UWB Echo Signal Detection With Ultra-Low Rate Sampling Based on Compressed Sensing

A major challenge in ultra-wide-band (UWB) signal processing is the requirement for very high sampling rate. The recently emerging compressed sensing (CS) theory makes processing UWB signal at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on the CS theory, a system for sampling UWB echo signal at a rate much lower than Nyquist rate and performing signal detection is proposed in this paper. First, an approach of constructing basis functions according to matching rules is proposed to achieve sparse signal representation because the sparse representation of signal is the most important precondition for the use of CS theory. Second, based on the matching basis functions and using analog-to-information converter, a UWB signal detection system is designed in the framework of the CS theory. With this system, a UWB signal, such as a linear frequency-modulated signal in radar system, can be sampled at about 10% of Nyquist rate, but still can be reconstructed and detected with overwhelming probability. The simulation results show that the proposed method is effective for sampling and detecting UWB signal directly even without a very high-frequency analog-to-digital converter.     

基于特征值能量的压缩采样信号检测方法

压缩采样能够较好地保持稀疏信号的结构和信息,可以在不重构原信号的条件下,直接处理采样数据完成信号检测。本文针对压缩采样信号的盲检测问题,提出一种基于特征值能量的检测算法。该算法对循环频率等于零时的循环自相关矩阵进行分析并实现重构,进而利用分解得到的特征值构造检测统计量,通过研究检测统计量的分布情况确定检测门限,最终实现检测判决。实验结果表明,在相同条件下,该算法具有更好的检测性能和相对低的复杂度。      

基于压缩感知的定位新型UWB信号抽样方法

Ultra-wide-band (UWB) signals are suitable for localization, since their high time resolution can provide precise time of arrival (TOA) estimation. However, one major challenge in UWB signal processing is the requirement of high sampling rate which leads to complicated signal processing and expensive hardware. In this paper, we present a novel UWB signal sampling method called UWB signal sampling via temporal sparsity (USSTS). Its sampling rate is much lower than Nyquist rate. Moreover, it is implemented in one step and no extra processing unit is needed. Simulation results show that USSTS can not recover the signal precisely, but for the use in localization, the accuracy of TOA estimation is the same as that in traditional methods. Therefore, USSTS gives a novel and effective solution for the use of UWB signals in localization.     

基于压缩感知的信号重构研究

按照Nyquist采样定理,信号的采样率必须为信号最高频率的2倍以上,这会产生大量的冗余数据。压缩感知是一种新兴的采样理论,对于可以稀疏表示的信号,它能够以远低于Nyquist采样速率对信号进行采样,并通过优化算法实现重构。介绍了压缩感知的基本理论,并分别选取时域稀疏、频域稀疏和图像信号进行了仿真分析,实验结果显示,压缩感知理论能较好的重构原始信号。     

基于压缩感知的红外与可见光图像融合算法

压缩感知是一种新的信号采样理论,突破了传统的Nyquist采样率须为信号最高频率的2倍以上的定理。对于稀疏信号,它能够以远低于Nyquist采样速率对信号进行采样,并通过重构算法恢复出原信号。提出了一种基于压缩感知的红外与可见光图像融合算法,对图像进行测量,并通过融合算法对测量值进行融合。仿真实验显示,压缩感知能较好地实现图像的融合。     

An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.     

基于压缩传感的重构算法研究

传统的奈奎斯特采样定理规定采样率必须是频率带宽两倍,浪费大量采样资源。如果信号可以稀疏表示,那么可以采用压缩传感技术重构原始信号,压缩传感能在采样的同时对数据进行适当压缩,节省系统资源。现存的压缩传感重构算法对图像边缘和纹理的重构效果都不太理想,提出一种基于全变差的图像重构算法,该算法能稳定有效地重构图像的边缘和纹理。     

基于压缩感知的脉冲超宽带信号检测

传统的信号检测算法基于奈奎斯特采样定理来实现,这对于带宽极宽的超宽带(ultra-wideband,UWB)信号而言由于要求采样速率过高而很难用硬件去实现。为此,本文研究了基于压缩感知(compressive sensing,CS)的脉冲超宽带(impulse radio UWB, IR-UWB)信号检测问题,利用IR鄄UWB 信号在时域上的稀疏特性,设计了一种基于压缩感知的IR鄄UWB 信号检测框架,在此基础上提出了一种自适应加权正交匹配追踪检测算法。仿真结果表明,新算法不仅能够通过远少于奈奎斯特定理所要求的采样速率检测出IR-UWB 信号,而且与基于匹配追踪的压缩感知检测算法相比,新算法在低信噪比的情况下对IR-UWB 信号的检测效果更佳。     

基于欠奈奎斯特采样的超宽带信号总体最小二乘重建算法

该文针对超宽带无线通信中需要设计高速模数转换器的问题,提出了一种欠奈奎斯特采样方法,该方法所要求的采样率仅与信号新息率相关,低于奈奎斯特率1个数量级。基于欠采样得到的离散时间超宽带信号,从理论上推导出信号的傅里叶频谱表达式,由此给出了一种总体最小二乘参数估计算法,能够准确地估计出冲激串信号的幅度和时移;通过将估计出的冲激串信号与高斯单脉冲波形卷积,完成超宽带信号的波形重建。仿真和实验结果表明,该文算法能够准确地重建原始超宽带信号,且算法性能优于现有的零化滤波重建算法。     

Sub‐Nyquist rate ADC sampling‐based compressive channel estimation

To realize high‐speed communication, broadband transmission has become an indispensable technique in the next‐generation wireless communication systems. Broadband channel is often characterized by the sparse multipath channel model, and significant taps are widely separated in time, and thereby, a large delay spread exists. Accurate channel state information is required for coherent detection. Traditionally, accurate channel estimation can be achieved by sampling the received signal with large delay spread by analog‐to‐digital converter (ADC) at Nyquist rate and then estimate all of channel taps. However, as the transmission bandwidth increases, the demands of the Nyquist sampling rate already exceed the capabilities of current ADC. In addition, the high‐speed ADC is very expensive for ordinary wireless communication. In this paper, we present a novel receiver, which utilizes a sub‐Nyquist ADC that samples at much lower rate than the Nyquist one. On the basis of the sampling scheme, we propose a compressive channel estimation method using Dantzig selector algorithm. By comparing with the traditional least square channel estimation, our proposed method not only achieves robust channel estimation but also reduces the cost because low‐speed ADC is much cheaper than high‐speed one. Computer simulations confirm the effectiveness of our proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Sampling, data transmission, and the Nyquist rate

The sampling theorem for bandlimited signals of finite energy can be interpreted in two ways, associated with the names of Nyquist and Shannon. 1) Every signal of finite energy and bandwidth W Hz may be completely recovered, in a simple way, from a knowledge of its samples taken at the rate of 2W per second (Nyquist rate). Moreover, the recovery is stable, in the sense that a small error in reading sample values produces only a correspondingly small error in the recovered signal. 2) Every square-summable sequence of numbers may be transmitted at the rate of 2W per second over an ideal channel of bandwidth W Hz, by being represented as the samples of an easily constructed band-limited signal of finite energy. The practical importance of these results, together with the restrictions implicit in the sampling theorem, make it natural to ask whether the above rates cannot be improved, by passing to differently chosen sampling instants, or to bandpass or multiband (rather than bandlimited) signals, or to more elaborate computations. In this paper we draw a distinction between reconstructing a signal from its samples, and doing so in a stable way, and we argue that only stable sampling is meaningful in practice. We then prove that: 1) stable sampling cannot be performed at a rate lower than the Nyquist, 2) data cannot be transmitted as samples at a rate higher than the Nyquist, regardless of the location of sampling instants, the nature of the set of frequencies which the signals occupy, or the method of construction. These conclusions apply not merely to finite-energy, but also to bounded, signals.     

基于光谱稀疏模型的高光谱压缩感知重构

提出了一种基于光谱稀疏化的压缩感知采样与重构模型,通过从训练样本中构建光谱稀疏字典提升光谱稀疏化效果,同时在重构时兼顾空间图像的全变分约束进一步提升重构精度.对200波段AVIRIS高光谱场景进行压缩感知重构的实验表明,利用构建的光谱稀疏字典与传统的DCT字典和Haar小波字典相比光谱稀疏化效果明显提升,同时在25%采样下基于光谱稀疏字典几乎无差别重构出了高光谱图像,同样条件下在空间和光谱的精度与现有常用方法相比有较大的提升.     

基于稀疏优化的图像压缩感知重建算法

在信号的稀疏表示方法中,传统的基于变换基的稀疏逼近不能自适应性地提取图像的纹理特征,而基于过完备字典的稀疏逼近算法复杂度过高.针对该问题,文章提出了一种基于小波变换稀疏字典优化的图像稀疏表示方法.该算法在图像小波变换的基础上构建图像过完备字典,利用同一场景图像的小波变换在纹理上具有内部和外部相似的属性,对过完备字典进行灰色关联度的分类,有效提高了图像表示的稀疏性.将该新算法应用于图像信号进行稀疏表示,以及基于压缩感知理论的图像采样和重建实验,结果表明新算法总体上提升了重建图像的峰值信噪比与结构相似度,并能有效缩短图像重建时间.     

Sparse Sampling of Signal Innovations [Theory, algorithms, and performance bounds]

Sparse sampling of continuous-time sparse signals is addressed. In particular, it is shown that sampling at the rate of innovation is possible, in some sense applying Occam's razor to the sampling of sparse signals. The noisy case is analyzed and solved, proposing methods reaching the optimal performance given by the Cramer-Rao bounds. Finally, a number of applications have been discussed where sparsity can be taken advantage of. The comprehensive coverage given in this article should lead to further research in sparse sampling, as well as new applications. One main application to use the theory presented in this article is ultra-wide band (UWB) communications.     

High‐resolution compressive channel estimation for broadband wireless communication systems

Broadband channel is often characterized by a sparse multipath channel where dominant multipath taps are widely separated in time, thereby resulting in a large delay spread. Accurate channel estimation can be done by sampling received signal with analog‐to‐digital converter (ADC) at Nyquist rate and then estimating all channel taps with high resolution. However, these Nyquist sampling‐based methods have two main disadvantages: (i) demand of the high‐speed ADC, which already exceeds the capability of current ADC, and (ii) low spectral efficiency. To solve these challenges, compressive channel estimation methods have been proposed. Unfortunately, those channel estimators are vulnerable to low resolution in low‐speed ADC sampling systems. In this paper, we propose a high‐resolution compressive channel estimation method, which is based on sampling by using multiple low‐speed ADCs. Unlike the traditional methods on compressive channel estimation, our proposed method can approximately achieve the performance of lower bound. At the same time, the proposed method can reduce communication cost and improve spectral efficiency. Numerical simulations confirm our proposed method by using low‐speed ADC sampling. Copyright © 2012 John Wiley & Sons, Ltd.     

稀疏多带信号的压缩采样技术的研究

实现宽带压缩采样的结构有多种类型,在分析调制宽带转换器的采样结构的原理的基础上,针对稀疏多带信号的压缩采样,搭建了四通道的宽带压缩采样系统的原型系统平台,其中,混频调制信号是现场可编程门阵列硬件电路产生的序列。采用稀疏多频带信号作为系统的输入测试信号,并且利用另一已知的稀疏多带信号作为系统的同步信号,对宽带压缩采样原型系统进行系统仿真。该系统中的混频调制信号容易生成、实现结构简单、参数设置灵活。软件仿真及硬件测试,验证了该宽带压缩采样系统的硬件平台的正确性和可行性。     

基于压缩感知稀疏信号重建的迭代硬阀值算法

Nyquist采样速率条件下的信号采样,采样系统表现良好并且信号可以被稀疏向量近似表示时,信号可以被有效而精确地重构。针对无噪声信号,利用确定的稀疏基和随机的观测矩阵,研究迭代硬阀值算法的有效性。若观测矩阵满足有限等距性质（RIP）,且稀疏基与随机观测矩阵不相干时,通过该算法,原始信号的稀疏投影可以被高概率重构。最后,利用哈达码正交矩阵作为稀疏基,高斯随机矩阵作为观测矩阵,对原始信号的稀疏投影进行重构,结果验证了该算法的有效性。     

CS与GPR联合反演目标成像

压缩传感(CS)理论是在已知信号具有稀疏性或可压缩性的条件下对信号数据进行采集、编解码的新理论。压缩传感采用非自适应线性投影来保持信号的原始结构,能通过数值最优化问题准确重构原始信号。压缩传感以远低于奈奎斯特频率进行采样,在高分辨压缩成像系统、视频图像采集系统、雷达成像以及MRI医疗成像等领域有着广阔的应用前景。阐述了压缩传感理论框架以及信号稀疏表示、CS编解码模型,并进行了压缩传感与探地雷达联合反演目标成像。反演结果表明,随机孔径压缩传感成像算法比递归反向投影算法和最小二乘法所需数据量少,成像效果好,目标旁瓣小,对噪声的鲁棒性更好。     

Compressive Sampling and Lossy Compression [Do random measurements provide an efficient method of representing sparse signals?]

Recent results in compressive sampling have shown that sparse signals can be recovered from a small number of random measurements. This property raises the question of whether random measurements can provide an efficient representation of sparse signals in an information-theoretic sense. Through both theoretical and experimental results, we show that encoding a sparse signal through simple scalar quantization of random measurements incurs a significant penalty relative to direct or adaptive encoding of the sparse signal. Information theory provides alternative quantization strategies, but they come at the cost of much greater estimation complexity.     

压缩域宽带跳频信号跳变时刻估计算法

为了在非协作情况下,对跳频信号的频率跳变时刻进行精确快速估计,提出一种基于压缩采样值的跳频信号跳变时刻快速估计算法。该算法首先通过压缩感知技术以远低于奈奎斯特采样定理要求的速率对跳频信号进行整周期滑动采样,然后根据不同时刻相邻两跳信号窗函数的特点,重构信号在傅里叶正交基上的2个权值最大的稀疏系数,并由此对前后两跳持续时间进行判断,从而对跳频信号的跳变时刻进行参数估计。仿真结果显示,该算法能有效地估计跳频信号的跳频转换时刻,且实时性优于现有时频估计类算法。