快速滤波器组在数字信号处理中的应用研究

论文总字数：39519字

摘 要

随着无线通信技术的不断发展，频谱资源也被日渐消耗。因此，人们提出认知无线电(Cognitive Radio，CR)技术以解决日益紧张的频谱资源矛盾。认知无线电与普通的无线电技术相比，结合了人工智能，具有自主学习能力，可以感知并利用所在空间的可用频谱，降低冲突的发生。在CR中，不得不提的一项技术就是频谱感知技术(Spectrum Sensing)。频谱感知往往需要精度较高的频率估计算法来为后续的频谱分析工作做准备。本文则对基于快速滤波器组的频率估计算法，开展了以下工作：

首先，介绍了频谱资源被日渐消耗的当前局面以及认知无线电的基本概念。对认知无线电中的关键技术——频率估计的研究背景和现状作出了详细介绍。介绍了快速滤波器组（Fast Filter Bank，FFB）的研究现状，并且分析了和快速傅里叶变换（Fast Fourier Transform，FFT）相比，快速滤波器组拥有的优越性。

然后，介绍了快速滤波器组的基础理论，首先给出了FFT滤波器组的详细推导，并在这基础上，分析了FFT滤波器组的局限性，提出了性能更优的FFB。然后给出了快速滤波器组中各级子滤波器的关系和快速滤波器组的构造方法，提出了一种快速滤波器组原型滤波器低复杂度优化设计方法和具体实现步骤。

接着，详细推导了近年来提出的比较经典的几种频率估计算法，对这些算法的性能做出了比较和评估。包括自适应直接频率估计算法（Adaptive algorithm for direct frequency， DFE）、修正协方差算法（Modified Covariance， MC）、Pisarenko谐波分解算法（Pisarenko harmonic decomposition，PHD）以及改进的Pisarenko谐波分解算法（Reformed Pisarenko harmonic decomposition，RPHD）。

最后，研究了基于离散傅里叶变换的频率估计算法，并在这基础上，提出复数最小二乘算法予以改进。然后把快速滤波器组替换离散傅里叶变换，进行频率估计。相似的，依然采用复数最小二乘法进行改进以进一步提高其频率估计性能。

关键词：频谱感知，频率估计，快速滤波器组，复数最小二乘法

Abstract

With the development of communications ，frequency spectrum resource is increasingly consumed. In order to solve the problem, cognitive radio (CR) is proposed, whose important component is spectrum sensing, which needs high precision frequency estimation algorithm to complete the spectrum analysis. The frequency estimation algorithms based on filter bank in this paper are organized as follows:

Firstly, this paper introduces the current situation of spectrum resource which is being increasingly consumed and the basic concept of cognitive radio. The research background and the current situation of frequency estimation ,the key technology of cognitive radio, are introduced in detail. And then, the current situation of Filter Bank Fast (FFB) is introduced, and the advantages of fast filter banks are compared with the Fast Fourier Transform( FFT).

Then, the basic theory of fast filter banks is introduced, the detailed derivation of FFT filter banks is given, and the limitations of FFT filter banks are analyzed, and the performance of FFB filter banks is proposed. Then the relationship of the every sub filter in fast filter bank and construction method of fast filter bank are given. Finally, it puts forward optimal design method and the specific implementation steps of the prototype filter of fast filter bank with low complexity .

Thirdly, several frequency estimation algorithms proposed in recent years based on the time domain and frequency domain are studied, consists of adaptive algorithm for direct frequency (DFE), modified covariance method (MC), Pisarenko harmonic decomposition (PHD), reformed Pisarenko harmonic decomposition (RPHD) .

Finally, the frequency estimation algorithm based on discrete Fourier transform is studied, and the complex least squares algorithm(CLS) is proposed to improve the performance of the algorithm. Then the discrete Fourier transform is replaced by fast filter bank, and the frequency estimation is performed. Similarly, the complex least square method is used to improve its frequency estimation performance.

Keywords: Spectrum sensing, Frequency estimation, Fast filter bank, Complex-valued least squares

目录

摘要 I

Abstract II

目录 III

第一章 绪论 1

1.1 研究背景 1

1.2 国内外研究现状 2

1.2.1频率估计国内外研究现状 2

1.2.2 快速滤波器组国内外研究现状 2

1.3 研究内容 3

1.4 论文结构安排 4

第二章 快速滤波器组研究及实现 5

2.1 FFT滤波器组 5

2.2快速滤波器组（FFB） 6

2.2.1快速滤波器组（FFB）及其树形结构 6

2.2.2 FFB原型滤波器低复杂度优化设计 7

2.3 本章小结 10

第三章 经典频率估计算法研究 11

3.1 自适应直接频率估计算法 11

3.2 修正协方差算法 15

3.3 Pisarenko谐波分解算法 15

3.4 改进的Pisarenko谐波分解算法 16

3.5 本章小结 22

第四章 基于DFT和FFB的频率估计算法 23

4.1基于DFT的单频实正弦信号频率估计 23

4.2 基于FFB的单频实正弦频率估计 26

4.3 本章小结 28

第五章 总结与展望 29

参考文献 30

致谢 33

1. 绪论

研究背景

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