非均匀天线组阵中引入对角加载的合成算法

针对非均匀天线组阵中常用的SUMPLE与PMFM(Proposed Matrix-Free Method)算法合成性能较差的问题,分别在SUMPLE与PMFM算法模型中引入对角加载技术,提出了一种新的信号合成算法.该算法利用权值幅度估计各路噪声功率,并对角加载到权值迭代算法中以得到准最优复权值向量.理论分析与数值仿真均表明,在不明显增加计算量的基础上,新算法在非均匀组阵中的合成损失明显低于SUMPLE与PMFM算法,同时新算法的收敛速度也与各自模型算法相当,因此更加适用于实际组阵系统,具有重要的工程应用价值.     

利用二阶统计量的图像盲提取方法

为了从混叠的图像信号中分离源图像,提出一种基于二阶统计量的图像盲抽取方法。首先根据图像信号的非平稳特性构造用于估计分离向量的代价函数;然后通过最小化其函数获得最优分离向量,并实现逐次恢复源图像信号的目的。仿真实验结果表明,本文方法不仅能较好地实现多幅图像的盲分离,还能同时分离服从亚高斯分布的图像信号和超高斯分布的语音信号;与其它传统方法相比较,它具有更优越的估计性能。     

零陷展宽对角载入算法

提出了零陷展宽对角载入算法,该算法既解决了干扰在快速运动时,干扰零陷过窄的问题,又解决了协方差矩阵误差和导向矢量误差存在时,算法稳定性变差的问题。同时,通过对角载入因子和采样协方差矩阵间的关系确定了对角载入算法载入因子的值。计算机仿真结果表明该算法有很好的稳健性,以及较宽的零陷。     

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.     

Equivalence of adaptive array diagonal loading and omnidirectionaljamming

Diagonal loading, where a diagonal matrix is added to the estimate of the covariance matrix, is often used in adaptive arrays to minimize the array's responsiveness to random fluctuations in the estimate of the interference environment. Poor estimates of the covariance matrix often result in high random sidelobes in the sample matrix inversion (SMI) adapted pattern. It is shown in this communication that an omnidirectional spread of uniform jammers arriving at a linear array of half-wavelength spaced elements with cosine element patterns also produces a diagonal matrix. This equivalence of form is useful in visualizing the effects of diagonal loading and understanding the resulting patterns     

An iterative method using conditional second-order statistics applied to the blind source separation problem

This paper is concerned with the problem of blind separation of an instantaneous mixture of sources (BSS), which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise, these methods fail and others (higher order statistics, etc.) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources that have a probability density function with unbounded domain of definition is described; here, the algorithm does not lead directly to a separation state but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources.     

Source enumeration in a correlated signal environment

The authors present a simple method for determining the number of signals impinging on a uniform linear array that is applicable even in the extreme case of fully correlated signals. This technique uses what they term modified rank sequences, which is a modification of the construction implicit in the matrix decomposition method of Di (1981). They prove that if a particular rank sequence stabilizes (the last two terms of the sequence are equal) to a value strictly less then the common row size of the defining block matrices, then this value equals the number of signals, provided that the number of signals has not exceeded a Bresler-Macovski (1986) type bound. Using the above characterization of stability, they formulate an algorithm that either determines the number of signals or indicates that the resolution capability of the algorithm has been exceeded. They also provide theorems that show that under certain conditions, a rank sequence can stabilize to a value strictly less than the number of signals. This result allows them to find simple counterexamples to all of the existing rank sequence methods     

Channel capacity and second-order statistics in Weibull fading

The second-order statistics and the channel capacity of the Weibull fading channel are studied. Exact closed-form expressions are derived for the average level crossing rate, the average fade duration, as well as the average Shannon's channel capacity of the Weibull fading process. Numerical results are presented to illustrate the proposed mathematical analysis and to examine the effects of the fading severity on the concerned quantities.     

A blind source separation technique using second-order statistics

Separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: The linear mixture should be “blindly” processed. This typically occurs in narrowband array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast with other previously reported techniques, the proposed approach relies only on stationary second-order statistics that are based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method     

一种基于自适应对角加载的雷达通道均衡算法

雷达通道均衡可以保证通道间的幅度和相位一致性。对角线加载技术能减弱均衡器阶数增加带来的矩阵病态的影响,改善了均衡性能,但是加载量的确定是一个比较困难的问题。文中提出采用自适应对角线加载进行雷达通道均衡的算法,提高了通道均衡的稳健性。仿真结果证明了该算法的有效性。     

一种基于二阶统计量的盲均衡算法

对于多输入多输出(MIMO)信道,使用有色输入的二阶统计量进行盲均衡是一种有效的方法.相对于原有的、基于自相关匹配原理的盲均衡算法,本文给出了一个在时域上不必先知道用户自相关序列值就能实现均衡的条件,并提出了相应的的时域均衡器训练算法,对含白噪声的情况也进行了讨论.     

Enhancing image watermarking methods with/without reference images by optimization on second-order statistics

The watermarking method has emerged as an important tool for content tracing, authentication, and data hiding in multimedia applications. We propose a watermarking strategy in which the watermark of a host is selected from the robust features of the estimated forged images of the host. The forged images are obtained from Monte Carlo simulations of potential pirate attacks on the host image. The solution of applying an optimization technique to the second-order statistics of the features of the forged images gives two orthogonal spaces. One of them characterizes most of the variations in the modifications of the host. Our watermark is embedded in the other space that most potential pirate attacks do not touch. Thus, the embedded watermark is robust. Our watermarking method uses the same framework for watermark detection with a reference and blind detection. We demonstrate the performance of our method under various levels of attacks.     

Pathset enumeration of directed graphs by the set theoretic method

The set theoretic method developed by the author in a previous paper for enumeration of pathsets of non-directed graphs has been modified in this paper and applied to directed graphs. The directed graph is represented mathematically by an expression using vertex sets defined in the text. Set operations like union and intersection are applied to the vertex set terms of this expression and these terms are gradually converted to complete pathsets of the directed graph. The developed method has been explained in the text using illustrations.     

Blind channel identification based on second-order statistics: afrequency-domain approach

In this communication, necessary and sufficient conditions are presented for the unique blind identification of possibly nonminimum phase channels driven by cyclostationary processes. Using a frequency domain formulation, it is first shown that a channel can be identified by the second-order statistics of the observation if and only if the channel transfer function does not have special uniformly spaced zeros. This condition leads to several necessary and sufficient conditions on the observation spectra and the channel impulse response. Based on the frequency-domain formulation, a new identification algorithm is proposed     

Blind two-input-two-output FIR channel identification based onfrequency domain second-order statistics

We present an analytical solution to the two-input-two-output blind crosswise mixture identification based on eigenvalue decomposition of second-order spectra correlations. The sources are independent and non-white, but otherwise, we consider their statistics to be unknown. We show that the cross channels cannot be uniquely determined by the analysis of the frequency domain covariance alone due to the unknown eigenvector permutations. However, the problem can be attacked with the help of two invariant indices that are immune to these permutations. Using these indices together with standard reconstruction-from-phase techniques, we show that the channels can be uniquely determined. Our theoretical results lead to a novel frequency domain second-order algorithm that identifies the unknown channels     

On the second-order statistics of the weighted sample covariance matrix

The second-order statistics of the sample covariance are encountered in many covariance based processing algorithms. This paper derives closed-form expressions for the covariance of the weighted sample covariance matrix with an arbitrary weight for both a real system and complex system. Given a system model, the results explicitly rely on the second-order and fourth-order statistics of the channel noise and inputs. They are shown to coincide with the existing results when the channel inputs and noise are Gaussian distributed. Our results can be directly applied to analyze the statistical properties of subspace-based channel estimation methods for single-input multiple-output (SIMO) systems and code-division multiple access (CDMA) systems. Numerical examples are provided to further verify analyses.     

Equalization and interference cancellation in linear multiusersystems based on second-order statistics

Potential applications of blind channel identification and equalization in data communication systems have recently been explored. For multiuser systems that are irreducible and column-reduced, second-order statistical methods normally can identify channel dynamics up to a unitary mixing matrix. Additional user separation (equalization) can rely on higher order statistics and other prior information. In this paper, we investigate the equalizability of user signals and the cancellation of unwanted interfering signals based only on second-order output statistics. We show that a user channel can be equalized if it has the longest memory. Furthermore, interfering user signals can be cancelled under a more relaxed multiuser channel condition     

SNR of generalized diversity selection combining with nonidenticalRayleigh fading statistics

A closed-form expression for the average signal-to-noise-ratio (SNR) of generalized diversity selection combining, using the m largest (in instantaneous SNR) diversity signals, for arbitrary m, assuming that the Rayleigh fading statistics on each diversity branch are identically, independently distributed (i.i.d.), already exists in the literature. In this paper, a similar closed-form expression, but for nonidentically distributed statistics, is derived, This expression specializes to known results, such as the average SNRs of maximal-ratio combining with either i.i.d. or non-i.i.d. diversity statistics and that of conventional selection combining (CSC) with i.i.d. diversity statistics. In addition, it provides, for the first time, a simple closed-form solution to the combined SNR of CSC with non-i.i.d. diversity statistics. Further, the closed-form solution for the SNR of selecting the m, largest diversity signals has negligible computational complexity     

Second-order statistics of maximal-ratio and equal-gain combining in Weibull fading

Exact expressions for the level crossing rate and average fade duration of M-branch equal-gain and maximal-ratio combining systems in a Weibull fading environment are presented. The expressions apply to unbalanced, nonidentical, independent diversity channels. In addition, new closed-form solutions for some special cases are obtained.