压缩感知信号检测和参数估计方法研究

发布时间：2018-07-08 17:33

本文选题：压缩采样 + 稀疏表示　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：信号采样是真实的物理世界通向数字信息世界的必经之路和必要手段,当前大多数信号的处理仍是以奈奎斯特(Nyquist)采样定理为理论基础,即为了信号在频域不发生混叠的现象,采样速率必须达到信号带宽的两倍以上。然而越来越宽的瞬时信号带宽,使得无论在信号检测还是后续参数估计时要求的信号存储空间及处理时间都面临着巨大的压力。压缩感知(Compressed Sensing)理论的出现给信号获取和处理方面提供了一种新思路。该理论指出只要信号满足稀疏性或可压缩性,都能以远低于奈奎斯特采样速率的要求得到采样值,并且保证这些采样值已然含有原始信号的必要信息,进而可在不精确重构信号的基础上直接对采样值进行信号检测和参数估计这类任务。本文中研究的压缩感知在信号检测和参数估计上的应用都是以部分重构为基础进行的,首先介绍了包括压缩感知的基本原理、处理过程和压缩感知中需要深入研究的三个核心问题。同时研究了在部分重构情况下基于压缩感知的信号检测算法及参数估计算法。压缩感知在信号检测中的应用主要研究了三种算法:基于正交匹配追踪的压缩感知信号检测算法,该算法将原始信号在变换域中的最大投影系数作为判决依据,完成信号检测,是一种基于信号部分重构思想的检测方法,改善了匹配追踪检测算法中特征量波动较大的缺点;基于稀疏系数位置信息的压缩感知信号检测算法,该算法是对正交匹配追踪检测算法中检测门限值选择时间过长影响检测性能而提出的,将求最大投影系数作为判决依据变为对两种假设下最大投影系数的位置信息进行研究,从而完成检测决策;基于采样值数字特征的压缩感知信号检测算法,该算法分析压缩感知过程的数学模型,获得了每个采样值在两种假设情况下的数字特征,将实际采样值与其在两种假设情况下数学期望的偏差作为判决依据,完成检测任务,该算法在低信噪比下依然适用。压缩感知的参数估计则是根据形态学成分分析的三种假设,对于不同信号的不同稀疏矩阵,只能唯一的表示该信号的基础上,对混合信号进行稀疏表示,使用多种字典,依据重构算法将非相关信号进行分离,只留下感兴趣信号,然后在对采样值进行处理寻找出最大系数的位置信息,从而找出字典中该位置信息对应的原子的参量即为需要估计的信号参数。
[Abstract]:Signal sampling is the only way and necessary means for the real physical world to flow to the digital information world. At present, most signal processing is still based on Nyquist sampling theorem, that is, in order to avoid the phenomenon of signal aliasing in frequency domain. The sampling rate must be more than twice the bandwidth of the signal. However, with the increasing bandwidth of the instantaneous signal, the storage space and processing time required for the signal detection and subsequent parameter estimation are under great pressure. The emergence of compressed sensing theory provides a new way for signal acquisition and processing. The theory states that as long as the signal satisfies the sparsity or compressibility, the sampling values can be obtained at a rate far lower than the Nyquist sampling rate, and ensure that these sampling values already contain the necessary information of the original signal. Furthermore, the task of signal detection and parameter estimation can be carried out directly on the basis of imprecise reconstruction of signal. In this paper, the application of compression sensing in signal detection and parameter estimation is based on partial reconstruction. Firstly, the basic principle of compression sensing is introduced. There are three core issues that need to be studied deeply in the process of processing and compression awareness. At the same time, the signal detection algorithm and parameter estimation algorithm based on compression sensing are studied in the case of partial reconstruction. The application of compression sensing in signal detection mainly studies three algorithms: the algorithm of compressed sensing signal detection based on orthogonal matching tracking, which takes the maximum projection coefficient of the original signal in the transform domain as the decision basis to complete the signal detection. It is a detection method based on the idea of signal partial reconstruction, which improves the shortcoming of feature fluctuation in matching tracking detection algorithm, and the detection algorithm of compressed perceptual signal based on sparse coefficient location information. The algorithm is put forward to study the location information of the maximum projection coefficient under two hypotheses, because the detection threshold selection time is too long and the detection performance is affected by the selection time of the detection threshold in the orthogonal matching tracking detection algorithm, which takes the maximum projection coefficient as the decision basis and is changed into the position information of the maximum projection coefficient under the two hypotheses. The algorithm analyzes the mathematical model of the compressed sensing process and obtains the digital features of each sample value under two hypotheses. Taking the deviation between the actual sampling value and its mathematical expectation under two hypotheses as the decision basis, the detection task is completed. The algorithm is still suitable for low SNR. The parameter estimation of compression perception is based on the three assumptions of morphological component analysis. For different sparse matrices of different signals, only on the basis of the unique representation of the signals, the mixed signals can be represented sparsely, using a variety of dictionaries. According to the reconstruction algorithm, the uncorrelated signal is separated, only the interested signal is left, and then the position information of the maximum coefficient is found in the processing of the sampling value. Thus, the parameters of the atom corresponding to the position information in the dictionary are the signal parameters that need to be estimated.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23

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