Direct blind MMSE channel equalization based on second-orderstatistics

A family of new MMSE blind channel equalization algorithms based on second-order statistics are proposed. Instead of estimating the channel impulse response, we directly estimate the cross-correlation function needed in Wiener-Hopf filters. We develop several different schemes to estimate the cross-correlation vector, with which different Wiener filters are derived according to minimum mean square error (MMSE). Unlike many known sub-space methods, these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors. Their implementation requires no adjustment for either single- or multiple-user systems. They can effectively equalize single-input multiple-output (SIMO) systems and can reduce the multiple-input multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. The implementations of these algorithms on SIMO system are given, and simulation examples are provided to demonstrate their superior performance over some existing algorithms     

Globally convergent blind source separation based on a multiuser kurtosis maximization criterion

We consider the problem of recovering blindly (i.e., without the use of training sequences) a number of independent and identically distributed source (user) signals that are transmitted simultaneously through a linear instantaneous mixing channel. The received signals are, hence, corrupted by interuser interference (IUI), and we can model them as the outputs of a linear multiple-input-multiple-output (MIMO) memoryless system. Assuming the transmitted signals to be mutually independent, i.i.d., and to share the same non-Gaussian distribution, a set of necessary and sufficient conditions for the perfect blind recovery (up to scalar phase ambiguities) of all the signals exists and involves the kurtosis as well as the covariance of the output signals. We focus on a straightforward blind constrained criterion stemming from these conditions. From this criterion, we derive an adaptive algorithm for blind source separation, which we call the multiuser kurtosis (MUK) algorithm. At each iteration, the algorithm combines a stochastic gradient update and a Gram-Schmidt orthogonalization procedure in order to satisfy the criterion's whiteness constraints. A performance analysis of its stationary points reveals that the MUK algorithm is free of any stable undesired local stationary points for any number of sources; hence, it is globally convergent to a setting that recovers them all.     

Blind identification and equalization based on second-orderstatistics: a time domain approach

A new blind channel identification and equalization method is proposed that exploits the cyclostationarity of oversampled communication signals to achieve identification and equalization of possibly nonminimum phase (multipath) channels without using training signals. Unlike most adaptive blind equalization methods for which the convergence properties are often problematic, the channel estimation algorithm proposed here is asymptotically ex-set. Moreover, since it is based on second-order statistics, the new approach may achieve equalization with fewer symbols than most techniques based only on higher-order statistics. Simulations have demonstrated promising performance of the proposed algorithm for the blind equalization of a three-ray multipath channel     

A unifying criterion for instantaneous blind source separation based on correntropy

Correntropy has recently been introduced as a generalized correlation function between two stochastic processes, which contains both high-order statistics and temporal structure of the stochastic processes in one functional form. Based on this blend of high-order statistics and temporal structure in a single functional form, we propose a unified criterion for instantaneous blind source separation (BSS). The criterion simultaneously exploits both spatial and spectral characteristics of the sources. Consequently, the new algorithm is able to separate independent, identically distributed (i.i.d.) sources, which requires high-order statistics; and it is also able to separate temporally correlated Gaussian sources with distinct spectra, which requires temporal information. Performance of the proposed method is compared with other popular BSS methods that solely depend on either high-order statistics (FastICA, JADE) or second-order statistics at different lags (SOBI). The new algorithm outperforms the conventional methods in the case of mixtures of sub-Gaussian and super-Gaussian sources.     

基于指导型盲源分离和非高斯准则的全双工认知

为了克服半双工认知中存在的静态感知问题和常规全双工认知中残余自干扰限制的影响,提出了一种基于指导型盲源分离和非高斯准则的新型全双工认知方法。该方法将频谱感知和数据传输设计于同位置执行,避免在感知信息中的任何不匹配和资源损失,利用同位置配置中已知的次用户信号作为指导信号辅助执行盲源分离工作。在分离处理后,利用相关性识别出次用户自发信号,另一个信号通过非高斯准则判定,进而判决主用户的活动状态。仿真实验分析和讨论验证了所提方法的有效性,与基于自干扰消除的全双工频谱感知方案相比在计算复杂度和感知性能上具有明显的优越性。     

Image restoration using truncated SVD filter bank based on an energy criterion

Image restoration is formulated using a truncated singular-value-decomposition (SVD) filter bank. A pair of known data patterns is used for identifying a small convolution operator. This is achieved by matrix pseudo-inversion based on SVD. Unlike conventional approaches, however, here SVD is performed upon a data-pattern matrix that is much smaller than the image size, leading to an enormous saving in computation. Regularisation is realised by first decomposing the operator into a bank of sub-filters, and then discarding some high-order ones to avoid noise amplification. By estimating the noise spectrum, sub-filters that produce noise energy more than that of useful information are abandoned. Therefore high-order components in the spectrum responsible for noise amplification are rejected. With the obtained small kernel, image restoration is implemented by convolution in the space domain. Numerical results are given to show the effectiveness of the proposed technique     

MIMO signal separation for FIR channels: a criterion andperformance analysis

Signal separation for a general system of an arbitrary number of signals is investigated. The signal separation research area deals with the problem of separating unknown source signals that are mixed in an unknown way when only these mixtures are available. A criterion, based on second-order statistics, is formulated to be used in estimating the mixing system. This estimate of the mixing system is used in a separation structure with a parameterization that minimizes the number of parameters to be estimated. Formulae for the gradient and Hessian of the criterion are derived. A formula for the lower bound for the variance of the estimated parameters of the mixing matrix is derived. This lower bound is the asymptotic (assuming the number of data samples to be large) Cramer-Rao lower bound (CRLB). The proposed algorithm is tested with simulations and compared with the CRLB     

Robust decision design using a distance criterion

An alternate formulation of the robust hypothesis testing problem is considered in which robustness is defined in terms of a maximin game with a statistical distance criterion as a payoff function. This distance criterion, which is a generalized version of signal-to-noise ratio, offers advantages over traditional error probability or risk criteria in this problem because of the greater tractability of the distance measure. Within this framework, a design procedure is developed which applies to a more general class of problems than do earlier robustness results based on risks. Furthermore, it is shown for the general case that when a decision rule exists that is robust in terms of risk, the same decision rule will be robust in terms of distance, a fact which supports the use of the latter criterion.     

Source separation in post-nonlinear mixtures

We address the problem of separation of mutually independent sources in nonlinear mixtures. First, we propose theoretical results and prove that in the general case, it is not possible to separate the sources without nonlinear distortion. Therefore, we focus our work on specific nonlinear mixtures known as post-nonlinear mixtures. These mixtures constituted by a linear instantaneous mixture (linear memoryless channel) followed by an unknown and invertible memoryless nonlinear distortion, are realistic models in many situations and emphasize interesting properties i.e., in such nonlinear mixtures, sources can be estimated with the same indeterminacies as in instantaneous linear mixtures. The separation structure of nonlinear mixtures is a two-stage system, namely, a nonlinear stage followed by a linear stage, the parameters of which are updated to minimize an output independence criterion expressed as a mutual information criterion. The minimization of this criterion requires knowledge or estimation of source densities or of their log-derivatives. A first algorithm based on a Gram-Charlier expansion of densities is proposed. Unfortunately, it fails for hard nonlinear mixtures. A second algorithm based on an adaptive estimation of the log-derivative of densities leads to very good performance, even with hard nonlinearities. Experiments are proposed to illustrate these results     

Creative and high-quality image composition based on a new criterion

Image compositing techniques are primarily utilized to achieve realistic composite results. Some existing image compositing methods, such as gradient domain and alpha matting, are widely used in the field of computer vision, and can typically achieve realistic results, especially for seamless boundaries. However, when the candidate composite images and the target images have obvious differences, such as color, texture and brightness, the composite results are unrealistic and inconsistent. At the same time, traditional compositing methods focus on basic feature matching, ignoring semantic rationality in composition processing. Quite a few compositing methods thus generate composite results without semantic rationality.In this paper, a new multi-scale image composition method has been presented. In the composition process, wavelet pyramid and basic feature handling were used to achieve multi-scale compositions. More importantly, a new criterion was established, based on the semantic rationality of images, which could ensure that the composite images are semantically valid. A large database was created to facilitate experimentation. The experiments showed that the methodology introduced in this paper produced superior results compared to traditional composition methods; the composite results were not only consistent and seamless, but were also semantically valid.     

Blind adaptive multiuser detection based on a constrained MMSE criterion

The proposed blind adaptive multiuser detector utilizes the signature waveform and time information of the desired user. With each received sample vector, the proposed algorithm updates the detector and gives the symbol estimate in the current time slot. Such property facilitates it to track time-varying channels.     

基于时间结构盲源分离算法的工频干扰消除

研究了基于时间结构盲源分离算法的基本原理,在分析其特点和适用范围的基础上,提出了采用时间结构盲源分离算法消除地震信号采集过程中工频干扰的方法,并与基于FastICA的方法进行了性能比较.研究结果表明,本方法能够有效地消除地震信号中的工频干扰,同时保护有用信号,且干扰消除性能具有明显优势.     

Adaptive filtering in subbands using a weighted criterion

Transform-domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence, thus improving the convergence rate. However, a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input/output delay as small as possible, thus imposing short transforms. This dilemma has been alleviated by the so-called “short-block transform domain algorithms” but is still apparent. This paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms (e.g., critically subsampled, lossless, perfect reconstruction filter banks), thus allowing better tradeoffs between algorithm improvement, arithmetic complexity, and input/output delay. The method proposed makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm. This method leads to improvements in the convergence rate compared with both LMS and classical frequency domain algorithms     

Parameter estimator based on a minimum discrepancy criterion: aBayesian approach

A new estimation criterion based on the discrepancy between the estimator's error covariance and its information lower bound is proposed. This discrepancy measure criterion tries to take the information content of the observed data into account. A minimum discrepancy estimator (MDE) is then obtained under a linearity assumption. This estimator is shown to be equivalent to the maximum likelihood estimator (MLE), if one assumes that a linear efficient estimator exists and the prior distribution of parameters is uniform. Moreover, it is equivalent to the minimum variance unbiased estimator (MVUE) if the MDE is required to be unbiased. Illustrative examples of MDE and its comparisons with other estimators are given     

Source localization for multiple speech sources using low complexity non-parametric source separation and clustering

This article presents a new method for localization of multiple concurrent speech sources that relies on simultaneous blind signal separation and direction of arrival (DOA) estimation, as well as a method to solve the intersection point selection problem that arises when locating multiple speech sources using multiple sensor arrays. The proposed method is based on a low complexity non-parametric blind signal separation method, making is suitable for real-time applications on embedded platforms. On top of reduced complexity in comparison to a previously presented method, the DOA estimation accuracy is also improved. Evaluation of the performance is done with both real recording and simulations, and a real-time prototype of the proposed method has been implemented on a DSP platform to evaluate the computational and the memory complexities in a real application.     

Blind multiuser detector based on LMK criterion

A new blind adaptive multiuser detector for synchronous DS/CDMA systems based on a low computational complexity high order statistics-based least mean kutosis (LMK) algorithm is proposed. The LMK algorithm is shown to perform better than the least mean-square algorithm     

Sequential decoding based on an error criterion

An analysis of sequential decoding is presented that is based on the requirement that a set probability error P_e be achieved. The error criterion implies a bounded tree or trellis search region: the shape of this is calculated for the case of a binary symmetric channel with crossover probability P and random tree codes of rate R. Since the search region is finite at all combinations of p and R below capacity, there is no cutoff rate phenomenon for any P_e>0. The decoder delay (search depth), the path storage size, and the number of algorithm steps for several tree search methods are calculated. These include searches without backtracking and backtracking searches that are depth- and metric-first. The search depth of the non-backtracking decoders satisfies the Gallager reliability exponent for block codes. In average paths searched, the backtracking decoders are much more efficient, but all types require the same peak storage allocation. Comparisons are made to well-known algorithms     

Design of a new restoration algorithm based on the constrained mean-square-error criterion

In this paper the joint optimization of different criteria is addressed, as a powerful means of incorporatinga priori information in linear image-restoration algorithms. Theconstrained mean-square-error (CMSE) approach is introduced, which enables the incorporation of both spatial and spectral information regarding the peculiarities of the problem. Depending on the nature of the spatial information, this approach can be interpreted as either a regularized or an adaptive scheme. As a regularized scheme, it offers an alternative to conventional approaches, in which the ringing artifacts are efficiently suppressed by means of the regularizing operator. As an adaptive scheme, the CMSE approach offers the flexibility of applying either linear Wiener filtering or inverse filtering, depending on the local signal activity. Optimal techniques for the selection of the regularization parameter in both nonadaptive and adaptive cases are introduced. The capabilities of the CMSE approach as a regularized scheme and an adaptive scheme, are demonstrated through restoration examples.     

Source localization using TDOA and FDOA measurements based on modified cuckoo search algorithm

This paper introduces a new algorithm for solving the localization problem of moving multiple disjoint sources using time difference of arrival and frequency difference of arrival. The localization of moving sources can be considered as a least-square problem. There are many algorithms used to solve this problem such as, two-step weighted least squares, constrained total least-square and practical constrained least-square. However, most of these algorithms suffer from either slow convergence or numerical instability and don’t attain Cramer–Rao lower bound. We introduce a free-gradient algorithm called cuckoo search which avoids the slow convergence problem. The cuckoo search provides a combined global and local search method. Simulation results show that the proposed algorithm achieves better performance than other algorithms and attains Cramer–Rao lower bound.     

一种基于对比度最优准则的调频斜率估计方法

在合成孔径雷达成像及其应用中,需要对调频斜率进行估计.常用的估计调频斜率的方法是图像对比度最优算法,但该算法需反复迭代,导致该算法计算量大、收敛速度慢、效率低.为此,提出了一种基于对比度最优准则的调频斜率估计方法——抛物线法.该方法是根据图像对比度与方位向调频斜率的关系,引入数学中的抛物线法来估计多普勒调频斜率,避免了传统算法中的反复迭代,大大提高了计算效率.最后,用机载SAR实测数据验证了该方法的可行性和高效性.