Burst-mode receivers are key components of optical transmission systems, including passive optical networks, and have received much attention in recent years. We present new, efficient methods for burst optical signal detection in burst-mode data transmission using a modified K-means clustering technique. We also develop a data-aided feedforward symbol-timing recovery method based on a polynomial interpolation and maximum-likelihood estimation theory. A performance criterion considering the error caused by the interpolation approximation is derived for this method. The proposed detection and timing recovery approaches can be implemented effectively and rapidly; therefore, they are very suitable for burst-mode receivers. We also provide some numerical examples to demonstrate the performance of the proposed methods.

Burst mode receivers are key components of optical transmission systems and have received much attention in recent years. We present new efficient methods for burst optical signal detection and blind channel estimation in burst-mode data transmission based on a modified K-means clustering technique. A data-aided feedforward symbol timing recovery method is also developed, based on polynomial interpolation and maximum likelihood estimation theory. It can be implemented rapidly and efficiently; therefore, it is suitable for burst mode receivers. A performance criterion of this method has also been derived. We also give some numerical examples to demonstrate the performance of the proposed methods.

Practical sensor arrays are characterized by certain parameters, related to the array shape and its electrical properties. Accurate direction finding requires calibration of these parameters to a relatively high accuracy. Off-line calibration of the array parameters is performed by transmitting signals from known locations and measuring the array response. This paper relates the parameter estimation accuracy achieved in off-line calibration to the direction-of-arrival errors during on-line operation. It then proposes a criterion for choosing the off-line calibration points so as to meet on-line accuracy requirements.

This paper presents an algorithm for exhaustive extrema computation of one-dimensional cost functions. Its applicability to array signal processing is demonstrated. We use it for antenna array design, and to solve a multiple source direction finding problem using MUSIC, beamformer and minimum variance methods.

The high-order ambiguity function (HAF) is a nonlinear operator designed to detect, estimate, and classify complex signals whose phase is a polynomial function of time. The HAF algorithm, introduced by Peleg and Porat (1991), estimates the phase parameters of polynomial-phase signals measured in noise. The purpose of this correspondence is to analyze the asymptotic accuracy of the HAF algorithm in the case of additive white Gaussian noise. It is shown that the asymptotic variances of the estimates are close to the Cramer-Rao bound (CRB) for high SNR. However, the ratio of the asymptotic variance and the CRB has a polynomial growth in the noise variance.

The paper develops a method of error analysis for Fourier-transform based sinusoidal frequency estimation in the presence of nonrandom interferences. A general error formula is derived, and then specialized to the cases of additive and multiplicative interferences. Approximate error formulas are derived for the case of additive polynomial-phase interference. Finally, an application to error-analysis in estimating the parameters of multiple polynomial-phase signals is discussed in detail.

The detection of transient signals is often performed in the time-frequency transform domain. An analytical framework is developed within which the performance of different detectors based on linear transforms can be easily compared, for different classes of signals. This framework is used to evaluate and compare the performance of detectors based on the Gabor (1946) transform and on the short-time Fourier transform.>

The problem of detecting short-duration nonstationary signals, which are commonly referred to as transients, is addressed. Transients are characterized by a signal model containing some unknown parameters, and by a 'model mismatch' representing the difference between the model and the actual signal. Both linear and nonlinear signal models are considered. The transients are assumed to undergo a noninvertible linear transformation prior to the application of the detection algorithm. Examples of such transforms include the short-time Fourier transform, the Gabor transform, and the wavelet transform. Closed-form expressions are derived for the worst-case detection performance for all possible mismatch signals of a given energy. These expressions make it possible to evaluate and compare the performance of various transient detection algorithms, for both single-channel and multichannel data. Numerical examples comparing the performance of detectors based on the wavelet transform and the short-time Fourier transform are presented.>

The measurement of the parameters of complex signals with constant amplitude and polynomial phase, measured in additive noise, is considered. A novel new integral transform that is adapted for signals of this type is introduced. This transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance. The algorithms are extended to constant amplitude and continuous nonpolynomial phase signals.>

Imposing a total-order on a two-dimensional discrete homogeneous random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic one. The purely indeterministic component is shown to have a two-dimensional white-innovations driven MA representation. The two-dimensional deterministic random field can be perfectly predicted from the field's past samples. This field is further orthogonally decomposed into a purely deterministic field that represents the remote past of the field and can thus be perfectly predicted given enough arbitrarily located data samples, and an evanescent component. The evanescent component can be further decomposed into a remote columnwise past component and a column-to-column renewal field.>

Two types of high-resolution direction-finding algorithms which use the fourth-order cumulants of the array data are derived. One is a MUSIC-like technique based on eigendecomposition of a suitably defined cumulant matrix. The other is an optimal (asymptotically minimum variance) estimator based on minimization of a certain cost function.>

An algorithm for detecting moving targets by imaging sensors and estimating their trajectories is proposed. The algorithm is based on directional filtering in the frequency domain, using a bank of filters for all possible target directions. The directional filtering effectively integrates the target signal, resulting in an improved signal-to-noise ratio. Working in the frequency domain facilitates a considerable reduction in computational requirements compared to time-domain algorithms. The algorithm is described in detail, and its false alarm and detection probabilities are analyzed.>

The authors present several algorithms for estimating the parameters of MA (moving average) and ARMA (autoregressive moving average) non-Gaussian processes from sample high-order moments. These algorithms use explicitly the second-order statistics of the sample moments, which is estimated from the measurements. The asymptotically minimum-variance algorithms are shown, by numerical simulations, to perform close to theoretical predictions. The optimal weighted least-squares algorithms do not reach their theoretical performance, but they still offer some improvement over simpler algorithms. Since the computational load for the minimum variance algorithm is similar to that of the weighted least-squares algorithm, while its statistical accuracy is considerably higher, it is preferable to the weighted least-squares for most applications. The main disadvantage of the minimum variance algorithm is its more complex implementation (programming), especially the need for an iterative optimization procedure.>

An algorithm for blind adaptive equalization of digital communication channels for QAM (quadrature amplitude modulation) signals is derived. The algorithm uses the fourth-order statistical moments of the symbol sequence explicitly. The algorithm is linear, and is fundamentally different from common gradient-type algorithms intended for the same purpose.>

The estimation of the covariances of a stationary time series with missing observations is considered. General formulas for the asymptotic second-order moments of the sample covariances of such a time series are given for either random or deterministic patterns of misses. Closed-form expressions are derived for the random Bernoulli pattern and for the deterministic periodic pattern of missing observations and are explicitly evaluated for autoregressive moving-average time series. These results are useful for constructing and analyzing parameter or spectrum estimation algorithms based on the sample covariances for a stationary time series with missing observations.>

The problem of spectral estimation through the autoregressive moving-average (ARMA) modeling of stationary processes with missing observations is considered. A class of estimators based on the sample covariances is presented, and an asymptotically optimal estimator in this class is proposed. The proposed algorithm is based on a nonlinear-least-squares fit of the sample covariances computed from the data to the true covariances of the assumed ARMA model. The statistical properties of the algorithm are explored and used to show that it is asymptotically optimal, in the sense of achieving the smallest possible asymptotic variance. The performance of the algorithm is illustrated by some numerical examples.>

Results are presented concerning the performance of moving-average (MA) estimation algorithms based on high-order moments. A general lower bound is presented for the variance of estimates based on high-order sample moments. Then, an expression is given for the variance of weighted least-squares estimates, of the type recently reported in the literature. The existence of an optimal-weight matrix for such estimates is exhibited. The analytic results are verified by Monte-Carlo simulations for some specific test cases.>

The authors provide an analytic performance evaluation of the errors of the direction-of-arrival estimates obtained by the MUSIC algorithm for uncorrelated sources. Explicit asymptotic formulas are given for the covariances of the estimates. The covariances are then compared to the Cramer-Rao lower bound. It is shown that, for a single source, the MUSIC algorithm is asymptotically efficient. For multiple sources, the algorithm is not efficient when the SNRs (signal-to-noise ratios) of all sources tend to infinity.>

Recently, Kumaresan and Tufts (KT) presented a method for estimating the parameters of damped exponential waveforms in additive white noise. The KT method uses singular value decomposition (SVD) of the data matrix, with truncation and backward prediction to improve the accuracy of the estimates. The KT method was demonstrated to have a very good performance, in comparison with traditional methods used for the same problem. In this paper we provide a quantitative accuracy analysis of the KT method. The analysis is based on first order Taylor series approximations of the estimated parameters around their true values. Results of the analysis were illustrated by some numerical examples in [3]. These results confirm the good performance of the KT method, and show the effect of the user chosen parameters on the accuracy of the estimates.

This paper proposes to use the Gabor representation for the detection of transient signals with unknown arrival times. We introduce a one-sided exponential window function, which seems to the most appropriate for transient modeling. Explicit expressions for the Gabor coefficients are given for this window function. When the given signal is random, so are the coefficients. The second-order moments of the Gabor coefficients are computed for a white noise signal. These are then used to introduce a detection statistic based on the Gabor coefficients. The proposed detector is capable of separating transients having different arrival times, even in the case where their waveforms partially overlap.

This paper proposes a new algorithm for detecting moving targets by mosaic sensors and estimating their trajectories. The algorithm is based on directional filtering in the frequency domain, using a bank of filters for all possible target directions. The proposed algorithm is described in detail, and its performance is illustrated by a numerical example.

The paper addresses the issue of estimating the parameters of stationary time series from finite or infinite sets of sample covariances. Several known results concerning finite sets of sample covariances are briefly reviewed. It is then shown that for certain Gaussian processes an efficient estimation of the process parameters is possible if the number of sample covariances used by the estimation algorithm tends to infinity. Next we examine stationary processes whose innovations are non-Gaussian. It is shown that the achievable accuracy of the parameter estimates based on the sample covariances is the same as that for the Gaussian case. Thus, parameter estimates based on sample covariances are insensitive to the process distribution and as a result, these estimates are generally statistically inefficient.

In this paper we consider the problem of spectral estimation through ARMA modeling of stationary time series witch missing observations. We consider estimators based on the sample covariances, and present an asymptotically optimal estimator among this group. The algorithm is based on a nonlinear least squares fit of the sample covariances computed from the data with missing observations to the true covariances of the assumed ARMA model. The statistical properties of the algorithm are shown to be asymptotically optimal. The performance of the algorithm is illustrated by a numerical example.

The sample variance is commonly used to estimate the variance of stationary time series. When the second-order statistics of the process are known up to a scaling factor, this estimator is generally inefficient. In the case of an autoregressive (AR) process with unknown parameters, the sample variance is shown to be asymptotically efficient. However, the sample variance of a moving-average (MA) process with unknown parameters is generally an inefficient estimator. Closed-form expressions are derived for the Cramer-Rao hound associated with the variance estimation problem and for the variance of the sample-variance estimator, for both AR and MA processes.

An asymptotic formula is derived for the Cramer-Rao lower bound on unbiased estimates of the parameters of Gaussian autoregressive moving-average (ARMA) processes, in the case where the measurements are not contiguous, but follow a periodic pattern of misses. The formula is then used to illustrate the behavior of the bound for some specific examples.

The accuracy of ARMA spectral estimation methods is investigated. A lower bound for spectral estimates based on sample covariances is derived. Numerical examples are presented to illustrate the potential loss of accuracy when using sample covariances rather than the data.

A new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise. The algorithm is composed of two cascaded parts. The first estimates the fundamental frequency and enhances the harmonic component in the input. The second estimates the harmonic amplitudes and phases. Performance analysis provides new results for the asymptotic Cramer-Rao bound (CRB) on the parameters of harmonic signals with additive white noise.

The paper discusses the problem of detecting transient signals of unknown waveforms in white Gaussian noise. The signals are modeled as impulse responses of rational transfer functions with unknown parameters. A generalized likelihood ratio test (GLRT) is proposed and its statistical properties are analyzed. The GLRT involves constrained maximum likelihood estimation of the signal parameters. The distribution of the likelihood ratio is shown to be a central quadratic form under H0, and a noncentral quadratic form under H1.

The problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered. A new ARMA method is proposed for this problem, based on nonlinear optimization of a weighted squared error criterion. The method can handle either regularly or randomly missing observations. As a special case, the method can handle the problem of missing sample covariances. The computational complexity is modest compared to exact maximum likelihood estimation of the same parameters.

The problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered. A new autoregressive moving-average (ARMA) method is proposed for this problem, based on nonlinear optimization of a weighted-squared-error criterion. The method can handle either regularly or randomly missing observations. As a special case, the method can handle the problem of missing sample covariances. The computational complexity is modest compared to exact maximum likelihood estimation of the same parameters. The performance of the algorithm is illustrated by some numerical examples and is shown to be statistically efficient in these cases.

An iterative frequency domain technique is presented for estimating autoregressive moving-average (ARMA) parameters. The technique is based on minimizing the error between the sample power spectrum and a spectral model. The variance of the estimation error is shown to be close to the Cramer-Rao bound for some examples.

The problem of estimating spatial and spectral parameters of multiple sources by sensor arrays is considered. A parametric model is derived for the multichannel measurement vector. Tbe model parameters are the time delays and the autoregressive moving-average parameters of all the sources. A suboptimal parameter estimation procedure is proposed, and simulation results are presented to illustrate its performance.

Estimating the time-delay between two received signals is formulated as a parameter estimation problem for a certain spectral model. The model parameters are computed by a two step procedure: The modified Yule-Walker equations are used to estimate the autoregressive coefficients of the source signal, and a frequency domain squared error criterion is minimized to provide the delay estimate. The proposed technique is compared by simulations to the parametric techniques of Hamon-Hannan and Chan-Riley-Plant and is found to have better performance.

Square-root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting. The so-called covariance case is presented here, with emphasis on two special cases, namely the growing memory and sliding memory covariance ladder algorithms. New ladder form realizations for the identified models are presented, leading to convenient methods for computing the model parameters from estimated reflection coefficients. Several application areas of the new algorithms are discussed.