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.     

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.     

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.     

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。     

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。     

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.     

Cyclostationary Signatures in Practical Cognitive Radio Applications

We define a cyclostationary signature as a feature which may be intentionally embedded in a digital communications signal, detected through cyclostationary analysis and used as a unique identifier. The purpose of this paper is to demonstrate how cyclostationary signatures can be exploited to overcome a number of the challenges associated with network coordination in emerging cognitive radio applications and spectrum sharing regimes. In particular we show their uses for signal detection, network identification and rendezvous and discuss these in the context of dynamic spectrum access. We present a theoretical discussion followed by application-oriented examples of the cyclostationary signatures used in practical cognitive radio and dynamic spectrum usage scenarios. We focus on orthogonal frequency division multiplexing (OFDM) based systems and present an analysis of a transceiver implementation employing these techniques developed on a cognitive radio test platform.     

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     

基于压缩感知的循环平稳特征检测方法

在认知无线电中,传统的循环平稳特征检测技术为了达到理想的感知效果,需要大量的数据采样点,导致其感知过程复杂度大,感知时间长.针对此问题,提出了一种基于压缩感知的改进循环平稳特征检测方法,该算法利用信号循环自相关函数(Cyclic Autocorrelation Function,CAF)的稀疏特性,基于分段平均的时变自相关函数估计值,通过压缩感知技术重构二维CAF矩阵,再根据重构结果实现循环平稳特征检测.该方法不仅可有效降低计算复杂度和检测时间,而且提高了二维CAF的估计精度.仿真结果表明该方法的检测性能优于基于经典CAF估计的循环平稳特征检测技术.     

Removing Cyclostationary Properties in a Chaos-Based Communication System

Chaotic signals are used in digital communications primarily in a bid to increase the security of transmissions. Moreover, second-order cyclostationary characteristics can easily be identified in chaotic signals used in communication systems. The detection of the cyclostationary properties in the transmitted signal decreases the security level for such systems. In this paper, we focus our attention on the eradication of cyclostationary properties present in chaotic signals, and to that end, we introduce a new method based on symbol period randomization to eliminate the spectral lines corresponding to the multiples of the baud rates. Finally, we compare our proposed method with another existing method in order to show the efficiency of ours in eliminating the cyclostationary properties.     

3PRK信号的循环平稳特性分析

脉冲位置相位翻转键控(3PRK)是一种超窄带(UNB)调制技术。相关文献已证明其已调信号是循环平稳信号,对其频谱也作了分析,但对该调制信号具有的循环平稳特性却没有相关论述。介绍了循环平稳信号的定义,推导了3PRK信号的循环谱数学表达式,提出了利用循环统计量对3PRK信号进行检测的方法,并进行了仿真实验。实验表明,该方法有很强的噪声抑制能力。     

高阶周期平稳连续随机信号离散化问题的研究

本文给出了高阶周期平稳随机过程连续时间信号与离散时间信号循环统计量之间的关系,该关系式较之文献［２］中的表达式更为简单明确;在讨论了连续信号循环频率的支撑区及循环矩支撑区的基础之上,给出了连续信号在时间离散化时不发生混迭的条件;从而由离散信号的循环统计量可以得到连续信号的循环统计量。     

On the Spectral Density of a Cyclostationary Process

A new approach to the spectral-density concept of a cyclostationary process is presented. This approach is based on the observation that a cyclostationary process can be split into a number of wide-sense stationary subprocesses. The spectral densities of these subprocesses, defined as the Fourier transform of their autocorrelation functions, are nonoverlapping functions of frequency. The sum of the spectral densities of these wide-sense stationary subprocesses yields the well-known expression for the spectral density of a cyclostationary process.     

An orthonormal Laguerre expansion yielding Rice's envelope densityfunction for two sine waves in noise

Through an orthonormal Laguerre expansion, expressions are derived for a lesser known Rician probability distribution-the probability density function (PDF) of the envelope of two fixed-amplitude randomly phased sine waves in narrowband Gaussian noise-and for the integral of the density, the cumulative distribution function (CDF). The principal formula derived has been checked analytically, numerically, and (approximately) graphically. Analytically, the moment-generating function for the PDF of the square of the envelope has been found to be a three-term product of elementary functions times an I₀ Bessel function (and thus to be in closed form); in confirmation, the same result has been secured via another, more direct route