Sanyogita Shamsunder

Multichannel ARMA processes

Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed. Identifiability results in connection with the HOS-based parameter estimation of causal and noncausal multivariate ARMA processes are established. Estimates of the parameters of causal ARMA models are obtained as the solution to a set of linear equations, whereas those of noncausal ARMA models are obtained as the solution to a cumulant matching algorithm. Conventional approaches based on second-order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix. HOS-based methods yield solutions that are unique to within post-multiplication by an (extended) permutation matrix; additionally, the multiminimum phase assumption can be relaxed, and the observations may be contaminated with colored Gaussian noise. Frequency-domain methods for nonparametric system identification are discussed briefly. Simulations results validating the multichannel parameter estimation algorithms are provided. >

High-order subspace-based algorithms for passive localization of near-field sources

A vast majority of the existing eigen-decomposition based localization schemes invoke the plane-wave assumption when estimating the direction-of-arrival of multiple sources. A fourth-order cumulant based TLS-ESPRIT like algorithm is proposed for passive localization of near-field sources using observations collected from a single uniform linear sensor array. The new approach exploits the multiple-rotational invariance among certain cumulant-domain signal sub-spaces for passive range and bearing estimation. The algorithm combines the Gaussian noise insensitivity and higher resolution capabilities of cumulants with the improved precision, accuracy and computational advantages of invariance and total least squares methods to yield simultaneous, search free estimates of near-field location parameters.

Estimating random amplitude polynomial phase signals: a cyclostationary approach

Modeling of a class of nonstationary signals with randomly time-varying amplitude and parametric polynomial phase is addressed. A novel approach is proposed for the estimation of the time-varying phase by exploiting the higher order cyclostationarity of these signals. The method does not require nonlinear search, is easy to implement, and yields consistent estimates for the parameters. The resulting algorithms are theoretically tolerant to a large class of noises including additive stationary non-Gaussian noise and any Gaussian noise. Simulation examples supporting the theory are provided. >

Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors

Abstract Multichannel, non-Gaussian linear processes are modeled via direct and inverse cumulant-based methods using noisy, multivariate output data. The proposed methods are theoretically insensitive to additive Gaussian noise (perhaps colored, with unknown covariance matrix), and are guaranteed to uniquely identify the system matrix within a post-multiplication by a permutation matrix. Asymptotically optimal and computationally less intensive modeling criteria are also discussed. Further, it is proved that using higher-than-second-order cumulants, it is possible to estimate more angles-of-arrival (or harmonics) with fewer sensors. The problem of detecting the number of sources (or inputs) using output cumulants only is also addressed. Simulation results show that the proposed algorithms outperform the traditional correlation-based methods.

Multichannel blind signal separation and reconstruction

The separation of multiple signals from their superposition recorded at several sensors is addressed. The methods employ polyspectra of the sensor data in order to extract the unknown signals and estimate the finite impulse response (FIR) coupling systems via a linear equation based algorithm. The procedure is useful for multichannel blind deconvolution of colored input signals with (possibly) overlapping spectra. An extension of the main algorithm, which can be applied for quasiperiodic signal separation, is also given. Simulation results corroborate the applicability of the algorithm.

Noise subspace techniques in non-gaussian noise using cumulants

We consider noise subspace methods for narrowband direction-of-arrival or harmonic retrieval in colored linear non-gaussian noise of unknown covariance and unknown distribution. The non-gaussian noise covariance is estimated via higher order cumulants and combined with correlation information to solve a generalized eigenvalue problem. The estimated eigenvectors are used in a variety of noise subspace methods such as multiple signal classification (MUSIC), MVDR and eigenvector. The noise covariance estimates are obtained in the presence of the harmonic signals, obviating the need for noise-only training records. The covariance estimates may be obtained nonparametrically via cumulant projections, or parametrically using autoregressive moving average (ARMA) models. An information theoretic criterion using higher order cumulants is presented which may be used to simultaneously estimate the ARMA model order and parameters. Third- and fourth-order cumulants are employed for asymmetric and symmetric probability density function (pdf) cases, respectively. Simulation results show considerable improvement over conventional methods with no prewhitening. The effects of prewhitening are particularly evident in the dominant eigenvalues, as revealed by singular value decomposition (SVD) analysis. >

Adaptive algorithms for channel equalization with soft decision feedback

A new approach based on joint entropy maximization (JEM) is taken and adaptive algorithms are developed for channel equalization with a decision feedback equalizer (DFE). The proposed work generalizes the existing algorithms for DFE with a hard decision device. Previous research has shown that when the hard decisions in a DFE are replaced with soft decisions, the performance of the adaptive algorithms [e.g., minimum mean square error (MMSE)] improves dramatically. The soft decisions can be introduced naturally via the viewpoint taken here. Additionally, constant modulus and other (blind) algorithms for DFE with soft decisions can be derived from this JEM approach.

Improved bearing and range estimation via high-order subspace based Unitary ESPRIT

Two new algorithms for the passive localization of near-field sources with a uniform linear array (ULA) are presented and compared in this paper. They exploit multiple invariances among certain fourth-order cross-cumulant matrices of non-zero and zero lags, respectively. Both algorithms utilize 2-D Unitary ESPRIT to obtain automatically paired bearing and range estimates. The resulting closed-form subspace-based methods incorporate forward-backward averaging, use efficient real-valued processing of the cumulant data, and outperform previously proposed high-order subspace-based algorithms for the localization of near-field sources. In the limit, the presented schemes also work for far-field sources.

Signal selective localization of nonGaussian cyclostationary sources

Novel direction-finding algorithms that exploit the nonGaussian and cyclostationary nature of communication signals are explored. The proposed methods that are appropriate for uniform linear arrays employ cyclic higher order statistics of the array output and suppress additive Gaussian noise of unknown spectral content, even when the noise shares common cycle frequencies with the nonGaussian signals of interest. In addition, cyclic higher order statistics are tolerant to nonGaussian interferences with cycle frequencies other than those of the desired signals and allow one to consistently estimate the angles of arrival of signal sources (per cycle) whose number can be greater than the number of sensors. >

Passive near-field localization of multiple non-Gaussian sources in 3-D using cumulants

Abstract In this paper an eigendecomposition technique based on cumulant matrices is proposed to passively localize narrowband non-Gaussian sources in the spherical coordinates, viz., azimuth, elevation and range, using signals recorded by a centro-symmetric 2-D cross array. The high-resolution algorithm exploits the multiple degrees of freedom available from cumulants to transform the near-field data into pseudo-data collected by a virtual rectangular array observing virtual far-field sources. The source locations are estimated directly from eigenvalues of certain cumulant matrices, thereby eliminating the multi-dimensional search inherent in the traditional methods like 3-D MUSIC. The centro-symmetric structure lost by a uniform linear array in the presence of near-field sources, is restored in the virtual rectangular array thus allowing efficient real-valued processing via Unitary ESPRIT.