循环平稳信号的联合稀疏表示DOA估计

基于联合稀疏表示的思想,本文提出了一种利用二阶循环统计量的循环平稳信号波达方向（DOA）估计算法。首先,对传统的谱相关信号子空间拟合算法进行分析研究;然后,通过在循环域构造过完备的阵列方向矩阵字典,建立了联合稀疏表示模型,从而将循环平稳信号的DOA估计问题转化为联合稀疏矩阵的恢复问题;最后,利用联合Ι_2,0范数逼近法求出联合稀疏矩阵的优化解,并根据优化矩阵中非零行的位置估计出循环平稳信号的DOA。与传统的SCSSF算法相比,所提算法具有更高的DOA估计精度,同时也适用于信号个数多于阵元个数的场合。理论分析和仿真实验结果都表明了算法的有效性。      

Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes

We study continuous-time multidimensional wide- sense stationary (WSS) and (almost) cyclostationary processes in the frequency domain. Under the assumption that the correlation function is uniformly continuous, we prove the existence of a unique sequence of spectral measures, which coincide with the restrictions to certain subdiagonals of the spectral measure in the strongly harmonizable case. Moreover, the off-diagonal measures are absolutely continuous with respect to the diagonal measure. As a consequence, for strongly harmonizable scalar improper almost cyclostationary processes, we obtain representation formulas for the components of the complementary spectral measure and the off-diagonal components of the spectral measure, in terms of the diagonal component of the spectral measure. We apply these results to analytic signals, which produces sufficient conditions for propriety for almost cyclostationary analytic signals.     

Series Representations for Rice's Ie Function

Two new series representations for the Rice functionIe (k, x)are presented. One of the series involves the modified Struve functions and the other involves the modified Bessel functions. These two series complement each other in their convergence speeds as functions of the values ofkandx. The truncation error bounds are derived for both series. Therefore, they can be used alternatively with high efficiency and known precision.     

Origin of Rice's formula

The origin of S.O. Rice's formula for the average rate of level crossings of a rather general random process is traced to his 1936 private notes entitled Singing Transmission Lines. The notes formulate an engineering problem in terms of the probability distribution of the absolute maximum of an envelope process in a closed interval. Rice showed that if the envelope of the reflected wave on a loaded transmission line were to equal or exceed the maximum value in the closed interval, then `singing' or oscillation could be expected to occur and the analog transmission system would become unstable and useless for the transmission of information. The formula and its generalizations are now basic for the analysis of level crossings and first and second passage times of random processes     

Target Detection for Heterogeneous Cyclostationary Sea Clutter

This paper mainly deals with the problem of target detection under the heterogeneous background of cyclostationary sea clutter. Conventional approaches generally assume the ideal condition requiring the secondary data to be homogeneous with the primary data in order to exactly estimate the clutter covariance matrix and implement the adaptive filters. To the contrary, the realistic clutter environments appear heterogeneous, leading to the performance degradation of these traditional processors. For the sake of alleviating the effect of the heterogeneity, the non-homogeneous detectors, especially with knowledge-aided (KA) method based on the prior knowledge, are presented under the heterogeneous Gaussian condition. However, the experimental data manifest that the compound-Gaussian distribution is successfully applied in modeling the heterogeneous sea clutter, which also presents the cyclostationarity. Accordingly, when lacking prior information as used in the KA method, a new non-homogeneous detector based on mean value (M-NHD) is proposed against the heterogeneous sea clutter with cyclostationarity by operating solely on the primary data, in terms of the generalized likelihood ratio test (GLRT) criterion. The expressions of the probabilities of detection and false alarm are subsequently given. Since the detection performance depends on the steering vector, an adaptive non-homogeneous detector based on the steering vector (SV-NHD) is proposed subject to the design method for the optimal steering vector. Finally, the numerical results evaluate the performance of the two proposed detectors with Monte Carlo method under heterogeneity.     

无源循环平稳信号检测方法

研究了无源接收条件下循环平筝信号的检测方法。在循环相关匹配滤波理论的基础上,分别给出了无源单 站和无源双站准循环相关匹配滤波器的设计方法,并研究了基于准循环相关匹配滤波的无源单站和无源双站信号检测方 法,得到了SPS无源单站信号循环检测子和SPB无源双站信号循环检测子。仿真分析针对BPSK信号给出了在白噪声和 时变噪声两种噪声背景条件下SPS、SPB和radiometry等检测子的ROC检测曲线,仿真结果充分说明了SPS和SPB检测 子的有效性。     

Collaborative Cyclostationary Spectrum Sensing for Cognitive Radio Systems

This paper proposes an energy efficient collaborative cyclostationary spectrum sensing approach for cognitive radio systems. An existing statistical hypothesis test for the presence of cyclostationarity is extended to multiple cyclic frequencies and its asymptotic distributions are established. Collaborative test statistics are proposed for the fusion of local test statistics of the secondary users, and a censoring technique in which only informative test statistics are transmitted to the fusion center (FC) during the collaborative detection is further proposed for improving energy efficiency in mobile applications. Moreover, a technique for numerical approximation of the asymptotic distribution of the censored FC test statistic is proposed. The proposed tests are nonparametric in the sense that no assumptions on data or noise distributions are required. In addition, the tests allow dichotomizing between the desired signal and interference. Simulation experiments are provided that show the benefits of the proposed cyclostationary approach compared to energy detection, the importance of collaboration among spatially displaced secondary users for overcoming shadowing and fading effects, as well as the reliable performance of the proposed algorithms even in very low signal-to-noise ratio (SNR) regimes and under strict communication rate constraints for collaboration overhead.     

一种稳健的周期平稳信号的盲波束形成算法

因为不需信号个数和导向向量等任何参考信息,基于周期平稳信号的盲波束形成算法在信号处理领域得到非常广泛的应用,然而这类方法是建立在循环频率准确已知基础上的,在实际应用中往往不是如此,循环频率的估计误差将导致算法性能变差,为了改进这点不足,在传统的循环自适应波束形成(CAB)算法的基础上,提出了一种改进的 CAB 盲波束形成算法,经理论分析和计算机仿真,证明了该算法是有效的.     

一种主用户随机到达情况下改进的循环平稳特征检测算法

在认知无线电(CR)网络中,针对检测频段突然被主用户(PU)占用导致次用户频谱检测性能较差的情况。该文提出一种基于反馈叠加原理的改进循环平稳特征检测算法,该算法通过将检测周期后半部分采样点的瞬时采样值累加到检测周期前半部分采样点的瞬时采样值上,在不延长检测时间的基础上,提高了整个检测周期的判决统计值,从而提高了系统检测性能。并且从理论上详细分析了该算法的检测概率,虚警概率与吞吐量。仿真结果表明,该算法的检测性能优于传统循环平稳特征检测算法和传统能量检测算法,并且保证了不错的用户数据吞吐量。     

基于多循环频率聚焦的宽带循环平稳信号阵列测向方法

宽带循环平稳信号多个离散循环频率处的信息能否进行综合利用以改善低信噪比条件下的阵列测向性能具有较大的研究价值。该文从阵列观测数据的循环谱相关函数入手,证明了低信噪比条件下不同循环频率处阵列观测数据的谱相关函数估计误差之间相互独立,表明不同循环频率信息之间具有较强的互补性,然后借鉴常规宽带信号频域聚焦思想提出了一种不同循环频率处信息综合利用的有效途径。仿真结果表明,基于多循环频率聚焦的方法能够有效改善低信噪比条件下宽带循环平稳信号的阵列测向性能。     

Novel Direction Findings for Cyclostationary Signals in Impulsive Noise Environments

We consider the problem of direction-of-arrival (DOA) estimation for cyclostationary signals in impulsive noise modeled as a complex symmetric α-stable (SαS) process. Since the DOA estimation based on second-order cyclic statistics degrades seriously in an α-stable distribution noise environment, we define a novel pth-order cyclic correlation by fusing the fractional lower order statistics and second-order cyclic correlation. After briefly introducing the statistical characteristics of pth-order cyclic correlation and building the extended data model, we first propose a novel extended pth-order cyclic MUSIC algorithm (EX-POC-MUSIC) by exploiting both pth-order cyclic correlation and pth-order cyclic conjugate correlation. The algorithm allows us to select desired signals and to ignore interference in the communication system. Second, in order to increase the resolution capabilities and the noise robustness significantly, an improved EX-POC-MUSIC algorithm called the extended pth-order cyclic Root-MUSIC (EX-POC-RMUSIC) algorithm is also presented. This algorithm has all the merits of the EX-POC-MUSIC algorithm, and it is also a fast DOA estimation algorithm because it avoids spatial spectrum searching. Under some conditions, both proposed algorithms are able to handle more sources than the number of sensors. Simulation results strongly verify the effectiveness of the two algorithms.     

Cyclostationary signature design for common control channel of cognitive radio

Embedding specific signatures in transmitted signals for identifying common control channels of cognitive radio are addressed in research laboratories because availability of the spectrum occupied by the common control channel might change in time. A novel solution to embed a unique cyclostationary signature for the common control channel of cognitive radio is proposed in this article. Based on linear periodically time-variant transformation (LPTV) model, the cyclic autocorrelation expression of the proposed signature is derived, which characterizes its cyclostationarity. Analysis of the cyclostationary signature is presented considering effects of additive white Gaussian noise(AWGN)and multiplath channels. Simulation results illustrating the reliability of signatures are given.     

一种稳健的循环时空波束形成算法

该文提出了一种新的基于信号平稳特性的自适应波束形成算法稳健的循环时空波束形成算法。该算法在利用信号的谱相关特性的同时使用了多个时延,将波束形成技术从空域扩展到了时空域,弥补了空域信息的不足,充分利用了信号的循环统计信息和信号的时域特征,提高了信号的选择能力和对干扰、噪声的抑制能力。仿真实验结果验证了该算法的有效性和稳健性。     

基于循环平稳特征的频谱检测

频谱检测是实现认知无线电的前提。从认知无线电的核心功能出发,分析了循环平稳特征检测抗噪方面的性能以及影响其检测性能的主要因素,通过理论推导和仿真验证了噪声对检测性能的影响,提出了一种基于小波变换的频谱检测方案。该方案通过小波变换将接收到的信号进行主信号与噪声分离,并对信号进行重构,提高了频谱检测的性能。仿真结果表明,在低信噪比情况下,采用基于小波变换的频谱检测方法,无论是系统的频谱检测虚警率还是频谱检测漏检率都有了显著的降低。     

A Class of Adaptive Cyclostationary Beamforming Algorithms

One of the main benefits of the cyclostationary beamforming algorithms is their ability to extract signals from co-channel interference with only a knowledge of the cycle frequency. In this paper, we study the popular cyclostationary beamformers, and propose five new algorithms, namely, the adaptive cyclic adaptive beamforming (ACAB), adaptive cross-SCORE (ACS), constrained least-squares (CLS), adaptive phase-SCORE (APS), and maximal constrained autocorrelation (MCA) algorithms. All these algorithms are adaptive and have a computational complexity of O(n ²) complex multiplications, where n is the number of array elements. A comparative study of these algorithms is made based on numerical simulations. Each of these algorithms has specific application scenarios. The ACS and the APS algorithms are particularly suited for very adverse signal environments. The ACAB, MCA and cyclic adaptive beamforming (CAB, from the work of Wu and Wong) algorithms can provide good performance in the case of medium or weak interference, while the CLS algorithm is especially suitable for weak interference. The CAB algorithm is shown to be a special case of the least-square self-coherent restoral (LS-SCORE) algorithm. Some insights as to how one can assign carrier frequency and symbol rate during digital modulation are also suggested. The proposed adaptive algorithms are easy to implement, and thus are very promising for applications in wireless and mobile communications. This work was supported by the NSERC of Canada.     

BFSK的循环平稳特性分析

首先介绍了循环平稳的基本概念,给出了BFSK的信号模型,推导了BFSK信号的循环相关函数和循环谱的数学表达式,分析了其循环平稳特性,说明了其具有循环平稳性,最后给出了计算机仿真实验。仿真结果表明,BFSK信号具有循环平稳特性,属于循环平稳信号。仿真同时说明了利用信号的循环平稳特性进行参数估计具有较高的循环频率分辨率。     

基于最小方差谱估计的循环平稳信号 到达角估计方法

文章提出了基于最小方差谱估计的多循环频率到达角估计方法.通过对指数函数进行Jacobi-Anger展开,将目标方向矩阵近似分解为两个独立矩阵相乘的形式,并构造相应的变换矩阵,将多个不同循环频率处阵列输出信号循环相关函数矩阵进行叠加,再利用最小方差谱估计方法实现对目标到达角的估计.新方法克服了已有基于信号循环平稳特性估计方法只利用信号单个循环频率信息的不足.仿真结果证实了新方法的有效性,同时也证实该方法确实具有较单循环频率SC-SSF方法和传统宽带聚焦方法更好的估计性能.     

基于连续稀疏恢复循环平稳信号的DOA估计

针对现有稀疏恢复算法在到达角(DOA)估计中存在的网格失配问题（即off-grid问题）,提出基于连续稀疏恢复循环平稳信号的DOA估计。首先,对传统的谱相关信号子空间拟合算法进行分析研究;然后,在循环域利用连续稀疏恢复的思想来构造循环平稳信号的稀疏恢复模型。与传统Cyclic MUSIC算法和现有基于离散稀疏恢复算法相比,文中算法能够克服off-grid问题,具有较高的稀疏恢复精度和较好的稀疏恢复性能;同时,也适用于信号个数多于阵元个数的场合。理论分析和仿真实验证明了算法的有效性。     

面向DS/FH信号的循环平稳空时频测向算法

综合采用直接序列扩频(DSSS)和跳频扩频(FHSS)体制的直序/跳频(DS/FH)通信信号显著降低了单位时频面积上的功率,经典的时频-多信号分类(TF-MUSIC)算法对这一类信号进行入射角(DOA)估计时误差较大。为解决该问题,本文对TF-MUSIC算法进行改进,在时频二维平面上计算DS/FH信号的时频特征值,并设计相应的时频掩膜滤波核函数,再根据估计出来的循环平稳频率计算相应的循环平稳空间自相关矩阵,得到了循环平稳可变核函数TF-MUSIC(CVCFTF-MUSIC)算法。该算法可显著提高DOA估计的精确度,数值仿真验证了上述观点。     

S.O. Rice's contributions to Shannon theory

The contributions of S.O. Rice to Shannon's formulations in communication theory are discussed. In `Communication in the presence of noise-Probability of error for two encoding schemes' (see Bell Syst. Tech. J., vol.29, p.60-93, Jan. 1950) Rice considered two explicit construction schemes for choosing the transmitted signals of duration T and exhibited an exact formula for the probability of error in the decoded messages. Rice evaluated these unwieldy expressions and presented tables and curves showing the trade-off between rate, delay, and error probability. He obtained asymptotic expressions for the error probability for large delay, and showed that with his scheme for choosing the signals, Shannon's results could be obtained. He recognized from his numerical calculations that the error probability seemed to approach zero much more rapidly than this and that, in his asymptotics, he had evidently made approximations that might one day be improved