本文選題：模擬域壓縮感知 + 抗噪恢復(fù)算法　； 參考：《北京郵電大學(xué)》2014年博士論文

【摘要】：壓縮感知理論打破了奈奎斯特采樣定理的限制,將采樣與壓縮合為一步,實(shí)現(xiàn)了低于奈奎斯特速率的采樣。因此,壓縮感知必將引起信號(hào)采樣領(lǐng)域的一次革命,并將對(duì)信息論、編碼、無(wú)線(xiàn)通信等應(yīng)用科學(xué)領(lǐng)域產(chǎn)生深遠(yuǎn)的影響。結(jié)構(gòu)壓縮感知,是指具有結(jié)構(gòu)測(cè)量矩陣的壓縮感知。本論文將基于結(jié)構(gòu)壓縮感知,研究模擬信號(hào)采樣的基本問(wèn)題,即進(jìn)行模擬壓縮感知的研究,并探討壓縮感知在認(rèn)知無(wú)線(xiàn)電網(wǎng)絡(luò)和無(wú)線(xiàn)傳感器網(wǎng)絡(luò)中的應(yīng)用,具體成果如下所述： (1)基于結(jié)構(gòu)矩陣的模擬壓縮感知研究：基于非調(diào)制Slepian基的時(shí)頻集中特性,用非調(diào)制Slepian基表達(dá)調(diào)制帶限的多帶信號(hào),從信號(hào)表達(dá)的角度提高了模擬壓縮感知的恢復(fù)性能,且與調(diào)制合并的Slepian基表達(dá)整個(gè)多帶信號(hào)相比,本論文所提出的方案降低了測(cè)量矩陣的維數(shù)和恢復(fù)信號(hào)的計(jì)算復(fù)雜度；基于隨機(jī)循環(huán)正交矩陣的結(jié)構(gòu)特性,用隨機(jī)循環(huán)移位的Zadoff-Chu序列代替相互獨(dú)立的偽隨機(jī)序列,將原來(lái)模擬壓縮感知中的硬件并行支路數(shù)目從m降到1,其中m的取值范圍是幾十到幾百,降低了模擬壓縮感知的硬件復(fù)雜度。 (2)模擬壓縮感知在認(rèn)知無(wú)線(xiàn)電寬帶頻譜感知中的應(yīng)用：利用模擬壓縮感知解決寬帶頻譜感知所需的極高采樣速率的挑戰(zhàn),引入多天線(xiàn)技術(shù)提高寬帶頻譜感知在低信噪比下的檢測(cè)性能；為充分利用多天線(xiàn)信號(hào)之間的共同稀疏特性,提出了多天線(xiàn)聯(lián)合恢復(fù)算法,提高了信號(hào)的恢復(fù)性能；為降低噪聲不確定性對(duì)頻譜感知檢測(cè)性能的影響,提出了一個(gè)低復(fù)雜度、高檢測(cè)性能的寬帶頻譜感知方法,提高了頻譜檢測(cè)的性能。仿真結(jié)果表明,本論文所提出的多天線(xiàn)壓縮寬帶頻譜感知方案,能夠以低于奈奎斯特速率對(duì)寬帶信號(hào)進(jìn)行采樣,并能在低SNR情況下取得較高的頻譜檢測(cè)性能。 (3)基于規(guī)則子空間的壓縮感知抗噪恢復(fù)算法研究：針對(duì)稀疏信號(hào)和測(cè)量向量均受噪聲污染的情況,提出了規(guī)則子空間追蹤的抗噪恢復(fù)算法：通過(guò)添加一個(gè)預(yù)處理的步驟,解決了稀疏信號(hào)中的噪聲在測(cè)量過(guò)程中噪聲被放大的問(wèn)題；通過(guò)規(guī)則化迭代過(guò)程中更新的測(cè)量矩陣中的列,使得所求得與非零元素下標(biāo)所對(duì)應(yīng)的測(cè)量矩陣的子矩陣,盡量滿(mǎn)足壓縮感知中的受限等距特性；采用最小均方誤差算法對(duì)稀疏信號(hào)進(jìn)行估計(jì),進(jìn)一步減小了噪聲對(duì)恢復(fù)性能的影響。仿真結(jié)果表明,與現(xiàn)有的抗噪恢復(fù)算法相比,本論文所提出的算法具有最高的正確恢復(fù)信號(hào)支撐的概率和最低的歸一化恢復(fù)誤差。 (4)離散壓縮感知在無(wú)線(xiàn)傳感器網(wǎng)絡(luò)中分布式數(shù)據(jù)存儲(chǔ)的應(yīng)用：分布式數(shù)據(jù)存儲(chǔ),是災(zāi)難環(huán)境下無(wú)線(xiàn)傳感器網(wǎng)絡(luò)實(shí)現(xiàn)可靠通信的有效方式。基于離散壓縮感知與網(wǎng)絡(luò)編碼技術(shù),通過(guò)降低分布式數(shù)據(jù)存儲(chǔ)所需的數(shù)據(jù)發(fā)送次數(shù)與數(shù)據(jù)接收次數(shù),提高了無(wú)線(xiàn)傳感器網(wǎng)絡(luò)的能效。理論分析證明,本論文所提出方案對(duì)應(yīng)的測(cè)量矩陣滿(mǎn)足壓縮感知理論中保證成功恢復(fù)信號(hào)的條件�；陔S機(jī)幾何圖論,推導(dǎo)了所提方案中發(fā)送次數(shù)與接收次數(shù)的表達(dá)式,并根據(jù)推得的表達(dá)式,提出了一個(gè)自適應(yīng)的方案,進(jìn)一步提高了無(wú)線(xiàn)傳感器網(wǎng)絡(luò)的能效。仿真結(jié)果表明,與現(xiàn)有方案相比,本論文所提出的方案具有最高的能效和最好的恢復(fù)性能。 本論文的上述研究成果可以歸結(jié)為,基于壓縮感知解決了無(wú)線(xiàn)通信中存在的四個(gè)挑戰(zhàn)：離散多頻帶信號(hào)的采樣問(wèn)題、認(rèn)知無(wú)線(xiàn)電網(wǎng)絡(luò)中寬帶頻譜感知需要極高采樣速率以及低檢測(cè)性能的挑戰(zhàn)、壓縮感知放大通信系統(tǒng)中噪聲功率的問(wèn)題、無(wú)線(xiàn)傳感器網(wǎng)絡(luò)中的高能效需求等問(wèn)題。此外,國(guó)際化標(biāo)準(zhǔn)組織3GPP也在討論壓縮感知在先進(jìn)長(zhǎng)期演進(jìn)(LTE-A)系統(tǒng)中信道估計(jì)方面的應(yīng)用。相信未來(lái),壓縮感知可以更好地解決無(wú)線(xiàn)通信領(lǐng)域中一些新的挑戰(zhàn)。
[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.
【學(xué)位授予單位】：北京郵電大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TN911.7

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