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摘要压缩感知（Compressed Sensing, CS）理论的出现突破了传统Nyquist信号采样理论,可以低速采样获取宽带信号信息，在宽带频谱感知中具有广泛的应用。调制宽带变换器（Modulated Wideband Converter, MWC）是建立在CS理论基础上针对于多频带信号进行采样的模型，具有很高的实用性。然而MWC系统采用多通道采样结构，每一通道需要独立的伪随机编码信号进行混频，增大了硬件存储量和计算复杂度。本文针对MWC的上述问题，提出利用移位寄存器实现多路伪随机编码，以简化MWC系统结构。在本文设计的简化结构中，利用移位寄存器对一组伪随机码进行移位操作，通过一些变换将生成的多个伪随机码作为混频信号与输入信号混频，以获得宽带信号的随机观测。本文通过仿真验证了MWC简化结构的可行性及其信号重构性能。仿真表明，本文所提出的结构可有效简化MWC系统结构，实现与MWC相一致的宽带频谱感知性能。41678
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关键字：压缩感知 调制宽带变换器 测量矩阵 重构算法
毕业论文设计说明书外文摘要
Title A Simplified Structure Design for Modulated Wideband Converter
Abstract
The emergence of compressed sensing (CS) has broken through the bottleneck of the conventional Nyquist sampling theorem. It can acquire information from wideband signals at a low rate and is widely used in wideband spectrum sensing. The modulated wideband converter (MWC) is a system designed to process multiband signals based on CS theory and turns out to be of high practicality. The MWC consists of several channels and each channel mixes the input signal with an independent pseudorandom sequence. Therefore, this structure increases the memory requirement and computational load greatly. In this paper, we propose to implement the multichannel structure with a shift register to simplify the structure of MWC. In the simplified structure, we use the shift register to generate many pseudorandom sequences by shifting a pseudorandom sequence. After some transformation, those pseudorandom sequences are mixed with the input signal to acquire random measurements. The feasibility of the simplified MWC structure and its reconstruction performance are analyzed by numerical simulations. It is shown that the proposed structure can simplify the MWC system efficiently and perform as well as the original MWC in wideband spectrum sensing.
Keywords Compressed Sensing(CS) Modulated Wideband Converter(MWC)
Measurement Matrix Recovery Algorithms
目 次
1 引言 1
1.1 压缩感知基础理论 1
1.2 模拟信息转换器 3
1.3 章节安排 5
2 调制宽带变换器（MWC）基本原理 6
2.1 信号模型 6
2.2 信号观测 7
2.3 信号重构 10
3 MWC系统简化结构设计 12
3.1 原理及框图 12
3.2 信号观测与重构方法 14
3.3 仿真结果 19
结论 26
致谢 28
参考文献 29
1 引言
1.1 压缩感知基础理论
信号的传统采样方法需满足香农/奈奎斯特采样定理，即采样速率要不低于信号带宽的两倍,才能无失真地重构出原始信号[1]。在一些实际应用中，输入信号的最大频率，已经超出现有设备能够处理的范围。因此，宽带模拟信号的采样处理往往需要很高的采样速率，大大增加了数据的采集、存储负担以及硬件成本。采样理论——由模拟通往数字的大门，需要突破现有采样速率的瓶颈[2]。2004年，D.Donoho、 E.Candes等人针对稀疏性信号建立了压缩感知（Compressed Sensing, CS）的理论框架。CS理论表明，如果信号在经过某种变换后,是可稀疏表示或是可压缩的，则可以远低于奈奎斯特采样率的速率对其进行全局观测，然后求解一个优化问题来高概率地重构信号[3]。下面分别从信号的稀疏表示，测量矩阵的设计原则以及信号重构算法三个方面对CS理论进行简要介绍。