Publication: Algoritmos para la reducción de los picos de potencia en los sistemas OFDM
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2014-12
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2014-12-05
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Abstract
La modulación OFDM (Orthogonal Frequency Division Multiplexing) es una técnica de
transmisión multiportadora, que debido a sus grandes ventajas se utiliza en numerosos estándares de comunicaciones de banda ancha. Sin embargo, uno de los principales inconvenientes que presenta la modulación OFDM, en el lado transmisor, es la presencia ocasional de grandes picos en su potencia instantánea con respecto a su potencia media, conocido en la literatura como el problema de la PAPR (Peak-to-Average Power Ratio) de los sistemas OFDM.
Al pasar la señal con PAPR elevada por el amplificador de alta potencia (HPA - High
Power Amplifier ) se produce saturación del dispositivo, provocando radiación fuera de banda, que afecta a las bandas adyacentes, y radiación dentro de banda, que produce rotación, atenuación y desplazamiento de la señal, provocando un incremento en la tasa de error de bit (BER - Bit Error Rate). Para contrarrestar estos efectos, se debe reducir la PAPR de la senñal OFDM transmitida con algún tipo de manipulación en la señal.
Una de las técnicas de reducción de la PAPR más prometedoras es la técnica CE (Constellation Extension), que mueve inteligentemente ciertos puntos externos de la constelación del símbolo OFDM en el dominio de la frecuencia, de tal forma que la señal en el dominio del tiempo tenga una PAPR menor. La extensión de la constelación de esta forma no afecta a la distancia mínima de la constelación y, consecuentemente, no se experimenta degradación en la BER del sistema. Además, no hay pérdida en la tasa de transmisión de datos porque no se requiere la transmisión de información de control. Sin embargo, se introduce un incremento de la energía por símbolo.
El objetivo principal de esta Tesis es proponer varios algoritmos de reducción de la PAPR, basados en técnicas CE. Por un lado, como primer objetivo (capítulo 4) se presentan algoritmos eficientes en energía, que se consiguen al combinar adecuadamente un esquema CE, basado en métrica, con secuencias piloto. Dicha combinación deja tres posibles arquitecturas de implementación dependiendo del orden en que se usa cada algoritmo. Se determina la arquitectura que proporciona un compromiso adecuado entre reducción de la PAPR y complejidad, esta última medida en términos del número de ciclos adicionales del procesador (que se traducen en energía consumida) que se requieren para procesar la reducción de la PAPR. Además, se demuestra que las tres arquitecturas propuestas demandan una energía
por símbolo menor que otras técnicas CE, si se insertan adecuadamente las secuencias piloto en el símbolo OFDM Por otro lado, como segundo objetivo se presentan los esquemas de reducción de la PAPR, basados en técnicas CE, que se formulan como problemas de optimización (capítulo 5). Se propone una solución óptima, en térrminos de reducción de la PAPR, llamada algoritmo GBDCE (Generalized Benders Decomposition for Constellation Extension), el cual se plantea
como un problema no lineal mixto-entero (MINLP - Mixed Integer Non-Linear Programming) y que sirve como cota inferior de referencia para comparar con otras técnicas CE. Además, se proponen los algoritmos subóptimos: BBCE (Branch-and-Bound for Constellation Extension) que se formula como un problema de programación entera, y DCE (Dynamic Constellation Extension) que combina un esquema BBCE con un algoritmo basado en métrica. El objetivo de ambos algoritmos subóptimos es reducir la complejidad del algoritmo óptimo.
OFDM (Orthogonal Frequency Division Multiplexing) modulation is a multicarrier transmission technique that, due to its important advantages, has been widely used in many wideband communication standards. However, one of the major drawbacks of the transmitted OFDM signal is the infrequent high peak power with respect to average power, which is known in the literature as the PAPR (Peak-to-Average Power Ratio) problem in OFDM systems. When the signal with high PAPR passes through an HPA (High Power Amplifier), it suffers from saturation, which causes both out-of-band radiation, that affects the adjacent channels, and in-band radiation, which produces rotation, attenuation and shift of the signal, that increases the BER (Bit Error Rate). In order to address the PAPR problem, the OFDM signal must be manipulated. One of the most promising PAPR techniques is CE (Constellation Extension), that intelligently moves certain outer constellation points of the OFDM signal in the frequency domain, in such way that the OFDM signal in the time domain has a lower PAPR. The constellation extension in this way does not affect the minimum distance of the constellation, and BER degradation is not consequently experienced by the system. Moreover, there is no user's data rate loss because these methods do not require side information. Nevertheless, they introduce an increase in the energy per symbol. The main aim of this Thesis is to propose several PAPR reduction algorithms, based on CE techniques. On one side, the first objective (chapter 4) is to present an energy efficient algorithm, which consists in the adequate combination of a metric-based CE technique with pilot sequences. The combination allows three possible implementation architectures, depending on the order of use of the algorithms. It has been determined the architecture that provides an adequate trade-o_ between PAPR reduction and complexity, the latter measured in number of additional CPU cycles (which translates into energy consumption) needed to perform the PAPR reduction. Moreover, the three proposed architectures require less energy per symbol than other CE techniques, if the pilot sequences are appropriately inserted in the OFDM symbol. On the other side, the second objective is to present CE based algorithms, which are formulated as an optimization problem (chapter 5). The optimal solution, in terms of PAPR reduction is called GBDCE (Generalized Benders Decomposition for Constellation Extension) algorithm. GBDCE is formulated as a MINLP (Mixed Integer Non-Linear Programming) problem, and it turns out to be a lower bound for CE schemes and provides a benchmark to compare with other CE technique. Moreover, two suboptimal algorithms are proposed: BBCE (Branch-and-Bound for Constellation Extension), which is formulated as Integer Programming, and DCE (Dynamic Constellation Extension), that combines a BBCE scheme with a metric-based algorithm. The objective of both suboptimal algorithms is to reduce the GBDCE complexity.
OFDM (Orthogonal Frequency Division Multiplexing) modulation is a multicarrier transmission technique that, due to its important advantages, has been widely used in many wideband communication standards. However, one of the major drawbacks of the transmitted OFDM signal is the infrequent high peak power with respect to average power, which is known in the literature as the PAPR (Peak-to-Average Power Ratio) problem in OFDM systems. When the signal with high PAPR passes through an HPA (High Power Amplifier), it suffers from saturation, which causes both out-of-band radiation, that affects the adjacent channels, and in-band radiation, which produces rotation, attenuation and shift of the signal, that increases the BER (Bit Error Rate). In order to address the PAPR problem, the OFDM signal must be manipulated. One of the most promising PAPR techniques is CE (Constellation Extension), that intelligently moves certain outer constellation points of the OFDM signal in the frequency domain, in such way that the OFDM signal in the time domain has a lower PAPR. The constellation extension in this way does not affect the minimum distance of the constellation, and BER degradation is not consequently experienced by the system. Moreover, there is no user's data rate loss because these methods do not require side information. Nevertheless, they introduce an increase in the energy per symbol. The main aim of this Thesis is to propose several PAPR reduction algorithms, based on CE techniques. On one side, the first objective (chapter 4) is to present an energy efficient algorithm, which consists in the adequate combination of a metric-based CE technique with pilot sequences. The combination allows three possible implementation architectures, depending on the order of use of the algorithms. It has been determined the architecture that provides an adequate trade-o_ between PAPR reduction and complexity, the latter measured in number of additional CPU cycles (which translates into energy consumption) needed to perform the PAPR reduction. Moreover, the three proposed architectures require less energy per symbol than other CE techniques, if the pilot sequences are appropriately inserted in the OFDM symbol. On the other side, the second objective is to present CE based algorithms, which are formulated as an optimization problem (chapter 5). The optimal solution, in terms of PAPR reduction is called GBDCE (Generalized Benders Decomposition for Constellation Extension) algorithm. GBDCE is formulated as a MINLP (Mixed Integer Non-Linear Programming) problem, and it turns out to be a lower bound for CE schemes and provides a benchmark to compare with other CE technique. Moreover, two suboptimal algorithms are proposed: BBCE (Branch-and-Bound for Constellation Extension), which is formulated as Integer Programming, and DCE (Dynamic Constellation Extension), that combines a BBCE scheme with a metric-based algorithm. The objective of both suboptimal algorithms is to reduce the GBDCE complexity.
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Keywords
Modulación OFDM, Comunicaciones de banda ancha, Peak-to-Average Power Ratio, PAPR, Picos de potencia, Algoritmos de reducción