NON-COHERENT RECEIVERS 45 10−8 10−7 10−6 10−5 10−4 10−3 10−2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 pd E Probability of detection SNR=6 dB SNR=7.5 dB SNR=9 dB SNR=10.5 dB SNR=12 dB SNR=13.5 dB SNR=15 dB Figure 5.8: Probability of detection for energy detection using Scholtz’s monocycle, Tf= 50 ns and random Tp, in terms of the threshold (pE d). Each curve corresponds to a certain SNR. 5.2.2 Accuracy: amplitude vs energy The accuracy of the measurement is directly related to the threshold. The higher the threshold (lower pd) is, the better the accuracy is. However, as we have seen in the previous subsection that the threshold also affects to the detection performance. Therefore, there exists a trade-off between the detection performance and the accuracy when we set the threshold. For both energy and amplitude detection, there is a boundary for the accuracy that cannot be improved even if we increase more and more the SNR. This is due to the false alarms which occur during the elapsed time until the pulse arrives when the received signal is only noise. Such boundary is directly related to the threshold, the frame duration and the latency at the slave and the used pulse shape does not affect. The shape only affect for low SNR, for which the probability of detection is low. Figures 5.7 and 5.8 show the accuracy in terms of the threshold (pd) for amplitude and energy detection, respectively using Scholtz’s monocycle. In Figure 5.11 the accuracy curves for both receivers are shown together, being pdequal for both and using Scholtz’s monocycle. For high SNR the accuracy is quite better with energy detection, but for low SNR amplitude detection is better (because amplitude detection requires lower SNR in order to achieve total detection). 46 CHAPTER 5. SIMULATIONS RESULTS 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−21 10−20 10−19 10−18 10−17 10−16 10−15 pd A Error variance (s2) SNR=28.5 dB Figure 5.9: Error variance for amplitude detection using Scholtz’s monocycle, Tf= 50 ns and random Tp, in terms of the threshold (pA d). 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−22 10−21 10−20 10−19 10−18 10−17 10−16 pd E Probability of detection SNR=28.5 dB Figure 5.10: Error variance for energy detection using Scholtz’s monocycle, Tf= 50 ns and random Tp, in terms of the threshold (pA d). Each curve corresponds to a certain SNR. 5.2. UWB NON-COHERENT RECEIVERS 47 0 5 10 15 20 25 30 10−18 10−17 10−16 10−15 SNR (dB) Error variance (s2) Amplitude detection Energy detection Figure 5.11: Comparison of the error variance for amplitude and energy detection, with pd= 10−3,Tf= 50 ns and random Tp, in terms of the SNR. 5.2.3 Influence of the propagation time and slave latency The best accuracy that can be achieved is related to the time elapsed until the pulse arrives, because as longer is such elapsed time, as more probable is to have a false alarm. Thus, in the same conditions, the accuracy will be better with shorter propagation time (or shorter distance), which is shown in Figures 5.12 and 5.13 for amplitude and energy detection, respectively. However, the detection performance is the same. It is worth to note that the slope is higher for amplitude detection than for energy detection3, i.e. the propagation time affects more to amplitude detection than to energy detection. Therefore, to support longer range it may be better to use energy detection. For the same reason, the latency at the slave to respond will also affect the accuracy performance. Figure 5.14 shows the error variance in terms of Twfor both amplitude and energy detection. As it has been explained before for the propagation time, the deterioration due to the latency increase is higher for energy detection than for amplitude detection. 3Note that the y-axis is shown in logarithmic scale and it seems that the slope is similar for both amplitude and energy detection, but actually it is higher for amplitude detection 48 CHAPTER 5. SIMULATIONS RESULTS 0 1 2 3 4 5 x 10−8 10−24 10−22 10−20 10−18 10−16 10−14 Propagation time (s) Error variance (s2) pd A=10−2 pd A=10−3 pd A=10−4 pd A=10−5 pd A=10−6 Figure 5.12: Error variance for amplitude detection using Scholtz’s monocycle in terms of the propagation time, with Tf= 100 ns and SNR = 16 dB. Each curve corresponds to a different threshold. 0 1 2 3 4 5 x 10−8 10−24 10−22 10−20 10−18 10−16 10−14 Propagation time (s) Error variance (s2) 10−2 10−3 10−4 10−5 10−6 Figure 5.13: Error variance for energy detection using Scholtz’s monocycle in terms of the propagation time, with Tf= 100 ns and SNR = 16 dB. Each curve corresponds to a different threshold. 5.2. UWB NON-COHERENT RECEIVERS 49 0 0.2 0.4 0.6 0.8 1 x 10−7 10−18 10−17 10−16 10−15 X: 1e−007 Y: 1.868e−017 Slave Latency (s) Error variance (s2) X: 0 Y: 1.476e−018 X: 0 Y: 8.413e−017 X: 1e−007 Y: 4.169e−016 Amplitude Detection Energy Detection Figure 5.14: Error variance for energy detection and amplitude detection using Scholtz’s monocycle in terms of Tw, with Tmax p= 50 ns and SNR = 15 dB. Each curve corresponds to a detection technique. 5.2.4 Influence of the integration interval for energy detection The accuracy of the measurements improves with longer integration intervals (see Figure 5.15). The reason is that in energy detection the noise is averaged, thus with longer integration the output of the integrator varies less. However, if the integration interval is too large, it may be very slow. Therefore, the value used in the previous simulations, TI= 5 ns is considered suitable. 50 CHAPTER 5. SIMULATIONS RESULTS 2 3 4 5 6 7 8 9 10 x 10−9 10−17 10−16 10−15 TI (s) Error variance (s2) gaussian pulse gaussian monocycle scholtz monocycle manchester monocycle rz manchester monocycle sine monocycle rectangle monocycle Figure 5.15: Error variance for energy detection in terms of the integration interval, with Tf= 100 ns and SNR = 16 dB. Each curve corresponds to a different pulse shape. Chapter 7 Conclusions Below is a brief list of conclusions that can be drawn from the results produced in this master thesis. •The UWB non-coherent receivers based on the RTT measurement seem to be suitable for the distance measurement. The performance is worse than with the ideal receiver, but the loss is not big. The main advantage is the low complexity. •Energy detection seems to present better performance regarding the accuracy, however, it requires higher SNR to work properly. •Amplitude detection may be useful where it is not possible to have a high SNR. However, for long distances or large slave latency, the accuracy can get worse considerably. •The slave latency is desirable to be as short possible in order to reduce the false alarm rate and therefore improve the accuracy, specially for amplitude detection since the accuracy is more affected than for energy detection. •The proposed receiver based on undersampling may improve the performance of the non-coherent receivers, at the cost of requiring a more complex design and very accurate sampling rate. At the moment it seems to be difficult to implement, but it could be used as a start point in future works. 57 58 CHAPTER 7. CONCLUSIONS 7.1 Discussion 7.1.1 Amplitude detection approach The non-coherent receiver using the amplitude detection approach is very simple and the receiver front end only need to compare the signal with a threshold after the filtering and amplification. The main advantage of the amplitude detection approach is the low required SNR to achieve high probability of detection. On the other hand, the long distances (large propagation time) and mainly the slave latency make the accuracy to get worse considerably. Therefore, for low SNR and if the slave latency is not too long, it can be a good choice to use the amplitude detection approach. 7.1.2 Energy detection approach The non-coherent receiver using the energy detection approach has also low complexity. It is more robust with long distances or large slave latencies. It requires a higher SNR to achieve a good probability of detection. Since which is compared with a threshold is the energy of the received signal, the noise is averaged and therefore the false alarm rate is lower, and therefore the accuracy is better. 7.1.3 UWB Pulse shapes In the results of chapter 5, it has been shown that the main difference between the different shapes is for the detection performance, and mainly for amplitude detection (see Figures 5.3 and 5.4). For energy detection the difference between the shapes is negligible, while for amplitude detection the required SNR to achieve a certain detection performance is different for the different shapes. Particularly, Scholtz’s monocycle presents the best detection performance. Therefore, such Scholtz’s monocycle seems to be the best choice for UWB ranging systems due to its higher efficiency. 7.1.4 Amplitude detection vs energy detection The design of both receivers is very similar. In energy detection approach, an energy detector is used instead of the comparator for amplitude detection (see chapter 4). Thus, regarding the complexity of the non-coherent receiver front end design, it does not seem that there is any preference between both approaches. For short round-trip-times (considering also the slave latency), the amplitude detection approach seems to present better performance because to achieve a certain accuracy, lower SNR is required than with energy detection (selecting the threshold from the SNR to achieve a minimum detection performance). However, as the accuracy is more affected in amplitude detection when increasing the RTT, energy detection would present better performance for higher 7.2. FUTURE WORK 59 RTTs. Since in practice the slave latency is quite long (it is actually several times higher than the propagation time), the energy detection approach is the best choice in general. Moreover, amplitude detection might be more robust in hostile environments where the SNR usually decrease because the detection performance changes slower with the SNR in amplitude detection than in energy detection (see 5.3 and 5.4). 7.1.5 UWB front end design The design provided in this thesis is flexible and low-complex. Both amplitude detection and energy detection have been implemented. Due to lack of time, it has not been possible to perform experiments with the implemented boards and compare it with the simulations. 7.1.6 UWB receiver with undersampling The proposed method to reconstruct a pulse from a burst of pulses using undersampling is an idea that could be used in the future. At the moment, it seems difficult to implement it because it requires very accurate sampling rate and pulses delay. 7.2 Future work The simulations performed in this thesis are valid and can be useful to extract several conclusions. However, it probably won’t match exactly the results of experiments. The reason is that the slave latency in practice is very long. In these simulations such slave latency has been considered zero or very short because otherwise the required time to perform each iteration of the simulations would have been increased considerably. Thus, a possible future work could be to carry out similar simulations, but with more realistic slave latency values. Furthermore, as said before, it has not been possible to perform experiments because of time restriction and I had to come back to Spain three months ago, so during that time it was not possible. Hence, the next step of this thesis would to carry out the experiments with the implemented boards presented in chapter 4. Another possible future work could be related to the signal processing part. An algorithm could be developed to adjust the threshold dynamically, setting a required probability of detection and increasing or decreasing the threshold to track such probability of detection. Thus, the accuracy would be the best which can be achieved for the given conditions. The UWB receiver using undersampling, which is presented in chapter 6, could be used as a start point in future research. The method might be improved 60 CHAPTER 7. CONCLUSIONS to allow using the undersampling on both sides (master and slave). Variable delays within the pulse burst could also be considered. The multipath characteristics of the UWB channels have not been considered in this thesis work. The UWB channels are actually highly dispersive, making that the leading-edge path is not necessarily the strongest path [18]. This is an issue to be further investigated in the context of UWB non-coherent receivers. Bibliography [1] A. De Angelis, S. Dwivedi and P. Händel, “Characterization of a Flexible UWB Sensor for Indoor Localization”. [2] H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of Wireless Indoor Positioning Techniques and Systems,” Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, vol. 37, no. 6, pp. 1067–1080, Nov. 2007. [3] I. Skog, P. Händel, J. Nilsson, and J. Rantakokko, “Zero-velocity detection – an algorithm evaluation,” IEEE Transactions on Biomedical Engineering, vol. 57, no. 11, pp. 2657–2666, Nov. 2010. [4] D. Zachariah and M. Jansson, “Camera-aided inertial navigation using epipolar points,” in Position Location and Navigation Symposium (PLANS), 2010 IEEE/ION, May 2010, pp. 303–309. [5] B. Andò, S. Baglio, S. La Malfa, A. Pistorio, and C. Trigona, “A smart wireless sensor network for AAL,” in IEEE International Workshop on Measurements and Networking Proceedings (M&N), Oct. 2011, pp. 122– 125. [6] J. Rantakokko, J. Rydell, P. Strömbäck, P. Händel, J. Callmer, D. Törnqvist, F. Gustafsson, M. Jobs, and M. Gruden, “Accurate and reliable soldier and first responder indoor positioning: multisensor systems and cooperative localization,” IEEE Wireless Communications, vol. 18, no. 2, pp. 10–18, Apr. 2011. [7] J. Rantakokko, P. Händel, M. Fredholm, and F. Marsten-Ekl ¨of, “User requirements for localization and tracking technology: a survey of missionspecific needs and constraints,” in International Conference on Indoor Positioning and Indoor Navigation (IPIN), Zurich, Switzerland, September 14-17 2010. [8] G. Santinelli, R. Giglietti, and A. Moschitta, “Self-calibrating indoor positioning system based on ZigBee R devices,” in IEEE Instrumentation and Measurement Technology Conference, May 2009, pp. 1205–1210. 61 62 BIBLIOGRAPHY [9] D. Macii, F. Trenti, and P. Pivato, “A robust wireless proximity detection technique based on RSS and ToF measurements,” in IEEE International Workshop on Measurements and Networking Proceedings (M&N), Oct. 2011, pp. 31–36. [10] A. De Angelis, M. Dionigi, R. Moschitta, A. Giglietti, and P. Carbone, “Characterization and Modeling of an Experimental UWB Pulse-Based Distance Measurement System,” IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 5, pp. 1479–1486, May 2009. [11] Y. Zhou, C. L. Law, Y. L. Guan, and F. Chin, “Indoor elliptical localization based on asynchronous UWB Range measurement,” IEEE Transactions on Instrumentation and Measurement, vol. 60, no. 1, pp. 248–257, Jan. 2011. [12] S. Gezici and H. Poor, “Position estimation via ultra-wide-band signals”, Proceedings of the IEEE, vol. 97, no. 2, pp. 386-403, 2009 . [13] C. De Dominicis, A. Flammini, S. Rinaldi, E. Sisinni, A. Cazzorla, A. Moschitta, and P. Carbone, “High-precision UWB-based timestamping,” in International IEEE Symposium on Precision Clock Synchronization for Measurement Control and Communication (ISPCS), Sept. 2011, pp. 50–55. [14] Revision of part 15 of the commission’s rules regarding ultra-wideband transmission systems, Federal Communication Commission Std., 2002, Report and order, in FCC 02 48, Apr. 2002. [15] Electromagnetic compatibility and Radio spectrum Matters (ERM); Ultra WideBand (UWB) technologies for communication purposes; ETSI EN 302 065, ETSI Std., Rev. V1.1.1, February 2008. [16] A. De Angelis, J. Nilsson, I. Skog, P. Händel, and P. Carbone, “Indoor Positioning by Ultrawide Band Radio Aided Inertial Navigation,” Metrology and Measurement Systems, vol. 17, no. 3, pp. 447–460, 2010. [17] H. Wymeersch, J. Lien, and M. Win, “Cooperative localization in wireless networks,” Proceedings of the IEEE, vol. 97, no. 2, pp. 427– 450, Feb. 2009. [18] I. Guvenc and Z. Sahinoglu, “Threshold-Based TOA Estimation for Impulse Radio UWB Systems”. [19] I. Guvenc, Z. Sahinoglu, and P. V. Orlik, “TOA Estimation for IR-UWB Systems With Different Transceiver Types” in IEEE Transactions on Microwave theory and techniques, vol. 54, no. 4, April 2006. [20] X. Chen and S. Kiaei, “Monocycle Shapes for Ultra Wideband System”. [21] H. Lee, B. Han, Y. Shin and S. Im, “Multipath Characteristics of Impulse Radio Channels”, Proceedings of the 1998 IEEE International Conference on Communications, ICC’98, vol.3, pp.1650-1654. BIBLIOGRAPHY 63 [22] H. Urkowitz, “Energy Detection of Unknown Deterministic Signals”, Proceedings of the IEEE, vol 55, no 4, April 1967. [23] D. Strömberg, A. De Angelis and P. Händel, “A low-complexity adaptivethreshold detector for pulse UWB systems,” in 2011 International Workshop on ADC Modelling, Testing and Data Converter Analysis and Design and IEEE 2011 ADC Forum, Orvieto, Italy, June 20 - July 1 2011. [24] A. De Angelis, m. Dionigi, R. Giglietti and P. Carbone, “Experimental comparison of low-cost sub-nanosecond pulse generators,” IEEE Transactions on Instrumentation and Measurement, vol. 60, no 1, pp. 310-318, Jan. 2011 [25] Freescale Semiconductor, MBC13720 Datasheet, Rev. 4, September 2011 [26] P. Withington, “Impulse Radio Overview”, Time Domain Corm. [27] S. M. Kay, “Fundamentals of Statistical Signal Processing Volume II”, Summary of Important PDF’s [28] M.K. Oh, B. Jong, R. Harjani, and D.J. Park, “A New Noncoherent UWB Impulse Radio Receiver” in IEEE Communications Letters, vol. 9, no. 2, February 2004. [29] A. Mariani, A. Giorgetti, and M. Chiani, “Energy Detector Design for Cognitive Radio Applications” in IEEE Invited paper, 2010. [30] K. Witrisal, G. Leus, G. J.M. Janssen, M. Pausini, F. Troesch, T. Zasowski, and J. Romme, “Noncoherent Ultra-Wideband Systems” in IEEE Signal Processing Magazine, July 2009.