spatial spectrum estimation in a location sector multiple narrowband source localization using arbitrarily configured arrays and spatial spectrum estimation is considered a new eigenspace based approach which uses projections onto a particular vector or vector set in the estimated noise only subspace is described several closest vector estimators are developed by using different measures of closeness first closest is a novel full dimensional element space approach to spatial spectrum estimation which has important performance advantages relative to pertinent established spatial spectrum estimators it incorporates a priori knowledge of the array manifold over a location sector of interest to provide snr spectral resolution thresholds which are lower than those of min norm for some arrays substantially lower second relationships between the closest approach and several established approaches to spatial spectrum estimation are established for a linear equispaced array min norm is shown to be a special case of the closest approach one which is based on projection onto a noise only subspace vector which is close to the array manifold over the entire field of view

oblique projections for direction of arrival estimation with prior knowledge estimation of directions of arrival doa is an important problem in various applications and a priori knowledge on the source location is sometimes available to exploit this information standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known doa in this paper we derive and analyze the cramer rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown doa are closely spaced and the associated sources are uncorrelated block diagonal source covariance to fill this need we propose to integrate a priori known locations of several sources into the music algorithm based on oblique projection of the steering manifold finally we show that the proposed approach is able to almost completely cancel the influence of the known doa on the unknown ones for block diagonal source covariance and for sufficient signal to noise ratio snr

nonlinear non extensive approach for identification of structured information the problem of separating structured information representing phenomena of differing natures is considered a structure is assumed to be independent of the others if can be represented in a complementary subspace when the concomitant subspaces are well separated the problem is readily solvable by a linear technique otherwise the linear approach fails to correctly discriminate the required information hence a non extensive approach is proposed the resulting nonlinear technique is shown to be suitable for dealing with cases that cannot be tackled by the linear one

efficient application of music algorithm under the coexistence of far field and near field sources this correspondence is concerned with source localization and classification for scenarios where both the far field and near field narrowband sources may coexist we propose an efficient music based solution that requires neither a multidimensional search nor high order statistics hos we also derive the stochastic cramer rao bound crb for the problem under consideration the performance of the proposed method is compared with an existing method and with the crb

nonlinear and nonideal sampling theory and methods we study a sampling setup where a continuous time signal is mapped by a memoryless invertible and nonlinear transformation and then sampled in a nonideal manner such scenarios appear for example in acquisition systems where a sensor introduces static nonlinearity before the signal is sampled by a practical analog to digital converter we develop the theory and a concrete algorithm to perfectly recover a signal within a subspace from its nonlinear and nonideal samples three alternative formulations of the algorithm are described that provide different insights into the structure of the solution a series of oblique projections approximated projections onto convex sets and quasi newton iterations using classical analysis techniques of descent based methods and recent results on frame perturbation theory we prove convergence of our algorithm to the true input signal we demonstrate our method by simulations and explain the applicability of our theory to wiener hammerstein analog to digital hybrid systems

estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to nmr spectroscopy data we present fast maximum likelihood fml estimation of parameters of multiple exponentially damped sinusoids the fml algorithm was motivated by the desire to analyze data that have many closely spaced components such as the nmr spectroscopy data of human blood plasma the computational efficiency of fml lies in reducing the multidimensional search involved in ml estimation into multiple 1 d searches this is achieved by using our knowledge of the shape of the compressed likelihood function clf in the parameter space the proposed fml algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the clf the other striking features of the proposed algorithm are that it provides procedures for initialization has a fast converging iteration stage and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal to noise ratio snr the computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction kiss iqml alternating projections ap and expectation maximization em

bi orthonormal polynomial basis function framework with applications in system identification numerical aspects are of central importance in identification and control many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections the aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems the proposed method is built on the introduction of bi orthonormal polynomials with respect to a data dependent bi linear form this bi linear form generalises the conventional inner product and allows for asymmetric and indefinite problems the proposed approach is shown to lead to optimal numerical conditioning kappa 1 in a recent frequency domain instrumental variable system identification algorithm in comparison it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches

constrained maximum likelihood solution of linear equations the total least squares tls is used to solve a set of inconsistent linear equations ax spl ap y when there are errors not only in the observations y but in the modeling matrix a as well the tls seeks the least squares perturbation of both y and a that leads to a consistent set of equations when y and a have a defined structure we usually want the perturbations to also have this structure unfortunately standard tls does not generally preserve the perturbation structure so other methods are required we examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations given an a priori perturbation probability density function while our approach is applicable to both gaussian and non gaussian distributions we show in the uncorrelated gaussian case that our method is equivalent to several existing methods our approach is therefore more general and can be applied to a wider variety of signal processing problems

blind adaptation of zero forcing projections and oblique pseudo inverses for subspace detection and estimation when interference dominates noise in much of modern radar sonar and wireless communication it seems more reasonable to model measurement noise as subspace interference plus broadband noise than as colored noise this observation leads naturally to a variety of detection and estimation problems in the linear statistical model to solve these problems one requires oblique pseudo inverses oblique projections and zero forcing orthogonal projections the problem is that these operators depend on knowledge of signal and interference subspaces and this information is often not at hand more typically the signal subspace is known but the interference subspace is unknown we prove a theorem that allows these operators to be estimated directly from experimental data without knowledge of the interference subspace as a byproduct the theorem shows how signal subspace covariance may be estimated when the strict identities of the theorem are approximated then the detectors estimators and beamformers of this paper take on the form of adaptive subspace estimators detectors and capon beamformers all of which are reduced in rank the fundamental operator turns out to be a certain reduced rank wiener filter which we clarify in the course of our derivations the results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation they may be applied to detection and estimation in radar sonar and hyperspectral imaging and to data decoding in multiuser communication receivers

complexity reduction for sign configurations through the kp ii equation and its information theoretic aspects we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

a deflation procedure for subspace decomposition a general deflation framework is described for the separation of a desired signal subspace of arbitrary dimensions from noisy multichannel observations the method simultaneously uses single and multichannel priors to split the desired and undesired subspaces even for coplanar intersecting subspaces by appropriate use of signal priors it can even extract signals from degenerate mixtures of signals and noise recorded from a few number of channels in low snr scenarios without the reduction of the data dimensions as a case study the performance of the proposed method is studied for the problem of extracting fetal cardiac signals from maternal abdominal recordings over simulated and real data a second case study deals with the degenerate problem of extracting diaphragmatic electromyogram from electrocardiograph artifacts a provisional patent application based on this method has been filed

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

prewhitening for rank deficient noise in subspace methods for noise reduction a fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank in order for the prewhitening step to be defined however there are important cases where this requirement is not fulfilled e g when the noise has narrowband characteristics or in the case of tonal noise we extend the concept of prewhitening to include the case when the noise covariance matrix is rank deficient using a weighted pseudoinverse and the quotient singular value decomposition and we show how to formulate a general rank reduction algorithm that works also for rank deficient noise we also demonstrate how to formulate this algorithm by means of a quotient ulv decomposition which allows for faster computation and updating finally we apply our algorithm to a problem involving a speech signal contaminated by narrowband noise

analysis and design of perfusion based event related fmri experiments perfusion based functional magnetic resonance imaging fmri using arterial spin labeling asl methods has the potential to provide better localization of the functional signal to the sites of neural activity compared to blood oxygenation level dependent bold contrast fmri at present experiments using asl have been limited to simple block and periodic single trial designs we present here an adaptation of the general linear model to perfusion based fmri that enables the design and analysis of more complicated designs such as random and semirandom event related designs formulas for the least squares estimate of the perfusion response and the f statistic for the detection of a response are derived exact expressions and useful approximations for detection power and estimation efficiency are presented and it is shown that the trade off between power and efficiency for perfusion experiments is similar to that previously observed for bold experiments the least squares estimate is compared with an estimate formed from the running subtraction of tag and control images the running subtraction estimate is shown to be approximately equal to a temporally low pass filtered version of the least squares estimate numerical simulations and results from asl experiments are used to support the theoretical findings

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

joint channel and symbol estimation by oblique projections the problem of simultaneous blind channel and symbol estimation of a single input multiple output simo communication channel is considered it is shown that the outer product of the channel vector and the channel input sequence can be obtained by a linear estimator that has the finite sample convergence property furthermore this estimator can be obtained by the use of oblique projections an order detection algorithm that avoids the use of subjective thresholding is also proposed applications to multiuser detection are also considered

existence and numerical approximations of periodic solutions of semilinear fourth order differential equations abstract a multiplicity result of existence of periodic solutions with prescribed wavelength for a class of fourth order nonautonomous differential equations related either to the extended fisher kolmogorov or to the swift hohenberg equation is proved variational approach is used some numerical solutions are calculated via the finite element method

application of manifold separation to polarimetric capon beamformer and source tracking two adaptive capon methods that jointly estimate the azimuth angle and polarization of the sources in a closed form are proposed it is shown that the azimuth angles of the sources may be estimated from the roots of a complex valued polynomial or by rooting a real valued polynomial instead the latter method is particularly useful in tracking arbitrarily polarized sources in a sequential snapshot by snapshot manner using root tracking techniques the proposed polynomial rooting based methods are applicable to polarization sensitive arrays regardless of the array geometry including conformal arrays and take into account array nonidealities a large sample analysis of the polarimetric capon method is also provided showing that it converges up to a multiplicative factor that depends on the interference plus noise power to the polarimetric music method in the high sinr regime such a result gives a new insight into the well known capon and music methods this paper also shows that employing manifold separation in robust capon beamforming as well as in transmit beamforming schemes leads to improved performance in terms of received sinr when array calibration measurements are used extensive numerical results employing real world polarimetric arrays are given results show that employing manifold separation leads to improved performance in many array processing tasks

a new subspace identification algorithm for high resolution doa estimation in this paper we propose a new direction of arrival doa estimator for sensor array processing the estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal plus interference model which we develop in this paper the estimator we propose is a signal subspace scaled music algorithm which we call ssmusic it is not a subspace weighted music because the scaling depends on the eigenstructure of the estimated signal subspace ssmusic has the advantage of simultaneously estimating the doa and the power of each source we employ a second order perturbation analysis of the estimator and derive stochastic representations for its bias and squared error we compare the new doa estimator with the music estimator based on these representations numerical results demonstrate the superior performance of ssmusic relative to music and the validity of the perturbation results

two channel constrained least squares problems solutions using power methods and connections with canonical coordinates the problem of two channel constrained least squares cls filtering under various sets of constraints is considered and a general set of solutions is derived for each set of constraints the solution is determined by a coupled asymmetric generalized eigenvalue problem this eigenvalue problem establishes a connection between two channel cls filtering and transform methods for resolving channel measurements into canonical or half canonical coordinates based on this connection a unified framework for reduced rank wiener filtering is presented then various representations of reduced rank wiener filters in canonical and half canonical coordinates are introduced an alternating power method is proposed to recursively compute the canonical coordinate and half canonical coordinate mappings a deflation process is introduced to extract the mappings associated with the dominant coordinates the correctness of the alternating power method is demonstrated on a synthesized data set and conclusions are drawn