On global and local convergence of half-quadratic algorithms.

This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint.     

Adaptive lattice IIR filtering revisited: convergence issues andnew algorithms with improved stability properties

Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with properties are derived. They are based on the cascade lattice structure, which allows the derivation of sufficient conditions for local stability     

Threshold values and convergence properties of majority-based algorithms for decoding regular low-density parity-check codes

This work presents a detailed study of a family of binary message-passing decoding algorithms for low-density parity-check (LDPC) codes, referred to as "majority-based algorithms." Both Gallager's algorithm A (G/sub A/) and the standard majority decoding algorithm belong to this family. These algorithms, which are, in fact, the building blocks of Gallager's algorithm B (G/sub B/), work based on a generalized majority-decision rule and are particularly attractive for their remarkably simple implementation. We investigate the dynamics of these algorithms using density evolution and compute their (noise) threshold values for regular LDPC codes over the binary symmetric channel. For certain ensembles of codes and certain orders of majority-based algorithms, we show that the threshold value can be characterized as the smallest positive root of a polynomial, and thus can be determined analytically. We also study the convergence properties of majority-based algorithms, including their (convergence) speed. Our analysis shows that the stand-alone version of some of these algorithms provides significantly better performance and/or convergence speed compared with G/sub A/. In particular, it is shown that for channel parameters below threshold, while for G/sub A/ the error probability converges to zero exponentially with iteration number, this convergence for other majority-based algorithms is super-exponential.     

On some convergence properties of 'learning with a probabilistic teacher' algorithms (Corresp.)

Satisfactory proof does not yet exist for the consistency of "learning with a probabilistic teacher" estimators, which are a class of randomized decision-directed estimators for adaptive multihypothesis decision making. Since a number of computer simulations described in the published literature indicate that the algorithms are convergent, we take as our starting point the assumption that this is generally true and develop an equation for use in determining for general distributions whether convergence is to the true parameter value. Using a numerical solution, we show that for the example of two one-dimensional Gaussian hypotheses and one unknown mean (the example appearing in the paper introducing the algorithm), if the estimator is convergent, convergence is to the true parameter value. Our formulation should be of help in constructing a more complete solution to the convergence problem and may be of use in investigating the consistency of other adaptive decision-making algorithms.     

Initial convergence of recursive maximum-likelihood identification algorithms

The effects of modifications proposed by S?derstr?m on the performance of the well known approximate maximum-likelihood identification algorithm based on recursive least squares arc tested on short records. The modified algorithm is found to be susceptible to instability and slow convergence.     

The challenge to realise convergence of fixed and mobilecommunications

Convergence of the fixed and mobile communication services (fixed and mobile convergence, or FMC) was the discussion subject for a panel session at the 6th IEE Conference on Telecommunications. Three invited speakers presented views from the perspectives of a fixed operator, a mobile operator and the business environment. This paper draws on the material presented and includes additional information to provide an updated overview of FMC. It also discusses the challenges that will be faced in realising the full vision of fixed and mobile service integration     

New algorithms for fixed and elastic geometric transformationmodels

This paper describes a new approach that leads to the discovery of substitutions or approximations for physical transformation by fixed and elastic geometric transformation models. These substitutions and approximations can simplify the solution of normalization and generation of shapes in signal processing, image processing, computer vision, computer graphics, and pattern recognition. In this paper, several new algorithms for fixed geometric transformation models such as bilinear, quadratic, bi-quadratic, cubic, and bi-cubic are presented based on the finite element theory. To tackle more general and more complicated problems, elastic geometric transformation models including Coons, harmonic, and general elastic models are discussed. Several useful algorithms are also presented in this paper. The performance of the proposed approach has been evaluated by a series of experiments with interesting results.     

Improved convergence of numerical device simulation iterative algorithms

Two techniques are described which serve to minimize the problem of slow Newton convergence and, at times, divergence sometimes experienced in applying this iterative technique to the solution of nonlinear semiconductor equations. The truncated correction method limits the wide excursions in the solution parameters which can occur during the Newton iterative procedure and thereby permits fewer voltage increments to be used in applying large bias voltages (1000 V)in simulating semiconductor power device operation. The doping-incrementation method uses the technique of gradually incrementing the doping levels in the heavily doped regions in a device structure to provide better solution first guesses in the simulation of devices containing such regions. Substantial savings in computer time are obtained in applying these two numerical procedures.     

A dynamic convergence analysis of blind equalization algorithms

Blind equalizers do not require a training sequence to start up or to restart after a communications breakdown, making them particularly useful in applications such as broadcast and point-to-multipoint networks. We study in parallel the dynamic convergence behavior of three blind equalization algorithms: the multimodulus algorithm (MMA), the constant modulus algorithm (CMA), and the reduced constellation algorithm (RCA). Using a conditional Gaussian approximation, we first derive the theoretical mean-squared-error (MSE) trajectory for MMA. This analysis leads to accurate but somewhat cumbersome expressions. Alternatively, we apply a Taylor series approximation to derive MSE trajectories for MMA, CMA, and RCA. This approach yields simpler but somewhat less accurate expressions. For the steady-state operation, however we derive even simpler formulas that accurately predict the asymptotic MSE values. We finally study the convergence rates of the three blind algorithms using their theoretical MSE trajectories, computer simulations, and a laboratory experiment     

Sign algorithms for blind equalization and their convergence analysis

In blind equalization a communication channel is adaptively equalized without resorting to the usual training sequence. In this paper we have introduced two new algorithms for blind equalization, which hard limit the equalizer input or the error at the output of the equalizer. These new algorithms are simple to implement and reduce the number of multiplications by approximately one-half. We show by way of simulations that the performance of the algorithm resulting from hardlimiting the error is comparable with the performance of the corresponding algorithm in which the error is not hardlimited. We formulate the new sign-error algorithm as a stochastic minimization of an error functional and demonstrate that the case of zero intersymbol interference corresponds to local minima of this error functional. We also present convergence analysis to predict the output mean square error in both these sign algorithms. Since the algorithms are highly nonlinear we incorporate several simplifying approximations and provide heuristic justifications for the validity of these approximations when the algorithms are operated in a typical practical environment. Computer simulations demonstrate the accuracy of the predicted convergence behavior.This research was supported in part by the Office of Naval Research under Contract N00014-89-J-1538.     

Comparative convergence analysis of EM and SAGE algorithms in DOAestimation

In this work, the convergence rates of direction of arrival (DOA) estimates using the expectation-maximization (EM) and space alternating generalized EM (SAGE) algorithms are investigated. The EM algorithm is a well-known iterative method for locating modes of a likelihood function and is characterized by simple implementation and stability. Unfortunately, the slow convergence associated with EM makes it less attractive for practical applications. The SAGE algorithm proposed by Fessler and Hero (1994), based on the same idea of data augmentation, has the potential to speed up convergence and preserves the advantage of simple implementation. We study both algorithms within the framework of array processing. Theoretical analysis shows that SAGE has faster convergence speed than EM under certain conditions on observed and augmented information matrices. The analytical results are supported by numerical simulations carried out over a wide range of signal-to-noise ratios (SNRs) and various source locations     

把握固移融合趋势，推动通信企业转型

20世纪90年代中期,通信产业界提出了固定通信网与移动通信网融为一体的FMC（fixed-mobile convergence）概念,用户无论是在固定环境中,还是在移动环境中都能享受到相同的服务,获得相同的应用。2008年电信三大运营商重组,电信产业格局发生了转变,产业链整合成为了重组后各运营商竞争的焦点和热点,全业务运营也随之成了各运营商发展的重中之重。固网与移动的比较优势,随着电信技术的发展与市场需求的演变此消彼长,固网与移动的网络融合成为必然。     

On the parallel simulation of fixed channel allocation algorithms

We present, in this paper, several channel allocation algorithms for use in cellular communications networks or mobile networks. The channel allocation algorithms make use of fixed allocation of channels and channel reorganization. The channel reorganization algorithms are used to free channels within a neighborhood of the cell in which the requesting call originates. The performance of these algorithms was evaluated via distributed simulation, making use of the Chandy–Misra–Bryant NULL message algorithm, on a BBN Butterfly multiprocessor. In addition to evaluating the performance of the channel allocation algorithms, we examine the efficiency of the NULL message algorithm as a tool for our simulations. The reason for making use of parallel simulation was to avoid the long simulation times and large memory consumption characteristic of sequential (uniprocessor) simulations. Our results indicate that our channel allocation algorithms performed efficiently. Upwards of 20% of the calls which were not initially connected by the borrowing schemes were connected after channel reorganization. The NULL message approach proved to be efficient when the message traffic was not extremely low.     

Improved convergence performance of RSER algorithms with modified gradient filtering

A modified gradient filtering technique is applied to a class of recursive sequential regression (RSER) algorithms, in order to improve the convergence performance. The performance behaviour of the new class of algorithms is studied using both all-pole and pole-zero examples.     

On the convergence of generalized simultaneous iterative reconstruction algorithms.

In this paper, we generalize the widely used simultaneous block iterative reconstruction algorithm and show that it converges, at a linear rate, to a weighted least-squares and weighted minimum-norm reconstruction. Our theoretical result provides a much simpler proof of the convergence properties obtained by Jiang and Wang and covers a much more general class of algorithms. The frequency domain iterative reconstruction algorithm is then introduced as a special application of our theory.     

Discrete constrained iterative deconvolution algorithms with optimized rate of convergence

In this paper, some new constrained discrete deconvolution algorithms based on an iterative equation are presented. The constraints are—the signal extent (signal support)—the positivity—the level bounds. The algorithms minimize either the error energy or a positive functional. The connections with previous works are studied. An experimental comparison of the algorithms convergence speed is studied with a synthetic sequence to be recovered. The restoration error and both the deconvoluted signal and its spectrum show clearly the performances of the algorithms and their ability to achieve a spectral extrapolation. The deconvolution from noisy data is investigated.     

The stability of variable step-size LMS algorithms

Variable step-site LMS (VSLMS) algorithms are a popular approach to adaptive filtering, which can provide improved performance while maintaining the simplicity and robustness of conventional fixed step-size LMS. Here, we examine the stability of VSLMS with uncorrelated stationary Gaussian data. Most VSLMS described in the literature use a data-dependent step-size, where the step-size either depends on the data before the current time (prior step-size rule) or through the current time (posterior step-size rule). It has often been assumed that VSLMS algorithms are stable (in the sense of mean-square bounded weights), provided that the step-size is constrained to lie within the corresponding stability region for the LMS algorithm. For a single tap fitter, we find exact expressions for the stability region of VSLMS over the classes of prior and posterior step-sizes and show that the stability region for prior step size coincides with that of fixed step-size, but the region for posterior step-size is strictly smaller than for fixed step-size. For the multiple tap case, we obtain bounds on the stability regions with similar properties. The approach taken here is a generalization of the classical method of analyzing, the exponential stability of the weight covariance equation for LMS. Although it is not possible to derive a weight covariance equation for general data-dependent VSLMS, the weight variances can be upper bounded by the solution of a linear time-invariant difference equation, after appropriately dealing with certain nonlinear terms. For prior step-size (like fixed step-size), the state matrix is symmetric, whereas for posterior step-size, the symmetry is lost, requiring a more detailed analysis. The results are verified by computer simulations     

Sufficient conditions for the local convergence of constant modulusalgorithms

The constant modulus (CM) criterion has become popular in the design of blind linear estimators of sub-Gaussian i.i.d. processes transmitted through unknown linear channels in the presence of unknown additive interference. The existence of multiple CM minima, however, makes it difficult for CM-minimizing schemes to generate estimates of the desired source (as opposed to an interferer) in multiuser environments. In this paper, we present three separate sufficient conditions under which gradient descent (GD) minimization of CM cost will locally converge to an estimator of the desired source at a particular delay. The sufficient conditions are expressed in terms of statistical properties of the initial estimates, specifically, CM cost, kurtosis, and signal-to-interference-plus-noise ratio (SINR). Implications on CM-GD initialization methods are also discussed     

小目标图像局部极值收敛提取算法

复杂背景下小目标自动提取技术尚不够完善,针对小目标自动提取问题,提出一种通过汇聚于同一极值点的所有路径来描述小目标区域的目标提取算法。该算法根据图像梯度特性筛选出路径的起始点位置;从起始点位置出发,沿着梯度最速下降方向,使路径收敛于图像的局部极小值点,收敛于同一极值点的所有路径构成独立核心区域;分析了焦点独立核心区域和噪声独立核心区域特征间的差异,以该特征中的内外均值比特征,对独立核心区域进行了滤波,分离出焦点核心区域;对独立核心区域聚合,得到目标核心区域。通过实验证明:该算法能够自动检测出焦点目标,和现有算法相比,提高了小目标提取的自动化程度。     

On the asymptotic convergence and numerical stability of theProteus EVD trackers

The asymptotic convergence and numerical stability of the previously introduced subspace tracking algorithms Proteus-1 and -2 are investigated by means of the ODE method. It is shown that (1) under weak conditions, both algorithms globally converge with probability one to the desired eigenvalue decomposition (EVD) components of the data covariance matrix, and (2) they have a built-in mechanism that prevents deviation from orthonormality in the eigenvector estimates over long periods of operation, i.e., numerical stability