Prediction error method for second-order blind identification

Blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest. In this paper, we introduce a second-order blind identification technique based on a linear prediction approach. In contrast to eigenstructure-based methods, it will be shown that the linear prediction error method is “robust” to order overdetermination. An asymptotic performance analysis of the proposed estimation method is carried out, consistency and asymptotic normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are finally presented to demonstrate the potential and the “robustness” of the proposed method     

New quadratic solid–shell elements and their evaluation on linear benchmark problems

This paper is concerned with the development of a new family of solid–shell finite elements. This concept of solid–shell elements is shown to have a number of attractive computational properties as compared to conventional three-dimensional elements. More specifically, two new solid–shell elements are formulated in this work (a fifteen-node and a twenty-node element) on the basis of a purely three-dimensional approach. The performance of these elements is shown through the analysis of various structural problems. Note that one of their main advantages is to allow complex structural shapes to be simulated without classical problems of connecting zones meshed with different element types. These solid–shell elements have a special direction denoted as the “thickness”, along which a set of integration points are located. Reduced integration is also used to prevent some locking phenomena and to increase computational efficiency. Focus will be placed here on linear benchmark problems, where it is shown that these solid–shell elements perform much better than their counterparts, conventional solid elements.     

A New Look at the Power Method for Fast Subspace Tracking

A class of fast subspace tracking methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method can be viewed as power-based methods. Unlike many non-power-based methods such as the Given's rotation based URV updating method and the operator restriction algorithm, the power-based methods with arbitrary initial conditions are convergent to the principal subspace of a vector sequence under a mild assumption. This paper elaborates on a natural version of the power method. The natural power method is shown to have the fastest convergence rate among the power-based methods. Three types of implementations of the natural power method are presented in detail, which require respectively O(n²p), O(np²), and O(np) flops of computation at each iteration (update), where n is the dimension of the vector sequence and p is the dimension of the principal subspace. All of the three implementations are shown to be globally convergent under a mild assumption. The O(np) implementation of the natural power method is shown to be superior to the O(np) equivalent of the Oja, PAST, and NIC methods. Like all power-based methods, the natural power method can be easily modified via subspace deflation to track the principal components and, hence, the rank of the principal subspace.     

Damped and delayed sinusoidal model for transient signals

In this work, we present the Damped and Delayed Sinusoidal (DDS) model: a generalization of the sinusoidal model. This model takes into account an angular frequency, a damping factor, a phase, an amplitude, and a time-delay parameter for each component. Two algorithms are introduced for the DDS parameter estimation using a subband processing approach. Finally, we derive the Crame/spl acute/r-Rao Bound (CRB) expression for the DDS model and a simulation-based performance analysis in the context of a noisy fast time-varying synthetic signal and in the audio transient signal modeling context.     

A subspace algorithm for certain blind identification problems

The problem of blind identification of p-inputs/q-outputs FIR transfer functions is addressed. Existing subspace identification methods derived for p=1 are first reformulated. In particular, the links between the noise subspace of a certain covariance matrix of the output signals (on which subspace methods build on) and certain rational subspaces associated with the transfer function to be identified are elucidated. Based on these relations, we study the behavior of the subspace method in the case where the order of the transfer function is overestimated. Next, an asymptotic performance analysis of this estimation method is carried out. Consistency and asymptotical normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are presented to demonstrate the potential of the subspace method. Finally, we take advantage of our new reformulation to discuss the extension of the subspace method to the case p>1. We show where the difficulties lie, and we briefly indicate how to solve the corresponding problems. The possible connections with classical approaches for MA model estimations are also outlined     

Blind system identification

Blind system identification (BSI) is a fundamental signal processing technology aimed at retrieving a system's unknown information from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation, and blind image restoration. This paper reviews a number of recently developed concepts and techniques for BSI, which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input     

Blind channel equalization and carrier frequency offset estimation for MC-CDMA systems using guard interval redundancy and excess codes

It is well known that multipath channel and carrier frequency offset (CFO) destroy the orthogonality between subcarriers in the downlink of MC-CDMA and degrade the system performance. In this paper, a new low complexity algorithm is proposed to iteratively estimate the CFO and the channel equalizer using only the guard interval (GI) redundancy, or excess codes (EC) or both GI and EC without additional pilots. Simulations illustrate and compare the performance efficiency of these schemes in different scenarios.     

Blind identification of multipath channels: a parametric subspaceapproach

In this paper, blind identification of single-input multiple-output (SIMO) systems using second-order statistics (SOS) only is considered. Using the assumption of a specular multipath channel, we investigate a parametric variant of the so-called subspace method. Nonparametric subspace-based methods require precise estimation of the model order; overestimation of the model order leads to inconsistent channel estimates. We show that the parametric subspace method gives consistent channel estimates when only an upper bound of the channel order is known. A new algorithm, which exploits parametric information on the channel structure, is presented. A statistical performance analysis of the proposed parametric subspace criterion is presented; limited Monte Carlo experiments show that the proposed algorithm is second-order optimal for a large class of channels     

Linear and quadratic solid–shell finite elements SHB8PSE and SHB20E for the modeling of piezoelectric sandwich structures

In this article, hexahedral piezoelectric solid–shell finite element formulations with linear and quadratic interpolation, denoted by SHB8PSE and SHB20E, respectively, are proposed for the modeling of piezoelectric sandwich structures. Compared to conventional solid and shell elements, the solid–shell concept reveals to be very attractive, due to a number of well-established advantages and computational capabilities. More specifically, the present study is devoted to the modeling and analysis of multilayer structures that incorporate piezoelectric materials in the form of layers or patches. The interest in this solid–shell approach is shown through a set of selective and representative benchmark problems. These include numerical tests applied to various configurations of beam, plate and shell structures, both in static and vibration analysis. The results yielded by the proposed formulations are compared with those given by state-of-the-art piezoelectric elements available in ABAQUS, in particular, the C3D20E quadratic hexahedral finite element with piezoelectric degrees of freedom.     

Blind Separation of Underdetermined Convolutive Mixtures Using Their Time–Frequency Representation

This paper considers the blind separation of nonstationary sources in the underdetermined convolutive mixture case. We introduce, two methods based on the sparsity assumption of the sources in the time-frequency (TF) domain. The first one assumes that the sources are disjoint in the TF domain, i.e., there is at most one source signal present at a given point in the TF domain. In the second method, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present (active) at a TF point should be strictly less than the number of sensors. In that case, the separation can be achieved thanks to subspace projection which allows us to identify the active sources and to estimate their corresponding time-frequency distribution (TFD) values. Another contribution of this paper is a new estimation procedure for the mixing channel in the underdetermined case. Finally, numerical performance evaluations and comparisons of the proposed methods are provided highlighting their effectiveness.