Modified Bayesian algorithm‐based compressive sampling for wideband spectrum sensing in cognitive radio network using wavelet transform

This paper presents the implementation of a modified version of Bayesian relevance vector machine (RVM)‐based compressive sensing method on cognitive radio network with wavelet transform for spectrum hole detection. Bayesian compressive sensing is used in this work to deal with the complexity and uncertainty of the process. The dependency of the Bayesian compressive sensing on the knowledge of noise levels in the measurement has been relaxed through the proposed Bayesian RVM‐based compressive sensing algorithm. This technique recovers the wideband signals even with fewer measurements maintaining considerably good accuracy and speed. Wavelet transform is used in this paper to enable the detection of primary user (PU) even in the low regulated transmission from unlicensed user. The advantage of this approach lies in the fact that it enables the evaluation of all possible hypotheses simultaneously in the global optimization framework. Simulation study is performed to evaluate the efficacy of the proposed technique over the cognitive radio environment. The performance of the proposed technique is compared with the conventional Bayesian approach on the basis of recovery error, recovery time and covariance to verify its superiority.     

采用压缩采样匹配追踪算法的频谱感知

频谱资源的匮乏成为无线电发展的瓶颈,解决频率匮乏有两类方法:一是提高频谱利用率;二是扩大可利用的频率范围。频谱感知技术能提高频谱利用率,但在高频的应用中会面对过高的采样速率、较大的数据量,这对硬件实现提出了艰巨的挑战。本文根据无线电频谱稀疏性介绍一种基于调制宽带转换器的压缩采样匹配追踪（CoSaMP）算法。本文利用调制宽带转换器对无线电信号进行亚奈奎斯特采样,再利用CoSaMP算法对采样后的自相关矩阵求解。本文的方法不仅能应用在更高的频谱,且能提高频谱利用率。仿真结果表明:该方法能在能以一个较低的采样速率对信号进行采样,且CoSaMP算法的恢复误差要小于OMP和ROMP算法。      

基于SWCoSaMP算法的稀疏信号重构

压缩感知(compressed sensing, CS)稀疏信号重构本质上是在稀疏约束条件下求解欠定方程组。针对压缩感知匹配追踪(compressed sampling matching pursuit, CoSaMP)算法直接从代理信号中选取非零元素个数两倍作为支撑集,但是不存在迭代量化标准,本文提出了分步压缩感知匹配追踪(stepwise compressed sampling matching pursuit, SWCoSaMP)算法。该算法从块矩阵的逆矩阵定义出发,采用迭代算法得到稀疏信号的支撑集,推出每次迭代支撑集所对应重构误差的L-2范数闭合表达式,从而重构稀疏信号。实验结果表明和原来CoSaMP算法相比,对于非零元素幅度服从均匀分布和高斯分布的稀疏信号,新算法具有更好的重构效果。      

用于宽带频谱感知的全盲亚奈奎斯特采样方法

亚奈奎斯特采样方法是缓解宽带频谱感知技术中采样率过高压力的有效途径。该文针对现有亚奈奎斯特采样方法所需测量矩阵维数过大且重构阶段需要确切稀疏度的问题,提出了将测量矩阵较小的调制宽带转换器(MWC)应用于宽带频谱感知的方法。在重新定义频谱稀疏信号模型的基础上,提出了一个改进的盲谱重构充分条件,消除了构建MWC系统对最大频带宽度的依赖;在重构阶段,将稀疏度自适应匹配追踪(SAMP)算法引入到多测量向量(MMV)问题的求解中。最终实现了既不需要预知最大频带宽度也不需要确切频带数量的全盲低速采样,实验结果验证了该方法的有效性。     

采用确定性测量矩阵的宽带压缩采样的研究

在对宽带信号进行处理的过程中,常运用压缩感知的理论来获得有效的信息。而在实践压缩感知理论的压缩采样的结构中,调制宽带转换器的采样结构更加适合用于处理宽频带信号。文中研究了调制宽带转换器的压缩采样原理,也介绍了随机测量矩阵和确定性测量矩阵。分别将随机矩阵和确定性矩阵作为该调制宽带转换器的测量矩阵,对比分析了该采样结构的重构性能。研究了在确定性测量矩阵的基础上,该采样结构在折叠和非折叠条件下的信号重构性能,同时,也对系统的通道数目对性能重构和信噪比的影响进行了补充分析。     

High precision ranging with IR‐UWB: a compressed sensing approach

Ranging has been regarded as one of the fundamental enabling technologies for a multitude of applications that require high accurate position information, such as automated navigation, vehicle platooning, asset management, etc. Among various ranging techniques, impulse‐radio ultra‐wideband is one of the most competitive technologies for high‐precision ranging, because of its capability of achieving centimeter‐level ranging accuracy, even for dense urban, indoor or cave like environments. However, two main challenges arise when fully exploiting the ranging capability of impulse‐radio ultra‐wideband: (i) the extremely high sampling rate to acquire the received multipath signal, and (ii) the optimal thresholding strategy to differentiate the first path. To efficiently tackle those challenges, in this work, we propose a ranging approach under the compressed sensing framework. Specifically, the received ranging signal is acquired by low‐rate compressed sampling through parallel random projections. Then, an algorithm named matching‐pursuit search‐back is proposed to detect the first arrival path, which integrates a backward iterative search and thresholding process starting from the peak path. The detection threshold is dynamically adjusted in each iteration to asymptotically minimize the averaged detection errors over false alarm and missed detection. Extensive simulations and experiments with field data are provided to demonstrate that the proposed approach can achieve high‐precision ranging with far fewer samples compared with the traditional Nyquist‐sampling based ones. Copyright © 2016 John Wiley & Sons, Ltd.     

基于压缩采样和DWPT的认知无线电频谱感知方案

认知无线电频谱感知技术要求能够快速、准确地对高达上千兆赫兹的带宽进行频谱感知,它需要很高速率的模数转换器（A/D）,这对传统的工作在Nyquist采样率下的频谱估计方法提出了很大的挑战。利用实际信号频谱在开放式频谱接入环境中的稀巯性,提出了基于压缩采样和小波包分解的宽带频谱感知方案。通过SIMULINK仿真表明,该方法对宽带信号能以远远低于Nyquist采样率的速率采样,并且能够精确地估计出可用信道列表。     

Probabilistic greedy pursuit for streaming compressed spectrum sensing

This paper presents a probabilistic greedy pursuit(PGP)algorithm for compressed wide-band spectrum sensing under cognitive radio(CR)scenario.PGP relies on streaming compressed sensing(CS)framework,which differs from traditional CS processing way that only focuses on fixed-length signal’s compressive sampling and reconstruction.It utilizes analog-to-information converter(AIC)to perform sub-Nyquist rate signal acquisition at the radio front-end(RF)of CR,the measurement process of which is carefully designed for streaming framework.Since the sparsity of wide-band spectrum is unavailable in practical situation,PGP introduces the probabilistic scheme by dynamically updating support confidence coefficient and utilizes greedy pursuit to perform streaming spectrum estimation,which gains sensing performance promotion progressively.The proposed algorithm enables robust spectrum estimation without the priori sparsity knowledge,and keeps low computational complexity simultaneously,which is more suitable for practical on-line applications.Various simulations and comparisons validate the effectiveness of our approach.     

Compressive spectrum sensing using chaotic matrices for cognitive radio networks

Compressive sensing is an emerging technique in cognitive radio systems, through which sub‐Nyquist sampling rates can be achieved without loss of significant information. In collaborative spectrum sensing networks with multiple secondary users, the problem is to find a reliable and fast sensing method and to secure communication between members of the same network. The method proposed in this paper provides both quick and reliable detection through compressive sensing and security through the use of deterministic chaotic sensing matrices. Deterministic matrices have an advantage over random ones since they are easier to generate and store. Moreover, it is much easier to verify whether a deterministic matrix satisfies the conditions for compressive sensing compared with random matrices, which is what makes them an interesting area of research in compressive sensing. Also, it would be a great advantage if the sensing matrices also provide inherent security, which is the motivation for using chaotic matrices in this paper, since any slight changes in the chaotic parameters result in highly uncorrelated chaotic sequences, hence entirely different sensing matrices. This makes it impossible to reconstruct the signal without proper knowledge of the parameters used to generate the sensing matrix. They can also be easily regenerated by knowing the correct initial values and parameters. Additionally, new modifications are proposed to the existing structures of chaotic matrices. The performance of chaotic sensing matrices for both existing and modified structures is compared with that of random sensing matrices.     

光子辅助压缩感知技术关键问题研究

为了保证光子辅助压缩感知系统在获取宽带信号的过程中,测量矩阵保持零均值,采用基于马赫-曾德尔调制器的并行结构,以实现待处理信号与零均值随机序列的混频;同时采用数字域后补偿的方式,改善了强度调制器非线性对系统恢复效果的负面影响,在一定范围内提升了系统的恢复效果。结果表明,改进后的光子辅助压缩感知结构在获取宽带射频稀疏信号时,具有更好的恢复效果。     

基于OMP算法的宽带频谱感知

频谱感知是认知无线电的一项关键技术,其能够检测出未被主用户占用的频谱空穴供次用户接入使用,提高频谱利用率.宽带频谱感知要求对数GHz 的带宽进行检测,过高的采样速率、大的数据量对现有的硬件设备提出了巨大的挑战.本文利用宽带频谱的稀疏性提出一种基于OMP算法的宽带频谱感知方法.该方法利用MWC采样实现对宽带模拟信号直接压缩采样;利用自相关矩阵对称分解特性和主用户信号独立性,得到有限维压缩采样信号模型,利用AIC/MDL准则估计稀疏度作为OMP算法迭代停止的条件,大大减少了算法复杂度;该方法不需要重构接收信号的PSD,直接在时域根据低速率采样信号,检测被占用信道.仿真结果表明,当带内信噪比大于9dB时,频谱检测概率高于90％.     

Non-reconstruction compressive detector for wideband spectrum sensing based on GLRT

Spectrum sensing is an essential ability to detect spectral holes in cognitive radio (CR) networks. The critical challenge to spectrum sensing in the wideband frequency range is how to sense quickly and accurately. Compressive sensing(CS) theory can be employed to detect signals from a small set of non-adaptive, linear measurements without fully recovering the signal. However, the existing compressive detectors can only detect some known deterministic signals and it is not suitable for the time-varying amplitude signal, such as spectrum sensing signals in CR networks. First, a model of signal detect is proposed by utilizing compressive sampling without signal recovery, and then the generalized likelihood ratio test (GLRT) detection algorithm of the time-varying amplitude signal is derived in detail. Finally, the theoretical detection performance bound and the computation complexity are analyzed. The comparison between the theory and simulation results of signal detection performance over Rayleigh and Rician channel demonstrates the validity of the performance bound. Compared with the reconstructed spectrum sensing detection algorithm, the proposed algorithm greatly reduces the data volume and algorithm complexity for the signal with random amplitudes.     

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。     

基于压缩感知信道能量观测的协作频谱感知算法

压缩感知为认知无线电宽带频谱感知提供了一种新思路。基于压缩感知原理,该文提出一种不需要重构宽带频谱本身,而是直接重构各信道能量的协作频谱感知方法。多个次用户使用宽带随机滤波器组获取信道能量的观测值。融合中心同步接收多个用户的能量观测,并利用同步稀疏自适应匹配追踪协作重构算法重构所有次用户的信道能量。仿真结果表明加性高斯白噪声环境下该协作感知方法所需的滤波器数目仅为传统方法的20%左右,瑞利衰落信道下也仅需传统方法的40%,有效降低了系统复杂度并改善感知性能。同时,该文提出的同步稀疏自适应匹配追踪算法对比经典的同步正交匹配追踪算法在重构精度及算法复杂度两方面都有所提升。     

Compressive sensing‐based signal compression and recovery in UWB wireless communication system

In this paper, we propose a new compressive sensing‐based compression and recovery ultra‐wideband (UWB) communication system. Compared with the conventional UWB system, we can jointly estimate the channel and compress the data, which can also simplify the design of hardware. No information about the transmitted signal is required in advance as long as the channel follows autoregressive process. As an application example, real‐world UWB signal is collected and processed to evaluate the performance of our proposed system. The compression procedure is so simple that we just multiply random Gaussian or Bernoulli matrix with the original data to capture all the information we want. Simulation results show that the data could be perfectly recovered if the compression ratio does not exceed 2.5:1 when Bernoulli matrix is chosen as the sensing matrix. Copyright © 2012 John Wiley & Sons, Ltd.     

基于OMP的非合作宽带脉冲压缩雷达信号的压缩感知研究

压缩感知技术可以用来实现对非合作宽带信号的欠采样快速处理。宽带脉冲压缩雷达能够有效解决雷达探测距离和距离分辨力的矛盾,在探测领域得到了广泛应用,为实现对非合作宽带脉冲压缩雷达信号的快速欠采样接收处理,本文首先开展了信号稀疏分解与重构算法研究,通过对贪婪算法、凸松弛类算法、组合类算法三大算法进行对比分析,选用了运行速度快且重构精度高的正交匹配追踪(OMP)算法针对非合作宽带脉冲压缩雷达信号进行压缩感知仿真分析。仿真结果表明:在一定信噪比条件下,OMP算法完全能够实现对非合作宽带脉冲压缩雷达信号的欠采样和信号重构,从而实现了对非合作宽带雷达信号的欠采样处理,为处理非合作超宽带雷达信号提供了很好的理论指导。     

一种基于能量的压缩感知稀疏度估计算法

压缩感知理论中,信号稀疏度直接关系到采样速率的设定以及观测矩阵的构造,而该先验信息往往受限.针对这一问题,本文从大维随机矩阵谱分析理论出发,分析了采样协方差矩阵的极限特征值概率分布特征,并结合其与观测信号能量的关系推导得到观测信号能量与压缩率、稀疏度和信噪比之间的对应关系,提出一种基于观测信号能量的稀疏度估计算法.相对于已有算法,该算法计算复杂度较低,且估计精度较好,并可通过增加采样开销进一步提升稀疏度估计精度,仿真实验验证了本文算法的有效性.     

基于一致优化的分布式宽带合作频谱感知算法

在压缩采样的框架下,提出一种基于一致优化的分布式宽带频谱压缩感知算法。算法思想如下:认知无线电网络中每个认知节点首先根据压缩采样理论获取压缩采样,并恢复本地的频谱信息,然后在一跳范围内交换频谱信息。认知节点将获取的邻居节点频谱信息进行加权平均,此加权平均作为频谱恢复一致优化问题的约束,以此来降低计算开销,加速算法的收敛。优化问题通过最优交替方向乘子法迭代求解来获取整个认知无线电网络的频谱估计。给出了算法的收敛性证明,并进行了仿真实验以验证算法的有效性。     

A performance comparison of measurement matrices in compressive sensing

Compressive sensing involves 3 main processes: signal sparse representation, linear encoding or measurement collection, and nonlinear decoding or sparse recovery. In the measurement process, a measurement matrix is used to sample only the components that best represent the signal. The choice of the measurement matrix has an important impact on the accuracy and the processing time of the sparse recovery process. Hence, the design of accurate measurement matrices is of vital importance in compressive sensing. Over the last decade, a number of measurement matrices have been proposed. Therefore, a detailed review of these measurement matrices and a comparison of their performances are strongly needed. This paper explains the foundation of compressive sensing and highlights the process of measurement by reviewing the existing measurement matrices. It provides a 3‐level classification and compares the performance of 8 measurement matrices belonging to 4 different types using 5 evaluation metrics: the recovery error, processing time, recovery time, covariance, and phase transition diagram. The theoretical performance comparison is validated with experimental results, and the results show that the Circulant, Toeplitz, and Hadamard matrices outperform the other measurement matrices.     

An Orthogonal Method for Measurement Matrix Optimization

Compressive sensing theory states that signals can be sampled at a much smaller rate than that required by the Nyquist sampling theorem, because the sampling of a signal in the former is performed as a relatively small number of its linear measurements. Thus, the design of a measurement matrix is important in compressive sensing framework. A random measurement matrix optimization method is proposed in this study based on the incoherence principle of compressive sensing, which requires the mutual coherence of information operator to be small. The columns with mutual coherence are orthogonalized iteratively to decrease the mutual coherence of the information operator. The orthogonalization is realized by replacing the columns with the orthogonal matrix \(\mathbf {Q}\) of their QR factorization. An information operator with smaller mutual coherence is acquired after the optimization, leading to an improved measurement matrix in terms of its relationship with the information operator. Results of several experiments show that the improved measurement matrix can reduce its mutual coherence with dictionaries compared with the random measurement matrix. The signal reconstruction error also decreases when the optimized measurement matrix is utilized.