Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Crame/spl acute/r-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.     

A comparison between different polarimetric measurement schemes

The usefulness of polarization information in remote sensing applications has been clearly demonstrated in the last two decades. Land covers and meteorological targets are complex and their backscatter returns are time varying. Their polarimetric characteristics should be determined in terms of second order statistics of scattering matrix elements. These are contained. in the polarimetric covariance matrix. Estimation of polarimetric covariance matrix elements has been addressed by different authors based on different scattering matrix measurement methods. The most widely used and implemented method consists in the alternate transmission of two orthogonal polarizations while. receiving with both. Recently, a method that considers simultaneous transmission of two orthogonal polarizations, which are phase coded with orthogonal signals, has been proposed. Another method, specifically developed to obtain the polarimetric covariance matrix, is based on transmitting three different polarizations and receiving their corresponding co-polar and cross-polar counterparts. Different data sets result from each measurement technique and different estimators of polarimetric covariance matrix elements have been developed for the different data sets available. These various methods are investigated in here. Based on simulated data the performance of the different estimators under different working conditions are analyzed. Effects on the estimators of operation frequency, pulse repetition frequency (PRF) and temporal properties of targets are discussed     

Power estimation methods for analog circuits for architecturalexploration of integrated systems

This paper describes methods for analog-power estimation and applies them practically to two different classes of analog circuits. Such power estimators, which return a power estimate given only a block's specification values without knowing its detailed circuit implementation, are valuable components for architectural exploration tools and hence interesting for high-level system designers. As an illustration, two estimators are presented: one for high-speed analog-to-digital converters (ADCs) and one for analog-continuous time filters. The ADC power estimator is a technology scalable closed formula and yields first-order results within an accuracy factor of about 2.2 for the whole class of high-speed Nyquist-rate ADCs. The filter-power estimator is of a more complex nature. It uses a crude filter synthesis, in combination with operational transconductor amplifier behavioral models to generate accurate results as well, but restricted to certain filter implementations     

Estimating the number of errors in a system using a martingaleapproach

A new, efficient procedure estimates the number of errors in a system. A known number of seeded errors are inserted into a system. The failure intensities of the seeded and real errors are allowed to be different and time dependent. When an error is detected during the test, it is removed from the system. The testing process is observed for a fixed amount of time τ. Martingale theory is used to derive a class of estimators for the number of seeded errors in a continuous time setting. Some of the estimators and their associated standard deviations have explicit expressions. An optimal estimator among the class of estimators is obtained. A simulation study assesses the performance of the proposed estimators     

An iterative algorithm for the computation of the MVDR filter

Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation     

Estimation of frequencies and damping factors by two-dimensionalESPRIT type methods

In this paper, we consider two-dimensional (2-D) signals modeled by the sum of damped cisoids. We propose two high-resolution approaches to estimate their frequencies and damping factors. Both high-resolution methods are based on the shift-invariance structure of the signal subspace related to each dimension. The first one estimates the frequency components in both dimensions as in the matrix enhancement and matrix pencil (MEMP) method before pairing them with a new algorithm. The second one consists of the direct estimation of the signal frequency pairs without an additional step to pair the frequencies related to each dimension. We show how these methods can estimate the scattering points of radar images     

Robust estimation of structured covariance matrices

In the context of the narrowband array processing problem, robust methods for accurately estimating the spatial correlation matrix using a priori information about the matrix structure are developed. By minimizing the worse case asymptotic variance, robust, structured, maximum-likelihood-type estimates of the spatial correlation matrix in the presence of noises with probability density functions in the ∈-contamination and Kolmogorov classes are obtained. These estimates are robust against variations in the noise's amplitude distribution. The Kolmogorov class is demonstrated to be the natural class to use for array processing applications, and a technique is developed to determine exactly the size of this class. Performance of bearing estimation algorithms improves substantially when the robust estimates are used, especially when nonGaussian noise is present. A parametric structured estimate of the spatial correlation matrix that allows direct estimation of the arrival angles is also demonstrated     

Near-optimal range and depth estimation using a vertical array in acorrelated multipath environment

This paper proposes a near-optimal procedure to localize a single stationary source in a two-path underwater acoustic environment. The investigation is for an M-element vertical array with omnidirectional sensors. The range and depth estimators are developed using a linear least-squares technique when a set of auto- and cross-correlators is used for time difference of arrival (TDOA) estimates. A weighting matrix is derived to achieve the approximate maximum likelihood (ML) performance of the weighted least-squares range and depth estimators. The expressions for error variances and covariances of the range and depth estimates are derived with a small error analysis technique. It is verified analytically that the error covariance matrix of the weighted least-squares solutions reaches the Cramer-Rao lower bound in the small error region. The correlation of the range and depth estimation errors is investigated. Results show that the range and depth estimation errors are highly correlated in a multipath environment. The accuracy properties of the proposed multipath localization procedure are analyzed using different array configurations. The results show that the performances of the range and depth estimators are significantly improved if the linear-dependent TDOA estimates are included for localizing and that the unweighted range and depth estimators, using the entire set of TDOAs, are approximately optimal for most of the applications. The theoretical development of error variance and covariance expressions of the range and depth estimates, which incorporates the correlation in the TDOA estimates, is corroborated with Monte Carlo simulations     

A comparative study of iterative channel estimators for mobile OFDM systems

We investigate two iterative channel estimators for mobile orthogonal-frequency division multiplexing. The first estimator is based on iterative filtering and decoding whereas the second one uses an a posteriori probability (APP) algorithm. The first method consists of two cascaded one-dimensional Wiener filters, which interpolate the unknown time-varying two-dimensional frequency response in between the known pilot symbols. As shown, the performance can be increased by feeding back the likelihood values at the output of the APP-decoder to iteratively compute an improved estimate of the channel frequency response. The second method applies two APP estimators, one for the frequency and the other one for the time direction. The two estimators are embedded in an iterative loop similar to the turbo decoding principle. As shown in detail, this iterative estimator is superior and its performance is independent of whether the chosen time-frequency pilot grid satisfies the two-dimensional sampling theorem or not. The bit-error rate as a function of the signal-to-noise ratio is used as a performance measure. In addition, the convergence of the iterative decoding loop is studied with the extrinsic information transfer chart.     

Fast nearly ML estimation of the parameters of real or complexsingle tones or resolved multiple tones

This paper presents new computationally efficient algorithms for estimating the parameters (frequency, amplitude, and phase) of one or more real tones (sinusoids) or complex tones (cisoids) in noise from a block of N uniformly spaced samples. The first algorithm is an interpolator that uses the peak sample in the discrete Fourier spectrum (DFS) of the data and its two neighbors. We derive Cramer-Rao bounds (CRBs) for such interpolators and show that they are very close to the CRB's for the maximum likelihood (ML) estimator. The new algorithm almost reaches these bounds. A second algorithm uses the five DFS samples centered on the peak to produce estimates even closer to ML. Enhancements are presented that maintain nearly ML performance for small values of N. For multiple complex tones with frequency separations of at least 4π/N rad/sample, unbiased estimates are obtained by incorporating the new single-tone estimators into an iterative “cyclic descent” algorithm, which is a computationally cheap nonlinear optimization. Single or multiple real tones are handled in the same way. The new algorithms are immune to nonzero mean signals and (provided N is large) remain near-optimal in colored and non-Gaussian noise     

Local Linear Estimators for the Bioelectromagnetic Inverse Problem

Linear estimators have been used widely in the bioelectromagnetic inverse problem, but their properties and relationships have not been fully characterized. Here, we show that the most widely used linear estimators may be characterized by a choice of norms on signal space and on source space. These norms depend, in part, on assumptions about the signal space and source space covariances. We demonstrate that two estimator classes (standardized and weight vector normalized) yield unbiased estimators of source location for simple source models (including only the noise-free case) but biased estimators of source magnitude. In the presence of instrumental (white) noise, we show that the nonadaptive standardized estimator is a biased estimator of source location, while the adaptive weight vector normalized estimator remains unbiased. A third class (distortionless) is an unbiased estimator of source magnitude but a biased estimator of source location.     

采用复高斯分布模型的两步噪声幅度谱估计算法

噪声幅度谱估计是有效抑制外界噪声干扰、提高语音增强算法整体输出性能的重要环节。但目前针对该问题的研究相对较少,常用的语音激活检测算法只能在语音不存在阶段对噪声信号的幅度谱进行更新或估计,无法适用于更为复杂的非平稳噪声环境。为克服这一问题,本文基于噪声频谱的复高斯分布模型假设,提出了新型的两步噪声幅度谱估计算法。算法首先采用软判决技术计算噪声信号的功率谱,然后再结合复高斯分布条件下信号幅度谱和功率谱之间的数学关系间接地获取噪声幅度谱的估计。文中基于这一结论给出了两种估计算法,并在多种噪声环境下对它们的性能进行了仿真评估,其测试结果有效表明了提出算法优良的估计性能。      

基于连续符号平均功率方差最小化的CM-OFDM系统盲载波频偏估计算法

针对数字信号在正交频分复用（OFDM）系统中传输受载波频率偏移(CFO)敏感的问题,提出一种基于连续符号平均功率方差最小化的恒模OFDM（CM-OFDM）系统盲载波频偏估计算法。该算法基于频域信号恒模特性构造出代价函数,通过试验三个频偏估计量对CM-OFDM系统中的时域信号进行补偿,并最终采用蒙特卡罗的方法估计出CFO。此外,利用快速傅里叶变换（FFT）的正反变换构成一个酉矩阵,从而降低算法计算过程的复杂度。仿真表明,提出的算法有效的提高了CFO估计的性能,并且具有较好的鲁棒性。      

Nonparametric Bayes-risk estimation

Two nonparametric methods to estimate the Bayes risk using classified sample sets are described and compared. The first method uses the nearest neighbor error rate as an estimate to bound the Bayes risk. The second method estimates the Bayes decision regions by applying Parzen probability-density function estimates and counts errors made using these regions. This estimate is shown to be asymptotically consistent in mean square. The results of experiments with these estimators on simulated and empirical data imply that the estimators both have acceptable small-sample properties; however, small-sample convergence of both estimators depends strongly on the choice of metric and local area or window size in the measurement space.     

Separation of multiple time delays using new spectral estimationschemes

The problem of estimating multiple time delays in presence of colored noise is considered. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target     

Class of cyclic-based estimators for frequency-offset estimation ofOFDM systems

We present a new class of blind cyclic-based estimators for carrier frequency-offset and symbol-timing error estimation of orthogonal frequency-division multiplexing (OFDM) systems. The proposed approach exploits the properties of the cyclic prefix subset to reveal the synchronization parameters in the likelihood function of the received vector. A new likelihood function for the joint timing and frequency-offset estimation is derived, which globally characterizes the estimation problem. The resulting probabilistic measure is used to develop three classes of unbiased estimators, namely, maximum-likelihood, minimum variance unbiased, and moment estimator. In comparison to the previously proposed methods, the proposed estimators in this study are computationally and statistically efficient, which makes the estimators more attractive for real-time applications. The performance of the estimators is assessed by simulation for an OFDM system     

Markov-based eigenanalysis method for frequency estimation

This paper proposes an eigenanalysis-based method for estimating the frequencies of complex-valued sine waves. The basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix. Exploiting that orthogonality condition gives an overdetermined system of linear equations, the unknown parameters of which are uniquely related to the frequencies. Analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations. Based on these expressions a Markov-like estimate of the unknown parameters is introduced, which asymptotically (with respect to either the number of data samples or the signal-to-noise ratio) provides the minimum variance frequency estimates in a fairly large class of consistent estimators. The paper includes Monte-Carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal-to-noise ratio     

Resource allocation for multiple classes of DS-CDMA traffic

We consider a packet data direct-sequence code-division multiple-access (DS-CDMA) system which supports integrated services. The services are partitioned into different traffic classes according to information rate (bandwidth) and quality of service (QoS) requirements. Given sufficient bandwidth, QoS requirements can be satisfied by an appropriate assignment of transmitted power and processing gain to users in each class. The effect of this assignment is analyzed for both a single class of data users and two classes of voice and data users. For a single class of data users, we examine the relationship between average delay and processing gain, assuming that ARQ with forward error correction is used to guarantee reliability. The only channel impairment considered is interference, which is modeled as Gaussian noise. A fixed user population is assumed and two models for generation of data packets are considered: (1) each user generates a new packet as soon as the preceding packet is successfully delivered and (2) each user generates packets according to a Poisson process. In each case, the packets enter a buffer which is emptied at the symbol rate. For the second traffic model, lowering the processing gain below a threshold can produce multiple operating points, one of which corresponds to infinite delay. The choice of processing gain which minimizes average delay in that case is the smallest processing gain at which multiple operating points are avoided. Two classes of users (voice/data and two data classes) are then considered. Numerical examples are presented which illustrate, the increase in the two-dimensional (2-D) capacity region achievable by optimizing the assignment of powers and processing gains to each class     

Transformation of oscillators using Op Amps,unity gain cells and CFOA

A new approach in the systematic synthesis of current conveyor based active RC canonic oscillators is given. The synthesis procedure is based on the generalized systematic synthesis framework using admittance matrix expansion. The resulting derived oscillators include many novel oscillators, using various types of current conveyors and inverting current conveyors. The oscillators considered in this paper uses the minimum number of passive elements namely two capacitors and three resistors necessary to have independent control on the condition of oscillation and on the frequency of oscillation. The generated oscillators employ two grounded capacitors and have the advantage of their ability to absorb parasitic element effects. Three classes are considered in this paper, class I oscillators have a common node between one of the capacitors and one of the two grounded resistors. Class II oscillators have a common node between one of the capacitors and the floating resistor. Class III has all three resistors being grounded and one of them shares a node with one of the capacitors. It should be noted that this is the first paper in the literature to use nodal admittance matrix expansion in the generation of current conveyor oscillators. Spice simulation results are included to support the theory. The proposed method can be generalized to other active devices.