【信息技术】【2011.12】【含源码】移动通信系统中语音信号的压缩感知

本文为美国德克萨斯大学泰勒分校（作者：SABIR AHMED）的硕士论文，共61页。

压缩感知是一种新兴的革命性技术，它强烈依赖于信号的稀疏性。在压缩感知中，通过对信号进行少量的随机投影实现稀疏的压缩采样，这些投影包含了大部分的显著信息。压缩感知技术已经在图像处理、雷达系统和声纳系统等领域得到了广泛的应用。这项研究工作将讨论压缩感知在移动通信系统中的潜在实现，以及它将如何影响其数据速率。

在典型的移动通信系统中，感兴趣的信号至少应当以奈奎斯特速率采样。奈奎斯特采样定理规定，用于信号的采样频率至少应为信号中包含的最大频率的两倍。然而，这不是压缩信号的最有效方法，因为它在对整个信号进行采样时会带来很大的负担，实际上只需要很小比例的变换系数来表示它。压缩采样（也称为压缩感知）的最新结果提供了一种用最少的观测值重建原始信号的新方法。在压缩感知中，直接获取有关信号/图像的重要信息，而不是获取最终会被丢弃的信息。

本研究的目的是提出一种新的移动通信系统，该系统采用压缩采样技术对发射机的语音信号进行压缩，并在接收机处对其进行解压缩。该系统的预期结果将是这些系统的传输数据速率增加。为了模拟压缩感知的应用，在MATLAB中记录了一小段语音信号。然后，发射机上的信号乘以测量矩阵，在这种情况下，测量矩阵由随机生成的数字组成。选择测量矩阵的方法是使用可行的不同优化技术之一，在接收机上再精确地恢复稀疏信号。一旦信号经过压缩采样过程，就可以通过移动通信系统进行传输，然后，通过使用任何可用的优化技术，接收机从大量样本中重建发射的信号。该算法在MATLAB中进行了仿真，结果表明，在传输的语音信号中，如果采用阈值窗口的方式，且信号长度保持不变，则语音信号的压缩率会提高。

Compressive sensing is an emerging andrevolutionary technology that strongly relies on the sparsity of the signal. Incompressive sensing the signal is sparsely compressively sampled by taking asmall number of random projections of the signal, which contain most of thesalient information. Compressive sensing has been previously applied in areaslike: image processing, radar systems and sonar systems. This research workwill discuss the potential implementation of compressive sensing in mobilecommunication systems and how it will influence their data rates.

In a typical mobile communication system,the signal of interest is sampled at least at the Nyquist rate. The Nyquistsampling theorem states that the frequency used to sample a signal should be atleast twice the maximum frequency contained within the signal. However, this isnot the most efficient way to compress the signal, as it places a lot of burdenin sampling the entire signal while only a small percentage of the transformcoefficients are needed to represent it. The recent results in compressivesampling (also known as compressive sensing) provide a new way to reconstructthe original signal with a minimal number of observations. In compressivesensing the significant information about the signal/image is directlyacquired, rather than acquiring the significant information that will beeventually thrown away.

The goal of this research is to propose anew mobile communication system which employs compressive sampling to compressthe speech signal at the transmitter and decompress it at the receiver. Theexpected results from the proposed system will be an increment in the datarates of these systems. In order to simulate how compressive sensing could beapplied, a small speech signal was recorded in MATLAB. The signal at thetransmitter is then multiplied by the measurement matrix which in this case iscomposed of randomly generated numbers. The measurement matrix is chosen insuch a way that the sparse signal can be exactly recovered at the receiverusing one of the different optimization techniques available. Once the signalhas gone through the process of compressive sampling, it is ready to betransmitted through the mobile system. The transmitted signal is thenreconstructed by the receiver from a significantly small number of samples byusing any of the multiple optimization techniques available. The algorithm issimulated in MATLAB. The results show that if a threshold window is applied tothe transmitted speech signal and the length of the signal is kept constant,the compression rate of the speech signal is increased.

1 引言
2 课题背景
3 分析与设计
4 研究结果
5 结论与未来工作展望
附录A 移动通信系统中基于压缩感知的语音信号采样的MATLAB代码（随机测量矩阵）
附录B 移动通信系统中基于压缩感知的语音信号采样的MATLAB代码（预定义测量矩阵）
附录C 通过randraw函数采样拉普拉斯语音信号的MATLAB代码
附录D 基于小波压缩的MATLAB测试信号
附录E 基于L1最小化技术语音重建技术的MATLAB代码

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