结构压缩感知的研究

发布时间：2018-06-21 16:19

本文选题：模拟域压缩感知 + 抗噪恢复算法　；参考：《北京邮电大学》2014年博士论文

【摘要】：压缩感知理论打破了奈奎斯特采样定理的限制,将采样与压缩合为一步,实现了低于奈奎斯特速率的采样。因此,压缩感知必将引起信号采样领域的一次革命,并将对信息论、编码、无线通信等应用科学领域产生深远的影响。结构压缩感知,是指具有结构测量矩阵的压缩感知。本论文将基于结构压缩感知,研究模拟信号采样的基本问题,即进行模拟压缩感知的研究,并探讨压缩感知在认知无线电网络和无线传感器网络中的应用,具体成果如下所述： (1)基于结构矩阵的模拟压缩感知研究：基于非调制Slepian基的时频集中特性,用非调制Slepian基表达调制带限的多带信号,从信号表达的角度提高了模拟压缩感知的恢复性能,且与调制合并的Slepian基表达整个多带信号相比,本论文所提出的方案降低了测量矩阵的维数和恢复信号的计算复杂度；基于随机循环正交矩阵的结构特性,用随机循环移位的Zadoff-Chu序列代替相互独立的伪随机序列,将原来模拟压缩感知中的硬件并行支路数目从m降到1,其中m的取值范围是几十到几百,降低了模拟压缩感知的硬件复杂度。 (2)模拟压缩感知在认知无线电宽带频谱感知中的应用：利用模拟压缩感知解决宽带频谱感知所需的极高采样速率的挑战,引入多天线技术提高宽带频谱感知在低信噪比下的检测性能；为充分利用多天线信号之间的共同稀疏特性,提出了多天线联合恢复算法,提高了信号的恢复性能；为降低噪声不确定性对频谱感知检测性能的影响,提出了一个低复杂度、高检测性能的宽带频谱感知方法,提高了频谱检测的性能。仿真结果表明,本论文所提出的多天线压缩宽带频谱感知方案,能够以低于奈奎斯特速率对宽带信号进行采样,并能在低SNR情况下取得较高的频谱检测性能。 (3)基于规则子空间的压缩感知抗噪恢复算法研究：针对稀疏信号和测量向量均受噪声污染的情况,提出了规则子空间追踪的抗噪恢复算法：通过添加一个预处理的步骤,解决了稀疏信号中的噪声在测量过程中噪声被放大的问题；通过规则化迭代过程中更新的测量矩阵中的列,使得所求得与非零元素下标所对应的测量矩阵的子矩阵,尽量满足压缩感知中的受限等距特性；采用最小均方误差算法对稀疏信号进行估计,进一步减小了噪声对恢复性能的影响。仿真结果表明,与现有的抗噪恢复算法相比,本论文所提出的算法具有最高的正确恢复信号支撑的概率和最低的归一化恢复误差。 (4)离散压缩感知在无线传感器网络中分布式数据存储的应用：分布式数据存储,是灾难环境下无线传感器网络实现可靠通信的有效方式。基于离散压缩感知与网络编码技术,通过降低分布式数据存储所需的数据发送次数与数据接收次数,提高了无线传感器网络的能效。理论分析证明,本论文所提出方案对应的测量矩阵满足压缩感知理论中保证成功恢复信号的条件。基于随机几何图论,推导了所提方案中发送次数与接收次数的表达式,并根据推得的表达式,提出了一个自适应的方案,进一步提高了无线传感器网络的能效。仿真结果表明,与现有方案相比,本论文所提出的方案具有最高的能效和最好的恢复性能。本论文的上述研究成果可以归结为,基于压缩感知解决了无线通信中存在的四个挑战：离散多频带信号的采样问题、认知无线电网络中宽带频谱感知需要极高采样速率以及低检测性能的挑战、压缩感知放大通信系统中噪声功率的问题、无线传感器网络中的高能效需求等问题。此外,国际化标准组织3GPP也在讨论压缩感知在先进长期演进(LTE-A)系统中信道估计方面的应用。相信未来,压缩感知可以更好地解决无线通信领域中一些新的挑战。
[Abstract]:Compressed sensing theory breaks the limitation of Nyquist's sampling theorem, combines sampling and compression as a step, realizes sampling below the Nyquist rate. Therefore, compression perception will certainly cause a revolution in the field of signal sampling, and will have a far-reaching impact on the application science of information theory, coding, wireless communication and other applications. Structure compression perception Based on structural compression perception, this paper will study the basic problem of analog signal sampling, that is, the research of analog compression perception, and the application of compressed sensing in cognitive radio network and wireless sensor network. The specific results are as follows:
(1) the study of analog compression based on the structure matrix: Based on the time frequency concentration characteristic of the non modulated Slepian base, the modulation band limited multi band signal is expressed by the non modulation Slepian base, and the recovery performance of the analog compressed sensing is improved from the angle of the signal expression. Compared with the Slepian based on the modulation, the whole multi band signal is expressed in this paper. The proposed scheme reduces the dimension of the measurement matrix and the computational complexity of the recovery signal. Based on the structure characteristics of the random cyclic orthogonal matrix, the random cyclic shifted Zadoff-Chu sequence is used to replace the independent pseudo random sequence, and the hardware parallel branch number of the original analog compression perception is reduced from m to 1, of which the range of M is a few. From ten to several hundred, the hardware complexity of analog compressed sensing is reduced.
(2) the application of analog compression perception in cognitive radio broadband spectrum sensing: the challenge of using analog compressed sensing to solve the high sampling rate required for broadband spectrum sensing, and introducing multi antenna technology to improve the detection performance of broadband spectrum sensing at low signal to noise ratio, and to make full use of the common sparse characteristics between multi antenna signals, In order to reduce the influence of noise uncertainty on spectrum sensing detection performance, a low complexity and high detection performance based wideband spectrum sensing method is proposed to improve the performance of the spectrum detection. The simulation results show that the multi antenna compression broadband frequency proposed in this paper has been shown in this paper. The spectrum sensing scheme can sample wideband signals below Nyquist rate and achieve high spectral detection performance at low SNR.
(3) research on the algorithm of compressed sensing anti noise recovery based on regular subspace: Aiming at the noise pollution of the sparse signal and measurement vector, an anti noise recovery algorithm for regular subspace tracking is proposed. By adding a preprocessing step, the noise in the sparse signal is amplified in the measurement process; The columns in the updated measurement matrix in the over regular iteration process make the submatrix of the measurement matrix corresponding to the non zero element subscript to meet the limited isometric characteristic in the compressed sensing. The minimum mean square error algorithm is used to estimate the sparse signal, and the influence of the noise to the recovery performance is further reduced. Simulation junction is further reduced. The results show that the algorithm proposed in this paper has the highest probability of restoring signal support and the lowest normalized recovery error compared with the existing anti noise recovery algorithm.
(4) the application of discrete compressed sensing in distributed data storage in Wireless Sensor Networks: distributed data storage is an effective way to achieve reliable communication in wireless sensor networks under disaster environment. Based on discrete compression perception and network coding technology, the number of data sent and data received by reducing distributed data storage and data receiving are reduced. The number of times improves the energy efficiency of the wireless sensor network. The theoretical analysis proves that the corresponding measurement matrix of the proposed scheme satisfies the condition of ensuring the successful recovery of the signal in the compression perception theory. Based on the random geometric graph theory, the expressions of the number of sending and receiving times in the proposed scheme are derived, and the proposed formula is proposed. An adaptive scheme further improves the energy efficiency of the wireless sensor network. The simulation results show that the proposed scheme has the highest energy efficiency and the best recovery performance compared with the existing schemes.
The above research results in this paper can be attributed to the four challenges in wireless communication based on compressed sensing: the sampling of discrete multiband signals, the challenge of high sampling rate and low detection performance in the cognitive radio network, and the noise power in the compressed sensing amplification communication system. In addition, the international standard organization 3GPP is also discussing the application of compressed sensing in the estimation of channel estimation in the advanced long term evolution (LTE-A) system. It is believed that in the future, compressed sensing can better solve some new challenges in the field of wireless communication.
【学位授予单位】：北京邮电大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.7

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