Average power analysis of sequential circuits using an autoregressive model

We present a new statistical technique for average power estimation in sequential circuits. Because of the feedback loops, power dissipations of sequential circuits in consecutive clock cycles are temporally correlated. The existence of data correlation makes it unsuitable to apply conventional techniques to average power inference, because the sample variance is no longer a maximum likelihood estimator. The convergence criterion derived from the biased variance estimation will be overly optimistic, causing power simulation to stop prematurely at a lower-than-specified estimation accuracy. To overcome this problem, we propose a systematic approach for modeling the power dissipation behavior of sequential circuits as an autoregressive random process. An accurate process variance can be obtained by the model parameters, which enables the derivation of a robust confidence interval of the average power. The interval is checked for convergence against a user-specified accuracy criterion. An iterative procedure is developed to invoke these steps repeatedly until the convergence specification is met. For a set of benchmark sequential circuits, this technique yields high accuracy and efficiency.     

A Novel Statistical Technique for the Estimation of DC Stability in Higher-Order Σ-Δ A/D Converters

The existing techniques available for the statistical estimation of the dc input signal stability in general-order Σ-Δ analog-to-digital (A/D) converters are based on the assumption that the constituent quantizer input signal has a Gaussian distribution. However, empirical investigations reveal that this assumption holds adequately true only for the special case of conventional first-order Σ-Δ A/D converters. This paper presents an alternative technique for the accurate estimation of the dc input signal stability for higher-order Σ-Δ A/D converters. This estimation technique is based on the practical assumption that the constituent quantizer operates in its overload-free region, permitting the characterization of the quantizer output signal digit-pattern for the determination of the statistical moments of the corresponding quantizer input signal. The resulting statistical moments are subsequently incorporated in a Gram-Charlier series for an accurate quasi-linear modeling of the quantizer. A typical application example is given to demonstrate the accuracy of the proposed statistical technique for predicting the existence of multiple regions of instability and stability in the Σ-Δ A/D converter operation, and particularly for predicting the point where the A/D converter operation becomes unstable.     

随机噪声信号的功率谱估计的仿真

在通讯与电子信息工程行业及领域中,大部分问题的解决需要进行估计一个随机信号在频率域上的功率谱分布,诸如此类的问题有很多,比如：设计滤波器消除噪声信号,振动随机信号的回波抵消,随机信号的特征抽取与表示等等。功率谱估计的分类：一般分为两大类,一类是参数法功率谱估计,一类是非参数法功率谱估计。参数法功率谱估计通常对数据进行一种建模,比如把数据建模成滑动平均模型（Moving Average）,或者自回归（Autoregressive）模型,而非参数法功率谱估计。除了要求信号满足广义平稳之外,不需要其它的统计假设。与非参数法相比较,参数法的优点是在一个给定的数据集合上能够有较少的误差、偏差与方差。     

Least-square estimation of average power in digital CMOS circuits

The estimation of average-power dissipation of a circuit through exhaustive simulation is impractical due to the large number of primary inputs and their combinations. In this work, two algorithms based on least square estimation are proposed for determining the average power dissipation in complementary metal-oxide-semiconductor (CMOS) circuits. Least square estimation converges faster by attempting to minimize the mean square error value during each iteration. Two statistical approaches namely, the sequential least square (SLS) estimation and the recursive least square estimation are investigated. The proposed methods are distribution independent in terms of the input samples, unbiased and point estimation based. Experimental results presented for the MCNC'91 and the ISCAS'89 benchmark circuits show that the least square estimation algorithms converge faster than other statistical techniques such as the Monte Carlo method and the DIPE     

Nonparametric estimation of mean Doppler and spectral width

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order     

Spatially Adaptive Estimation via Fitted Local Likelihood Techniques

This paper offers a new technique for spatially adaptive estimation. The local likelihood is exploited for nonparametric modeling of observations and estimated signals. The approach is based on the assumption of a local homogeneity of the signal: for every point there exists a neighborhood in which the signal can be well approximated by a constant. The fitted local likelihood statistics are used for selection of an adaptive size and shape of this neighborhood. The algorithm is developed for a quite general class of observations subject to the exponential distribution. The estimated signal can be uni- and multivariable. We demonstrate a good performance of the new algorithm for image denoising and compare the new method versus the intersection of confidence interval (ICI) technique that also exploits a selection of an adaptive neighborhood for estimation.     

On nonparametric spectral estimation

In this paper the Cramér-Rao bound (CRB) for a general nonparametric spectral estimation problem is derived under a local smoothness condition (more exactly, the spectrum is assumed to be well approximated by a piecewise constant function). Further-more, it is shown that under the aforementioned condition the Thomson method (TM) and Daniell method (DM) for power spectral density (PSD) estimation can be interpreted as approximations of the maximum likelihood PSD estimator. Finally the statistical efficiency of the TM and DM as nonparametric PSD estimators is examined and also compared to the CRB for autoregressive moving-average (ARMA)-based PSD estimation. In particular for broadband signals, the TM and DM almost achieve the derived nonparametric performance bound and can therefore be considered to be nearly optimal.This work was supported in part by the Swedish Foundation for Strategic Research (SSF) through the Senior Individual Grant Program.     

Nonparametric multivariate density estimation: a comparative study

The paper algorithmically and empirically studies two major types of nonparametric multivariate density estimation techniques, where no assumption is made about the data being drawn from any of known parametric families of distribution. The first type is the popular kernel method (and several of its variants) which uses locally tuned radial basis (e.g., Gaussian) functions to interpolate the multidimensional density; the second type is based on an exploratory projection pursuit technique which interprets the multidimensional density through the construction of several 1D densities along highly “interesting” projections of multidimensional data. Performance evaluations using training data from mixture Gaussian and mixture Cauchy densities are presented. The results show that the curse of dimensionality and the sensitivity of control parameters have a much more adverse impact on the kernel density estimators than on the projection pursuit density estimators     

Theoretical and Experimental Studies of a Probabilistic-Based Memoryless PA Linearization Technique

This paper studies the performance of a memoryless power amplifier (PA) linearization technique based on a probabilistic approach. This technique employs a nonparametric method to derive a predistorter function, which does not need any parametric modeling and explicit parameter estimation. It only needs to calculate a probabilistic cumulative distribution function (CDF) and a quantile function (an inverse function of the CDF). Histogram and order statistic methods are proposed to perform the calculation. A rigorous analytic formula is derived for the inter-modulation product power (IMPP) of the PA output signal when a finite number of samples as well as a finite number of bins are used to calculate the CDF and the quantile function. The analytic results show that, with the probabilistic-based technique, the IMPP approaches zero as the number of samples approaches infinity and the bin width approaches zero. Computer simulations are utilized to verify the theoretical analysis and to compare the performance of the probabilistic-based linearization technique with those of other memoryless PA linearization techniques, while a prototype experiment is carried out to demonstrate its performance in a practical application. Results show that the technique can accurately determine the predistortion function that effectively compensates for the nonlinearity in the PA, and that it achieves a much better linearization performance compared to other existing methods, especially in the presence of a loop delay in the feedback circuit.     

Multivariate statistical modeling for image denoising using wavelet transforms

Recently a variety of efficient image denoising methods using wavelet transforms have been proposed by many researchers. In this paper, we derive the general estimation rule in the wavelet domain to obtain the denoised coefficients from the noisy image based on the multivariate statistical theory. The multivariate distributions of the original clean image can be estimated empirically from a sample image set. We define a parametric multivariate generalized Gaussian distribution (MGGD) model which closely fits the sample distribution. Multivariate model makes it possible to exploit the dependency between the estimated wavelet coefficients and their neighbours or other coefficients in different subbands. Also it can be shown that some of the existing methods based on statistical modeling are subsets of our multivariate approach. Our method could achieve high quality image denoising. Among the existing image denoising methods using the same type of wavelet (Daubechies 8) filter, our results produce the highest peak signal-to-noise ratio (PSNR).     

The use of nonparametric statistics in quantitative electron microscopy

Parametric statistical methods assume samples that have a normal distribution and representative sample sizes (i.e. n >20). Quantitative electron microscopy is inherently restricted to small sample sizes and a priori there is no way to know if the expression of the ligand being studied has a normal distribution. Thus to make statistical inferences based on data generated by quantitative electron microscopy using parametric methods may not be justified. Nonparametric statistical methods offer a tool for the evaluation of data that do not meet the criteria for analysis by parametric methods. In this report I show the utility of using nonparametric statistical methods for the analysis of data generated by quantitative electron microscopy.     

电子倍增CCD噪声参数的估计方法

为定量评价电子倍增CCD(EMCCD)图像噪声的大小,实现对EMCCD 图像噪声参数的准确估计,研究了EMCCD 的噪声分布模型及其参数估计方法。首先,讨论了EMCCD 图像的噪声来源及其统计特性,由此建立了适于EMCCD 的噪声分布模型。然后,提出了两种EMCCD 噪声参数估计方法矩估计法和高斯-牛顿法,采用Monte Carlo 仿真验证其性能。仿真结果表明,矩估计法和高斯-牛顿法的平均相对误差和相对标准偏差均为10-2 量级,估计精度较高,且高斯-牛顿法的估计精度要高于矩估计法。采集一系列无增益时积分时间为50 s的暗场图片和增益为50 的本底图片,利用矩估计法和高斯-牛顿法分别估计出EMCCD 的暗电流噪声、时钟感生电荷噪声和读出噪声,实验结果表明,估计值与EMCCD 指标值一致,证明矩估计法和高斯-牛顿法能有效估计噪声参数且具有较高的精度。     

Confidence assessment of quality prediction from processmeasurement in sequential manufacturing processes

Sequential manufacturing processes are common in many manufacturing industries. We can use an artificial neural network (ANN) technique to build a model of manufacturing processes to capture the relationship between process measures and production unit quality. Using the ANN model, the quality value of a production unit can be predicted for its process measures. In addition to the predicted quality value, we need to assess our confidence in the predicted quality value through a confidence interval (prediction interval). Little work exists to assess the confidence in ANN outputs. This paper presents a comparative study of several methods in assessing the confidence in ANN outputs for quality prediction. We investigate two new methods: the variance estimation method and the distribution estimation method, in comparison with two existing methods: the error estimation method and the linear regression method. With respect to prediction accuracy and power, our results show that the distribution estimation method appears very promising among the four methods. However, the distribution estimation method requires much computation and storage during training and prediction, which may create difficulty in real-time quality monitoring and control. For the consideration of computation and storage requirement, the variance estimation method provides an acceptable solution. The error estimation method produces the worst performance among the four methods     

Bayes inference for a non-homogeneous Poisson process with powerintensity law [reliability]

Monte Carlo simulation is used to assess the statistical properties of some Bayes procedures in situations where only a few data on a system governed by a NHPP (nonhomogeneous Poisson process) can be collected and where there is little or imprecise prior information available. In particular, in the case of failure truncated data, two Bayes procedures are analyzed. The first uses a uniform prior PDF (probability distribution function) for the power law and a noninformative prior PDF for α, while the other uses a uniform PDF for the power law while assuming an informative PDF for the scale parameter obtained by using a gamma distribution for the prior knowledge of the mean number of failures in a given time interval. For both cases, point and interval estimation of the power law and point estimation of the scale parameter are discussed. Comparisons are given with the corresponding point and interval maximum-likelihood estimates for sample sizes of 5 and 10. The Bayes procedures are computationally much more onerous than the corresponding maximum-likelihood ones, since they in general require a numerical integration. In the case of small sample sizes, however, their use may be justified by the exceptionally favorable statistical properties shown when compared with the classical ones. In particular, their robustness with respect to a wrong assumption on the prior β mean is interesting     

Distributed source modeling and direction-of-arrival estimationtechniques

In direction-of-arrival (DOA) estimation, the direction of a signal is usually assumed to be a point. If the direction of a signal is distributed due to some environmental phenomenon, however, DOA estimation methods based on the point source assumption may result in poor performance. We consider DOA estimation when the signal sources are distributed. Parametric and nonparametric models are proposed, and estimation methods are considered under these models. In addition, the asymptotic distribution of estimation errors is obtained to show the models' statistical properties     

On adaptive nonparametric detection systems using dependent samples

A procedure is obtained for modifying given sampled-data parametric detectors to make them asymptotically nonparametric. Unlike standard nonparametric devices, these detectors do not require the assumption of independent samples but only a knowledge of the input spectral shapes. As examples of this technique, two types of conventional array detectors are modified to produce nonparametric systems.     

Nonparametric Model Comparison and Uncertainty Evaluation for Signal Strength Indoor Location

Indoor Location (IL) using Received Signal Strength (RSS) is receiving much attention, mainly due to its ease of use in deployed IEEE 802.11b (WiFi) wireless networks. Fingerprinting is the most widely used technique. It consists of estimating position by comparison of a set of RSS measurements, made by the mobile device, with a database of RSS measurements whose locations are known. However, the most convenient data structure to be used and the actual performance of the proposed fingerprinting algorithms are still controversial. In addition, the statistical distribution of indoor RSS is not easy to characterize. Therefore, we propose here the use of nonparametric statistical procedures for diagnosis of the fingerprinting model, specifically: 1) A nonparametric statistical test, based on paired bootstrap resampling, for comparison of different fingerprinting models and 2) new accuracy measurements (the uncertainty area and its bias) which take into account the complex nature of the fingerprinting output. The bootstrap comparison test and the accuracy measurements are used for RSS-IL in our WiFi network, showing relevant information relating to the different fingerprinting schemes that can be used.     

Interconnect-based system-level energy and power prediction to guide architecture exploration

We present a novel technique to predict energy and power consumption in an electronic system, given its behavioral specification and library components. The early prediction gives circuit designers the freedom to make numerous high-level choices (such as die size, package type, and latency of the pipeline) with confidence that the final implementation will meet power and energy as well as cost and performance constraints. Our unique statistical estimation technique associates low-level, technology dependent physical and electrical parameters, with expected circuit resources and interconnect. Further correlations with switching activity yield accurate results consistent with implementations. All feasible designs are investigated using this technique and the designer may tradeoff between small size, high speed, low energy, and low power. The results for designs of two popular signal processing applications, predicted prior to synthesis, are within 10% accuracy of power estimates performed on synthesized layouts.     

Wavelet thresholding techniques for power spectrum estimation

Estimation of the power spectrum S(f) of a stationary random process can be viewed as a nonparametric statistical estimation problem. We introduce a nonparametric approach based on a wavelet representation for the logarithm of the unknown S(f). This approach offers the ability to capture statistically significant components of ln S(f) at different resolution levels and guarantees nonnegativity of the spectrum estimator. The spectrum estimation problem is set up as a problem of inference on the wavelet coefficients of a signal corrupted by additive non-Gaussian noise. We propose a wavelet thresholding technique to solve this problem under specified noise/resolution tradeoffs and show that the wavelet coefficients of the additive noise may be treated as independent random variables. The thresholds are computed using a saddle-point approximation to the distribution of the noise coefficients