blind deconvolution of multi input single output systems with binary sources the problem of blind source separation for multi input single output miso systems with binary inputs is treated in this paper our approach exploits the constellation properties of the successor values for each output sample in the absence of noise the successors of each output value form a characteristic finite set of clusters successor constellation the shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap consequently the localization of the successors constellation can lead to the removal of the last filter tap thus reducing the length of the filter a process we call channel deflation based on the successor observation clustering soc we develop two algorithms for blind source separation soc 1 and soc 2 differing mainly on the required size of the data set furthermore the treatment of the system in the presence of noise is described using data clustering and data correction the problem of noise is attacked using a statistical mode based method moreover we correct the problem of misclassified observations using an iterative scheme based on the viterbi algorithm for the decoding of a hidden markov model hmm

robust beamforming via worst case sinr maximization minimum variance beamforming which uses a weight vector that maximizes the signal to interference plus noise ratio sinr is often sensitive to estimation error and uncertainty in the parameters steering vector and covariance matrix robust beamforming attempts to systematically alleviate this sensitivity by explicitly incorporating a data uncertainty model in the optimization problem in this paper we consider robust beamforming via worst case sinr maximization that is the problem of finding a weight vector that maximizes the worst case sinr over the uncertainty model we show that with a general convex uncertainty model the worst case sinr maximization problem can be solved by using convex optimization in particular when the uncertainty model can be represented by linear matrix inequalities the worst case sinr maximization problem can be solved via semidefinite programming the convex formulation result allows us to handle more general uncertainty models than prior work using a special form of uncertainty model we illustrate the method with a numerical example

norm constrained capon beamforming using multirank signal models with kalman filter implementation the performance of the capon beamforming is known to degrade dramatically in the presence of model mismatches especially when the desired signal is present in the training data to improve the robustness the diagonal loading technique was introduced however the major drawback is the selection of the diagonal loading level which is related to the unknown signal powers another way to alleviate performance degradation is to use a more accurate signal model of the array response in this paper a norm constrained capon beamforming using multirank signal models is proposed based on the pseudo observation method the quadratic constraints can be easily constructed the problem is solved by a nonlinear kalman filter which can be implemented on line the simulation results show that the design of the norm constraint value is less sensitive to the signal powers small angle mismatches and number of sensors with a standard linear array further it is shown that the use of a multirank signal model and kalman filter technique result in less self cancellation and performance degradation than that of the rank 1 signal model and the estimation of sample matrix

adaptive uncertainty based iterative robust capon beamformer using steering vector mismatch estimation to overcome the signal to interference and noise ratio sinr performance degradation in the presence of large steering vector mismatches we propose an iterative robust capon beamformer ircb with adaptive uncertainty level the approach iteratively estimates the actual steering vector sv based on conventional robust capon beamformer rcb formulation that uses an uncertainty sphere to model the mismatch between the actual and presumed sv at each iteration the adaptive uncertainty algorithm self adjusts the uncertainty sphere according to the estimated mismatch sv this estimation is derived based on the geometrical interpretation of the mismatch and can be expressed as a simple closed form expression as a function of the presumed sv and the signal subspace projection the other variant of the proposed algorithm that uses a flat ellipsoid to model the mismatch is also proposed simulation results show that the proposed approaches offer better interference suppression capability and achieve higher output sinr as compared to other diagonal loading based approaches

new results on hermitian matrix rank one decomposition in this paper we present several new rank one decomposition theorems for hermitian positive semidefinite matrices which generalize our previous results in huang and zhang math oper res 32 3 758 768 2007 ai and zhang siam j optim 19 4 1735 1756 2009 the new matrix rank one decomposition theorems appear to have wide applications in theory as well as in practice on the theoretical side for example we show how to further extend some of the classical results including a lemma due to yuan math program 47 53 63 1990 the classical results on the convexity of the joint numerical ranges pang and zhang in unpublished manuscript 2004 au yeung and poon in southeast asian bull math 3 85 92 1979 and the so called finsler s lemma bohnenblust in unpublished manuscript au yeung and poon in southeast asian bull math 3 85 92 1979 on the practical side we show that the new results can be applied to solve two typical problems in signal processing and communication one for radar code optimization and the other for robust beamforming the new matrix decomposition theorems are proven by construction in this paper and we demonstrate that the constructive procedures can be implemented efficiently stably and accurately the url of our matlab programs is given in this paper we strongly believe that the new decomposition procedures as a means to solve non convex quadratic optimization with a few quadratic constraints are useful for many other potential engineering applications

robust adaptive beamforming using multidimensional covariance fitting over the last decade several set based worst case beamformers have been proposed it has been shown that some of these beamformers can be formulated equivalently as one dimensional id covariance fitting problems based on this formulation we show that these beamformers lead to inherently nonoptimum results in the presence of interferers to mitigate the detrimental effect of interferers we extend the id covariance fitting approach to multidimensional md covariance fitting modeling the source steering vectors by means of uncertainty sets the proposed md covariance fitting approach leads to a nonconvex optimization problem we develop a convex approximation of this problem which can be solved for example by means of the logarithmic barrier method the complexity required to compute the barrier function and its first and second order derivatives is derived simulation results show that the proposed beamformer based on md covariance fitting achieves an improved performance as compared to the state of the art narrowband beamformers in scenarios with large sample support

doubly constrained robust capon beamformer the standard capon beamformer scb is known to have better resolution and much better interference rejection capability than the standard data independent beamformer when the array steering vector is accurately known however the major problem of the scb is that it lacks robustness in the presence of array steering vector errors in this paper we will first provide a complete analysis of a norm constrained capon beamforming nccb approach which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise our analysis of nccb is thorough and sheds more light on the choice of the norm constraint than what was commonly known we also provide a natural extension of the scb which has been obtained via covariance matrix fitting to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector viz a constant norm constraint and a spherical uncertainty set constraint which we refer to as the doubly constrained robust capon beamformer dcrcb nccb and dcrcb can both be efficiently computed at a comparable cost with that of the scb performance comparisons of nccb dcrcb and several other adaptive beamformers via a number of numerical examples are also presented

maximally robust capon beamformer the standard capon beamformer scb achieves the maximum output signal to interference plus noise ratio in the error free case however estimation errors of the signal steering vector and the array covariance matrix can result in severe performance deteriorations of the scb especially if the training data contains the desired signal component a popular technique to improve the robustness against model errors is to compute the capon beamformer with the maximum output power considering an uncertainty set for the signal steering vector however maximizing the total beamformer output power may result in an insufficient suppression of interferers and noise as an alternative approach to mitigate the detrimental effect of model errors we propose to compute the capon beamformer with the minimum sensitivity considering the uncertainty set for the signal steering vector the proposed maximally robust capon beamformer mrcb is at least as robust as the maximum output power capon beamformer with the same uncertainty set for the signal steering vector we show that the mrcb can be implemented efficiently using lagrange duality simulation results demonstrate that the mrcb outperforms state of the art robust adaptive beamformers in many scenarios

multi input single output nonlinear blind separation of binary sources the problem of blindly separating multiple binary sources from a single nonlinear mixture is addressed through a novel clustering approach without the use of any optimization procedure the method is based on the assumption that the source probabilities are asymmetric in which case the output probability distribution can be expressed as a linear mixture of the sources we are then able to solve the problem by using a known linear multiple input single output miso blind separation method the overall procedure is very fast and in theory it works for any number of independent binary sources and for a wide range of nonlinear functions in practice the accuracy of the method depends on the estimation accuracy of the output probabilities and the cluster centers it can be quite sensitive to noise especially as the number of sources increases or the number of data samples is reduced however in our experiments we have been able to demonstrate successful separation of up to four sources

complementarity problems for multivalued monotone operator in banach spaces we utilize s park s maximal element theorem in this paper to prove the existence theorems of solutions of the complementarity problems for multivalued monotone operator in banach spaces

robust design of radar doppler filters this paper considers the design of robust filters for radar pulse doppler processing when the interference is a wide sense stationary random process the figure of merit which is optimized is the signal to interference plus noise ratio sinr at the filter output under a multitude of constraints accounting for doppler filter sidelobes as well as uncertainties both in the received useful signal component and interference covariance matrix the design is analytically formulated as a constrained optimization problem whose solvability is thoroughly studied precisely a polynomial time solution technique to get the optimal filter is proposed exploiting the representation of non negative trigonometric polynomials via linear matrix inequalities the spectral factorization theorem and the duality theory last but not least a detailed analysis of the optimum filter performance is provided showing the tradeoffs involved in the design and the gain achievable over some already known counterparts

unified optimization framework for multi static radar code design using information theoretic criteria in this paper we study the problem of code design to improve the detection performance of multi static radar in the presence of clutter i e a signal dependent interference to this end we briefly present a discrete time formulation of the problem as well as the optimal detector in the presence of gaussian clutter due to the lack of analytical expression for receiver operation characteristic roc code design based on roc is not feasible therefore we consider several popular information theoretic criteria including bhattacharyya distance kullback leibler kl divergence j divergence and mutual information mi as design metrics the code optimization problems associated with different information theoretic criteria are obtained and cast under a unified framework we propose two general methods based on majorization minimization to tackle the optimization problems in the framework the first method provides optimal solutions via successive majorizations whereas the second one consists of a majorization step a relaxation and a synthesis stage moreover derivations of the proposed methods are extended to tackle the code design problems with a peak to average ratio power par constraint using numerical investigations a general analysis of the coded system performance computational efficiency of the proposed methods and the behavior of the information theoretic criteria is provided

test of mean field equations for two types of hard sphere systems by a brownian dynamics simulation and a molecular dynamics simulation a mean field nonlinear equation for the mean square displacement recently proposed by one of the present authors m tokuyama phys rev e 62 r5915 2000 physica a 289 57 2001 for concentrated equilibrium suspensions of hard spheres is extended to describe equilibrium atomic systems of hard spheres the validity of two types of mean field equations is investigated by two kinds of computer simulations a brownian dynamics simulation on suspensions of hard spheres and a molecular dynamics simulation on atomic systems of hard spheres a good agreement between the mean field equations and simulations is then shown for different volume fractions the two types of model systems of hard spheres are thus shown to be identical to each other on the study of the liquid solid transition however analyses suggest that a new interaction is indispensable to understand the mechanism for the liquid glass transition in both systems

minimum variance beamforming with soft response constraints soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming a quadratic constraint on the beamformer weights is used to control the mean squared error between a desired response and the actual response in the signal direction the constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation under the assumptions of known signal direction and spectral shape the signal to noise ratio is shown to be a nondecreasing function of the mean square distortion the distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired properties of this beamforming method and its relationship to linear constrained beamforming are discussed simulations verify analytic results and illustrate the utility of the soft constrained approach

the probability of a subspace swap in the svd we extend the work of tufts kot and vaccaro tkv published in 1980 to improve the analytical characterization of threshold breakdown in svd methods our results sharpen the tkv results by lower bounding the probability of a subspace swap in the svd our key theoretical result is the characteristic function for a random variable whose probability of exceeding zero bounds the probability of a threshold breakdown

robust adaptive beamforming based on steering vector estimation with as little as possible prior information a general notion of robustness for robust adaptive beamforming rab problem and a unified principle for minimum variance distortionless response mvdr rab techniques design are formulated this principle is to use standard mvdr beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information differences between various mvdr rab techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques a new mvdr rab technique which uses as little as possible and easy to obtain imprecise prior information is developed the objective for estimating the steering vector is the maximization of the beamformer output power while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations the prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies mathematically the proposed mvdr rab is expressed as the well known non convex quadratically constrained quadratic programming problem with two constraints which can be efficiently and exactly solved some new results for the corresponding optimization problem such as a new algebraic way of finding the rank one solution from the general rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank one are derived our simulation results demonstrate the superiority of the proposed method over other previously developed rab techniques

fractional qcqp with applications in ml steering direction estimation for radar detection this paper deals with the problem of estimating the steering direction of a signal embedded in gaussian disturbance under a general quadratic inequality constraint representing the uncertainty region of the steering we resort to the maximum likelihood ml criterion and focus on two scenarios the former assumes that the complex amplitude of the useful signal component fluctuates from snapshot to snapshot the latter supposes that the useful signal keeps a constant amplitude within all the snapshots we prove that the ml criterion leads in both cases to a fractional quadratically constrained quadratic problem qcqp in order to solve it we first relax the problem into a constrained fractional semidefinite programming sdp problem which is shown equivalent via the charnes cooper transformation to an sdp problem then exploiting a suitable rank one decomposition we show that the sdp relaxation is tight and give a procedure to construct in polynomial time an optimal solution of the original problem from an optimal solution of the fractional sdp we also assess the quality of the derived estimator through a comparison between its performance and the constrained cramer rao lower bound crb finally we give two applications of the proposed theoretical framework in the context of radar detection

optimal glrt based robust spectrum sensing for mimo cognitive radio networks with csi uncertainty in this paper we develop generalized likelihood ratio test glrt based detectors for robust spectrum sensing in multiple input multiple output mimo cognitive radio networks considering uncertainty in the available channel state information csi initially for a scenario with known csi uncertainty statistics we derive the novel robust estimator correlator detector recd and the robust generalized likelihood detector rgld which are robust against the uncertainty in the available estimates of the channel coefficients subsequently for a scenario with unknown csi uncertainty statistics we develop a generalized likelihood ratio test glrt based composite hypothesis robust detector chrd for spectrum sensing closed form expressions are presented for the probability of detection p d and the probability of false alarm p fa to characterize the detection performance of the proposed robust spectrum sensing schemes further a deflection coefficient based optimization framework is also developed and solved to derive closed form expressions for the optimal beacon sequences simulation results are presented to demonstrate the performance improvement achieved by the proposed robust spectrum sensing schemes and to verify the analytical results derived

a new interpretation of capon s maximum likelihood method of frequency wavenumber spectral estimation the maximum likelihood method of frequency wavenumber spectral estimation mlm is a high resolution alternative to conventional fourier analysis this paper provides a new interpretation for mlm the point of view taken is that at each wavenumber we attempt to estimate the power of a discrete planewave at that wavenumber a problem complicated by the presence of interfering energy at other wavenumbers noise with an unknown spectral density matrix it is shown that subject to some assumptions the problem of choosing the variance of the planewave complex amplitude that is the plane wave power and the noise covariance matrix jointly to maximize the likelihood function for the observations has no unique solution there is a continuous range of values for the estimates all of which have the same maximum likelihood the lower bound on the planewave power estimate being zero and the upper bound being the mlm power estimate some important differences between the problem of estimating the planewave complex amplitude for each independent data segment and the problem of estimating the variance of the planewave complex amplitude are indicated

robust array beamforming with sidelobe control using support vector machines robust beamforming is a challenging task in a number of applications radar sonar wireless communications etc due to strict restrictions on the number of available snapshots signal mismatches or calibration errors we present a new approach to adaptive beamforming that provides increased robustness against the mismatch problem as well as additional control over the sidelobe level we generalize the conventional linearly constrained minimum variance cost function by including a regularization term that penalizes differences between the actual and the target ideal array responses by using the so called epsi insensitive loss function for the penalty term the final cost function adopts the form of a support vector machine svm for regression in particular the resulting cost function is convex with a unique global minimum that has traditionally been found using quadratic programming qp techniques to alleviate the computational cost of conventional qp techniques we use an iterative reweighted least squares irwls procedure which also converges to the svm solution computer simulations demonstrate an improved performance of the proposed svm based beamformer in comparison with other recently proposed robust beamforming techniques

blind underdetermined mixture identification by joint canonical decomposition of ho cumulants a new family of cumulant based algorithms is proposed in order to blindly identify potentially underdetermined mixtures of statistically independent sources these algorithms perform a joint canonical decomposition cand of several higher order cumulants through a cand of a three way array with special symmetries these techniques are studied in terms of identifiability performance and numerical complexity from a signal processing viewpoint the proposed methods are shown i to have a better estimation resolution and ii to be able to process more sources than the other classical cumulant based techniques second from a numerical analysis viewpoint we deal with the convergence speed of several procedures for three way array decomposition such as the acdc scheme we also show how to accelerate the iterative cand algorithms by using differently the symmetries of the considered three way array next from a multilinear algebra viewpoint the paper aims at giving some insights on the uniqueness of a joint cand of several hermitian multiway arrays compared to the cand of only one array this allows us as a result to extend the concept of virtual array va to the case of combination of several vas

randomized algorithms for optimal solutions of double sided qcqp with applications in signal processing quadratically constrained quadratic programming qcqp with double sided constraints has plenty of applications in signal processing as have been addressed in recent years qcqp problems are hard to solve in general and they are typically approached by solving a semidefinite programming sdp relaxation followed by a postprocessing procedure existing postprocessing schemes include gaussian randomization to generate an approximate solution rank reduction procedure the so called purification and some specific rank one matrix decomposition techniques to yield a globally optimal solution in this paper we propose several randomized postprocessing methods to output not an approximate solution but a globally optimal solution for some solvable instances of the double sided qcqp i e instances with a small number of constraints we illustrate their applicability in robust receive beamforming radar optimal code design and broadcast beamforming for multiuser communications as a byproduct we derive an alternative shorter proof for the sturm zhang rank one matrix decomposition theorem

performance of dmi and eigenspace based beamformers the performance of the direct matrix inversion dmi method for antenna arrays of arbitrary geometry is analyzed by asymptotic statistical techniques the effects of eigenspace disturbance caused by finite samples on the output interference and noise powers are examined under the unit gain constraint in the direction of the desired signal the results show that the performance of the dmi method is degraded mostly by the disturbed noise subspace that suggests the use of an eigenspace based beamformer in which the weight vector is computed by using the signal plus interference subspace component of the sample correlation matrix convergence properties of the eigenspace based beamformer are evaluated for the cases in which the source number is known and in which it is overestimated theoretical analyses validated by computer simulations indicate that the eigenspace based beamformer has faster convergence rate than the dmi method

the quasi complementarity problem abstract variational inequality techniques are used to suggest a unified and general iterative algorithm for computing the approximate solution of a new class of complementarity problems the convergence properties of this algorithm are also discussed

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

some existence results for multivalued complementarity problems this paper presents some new results for the existence of a solution to a multivalued complementary problem these results are derived under a upper limiting homogeneity ulh property on the multifunction defining the complementarity problem and on a certain closedness interiority condition the closedness condition seems to be new in the context of existence proof for the multivalued complementarity problem we show that this closedness condition is satisfied by the class of polyhedral multifunctions

penalty function based joint diagonalization approach for convolutive blind separation of nonstationary sources a new approach for convolutive blind source separation bss by explicitly exploiting the second order nonstationarity of signals and operating in the frequency domain is proposed the algorithm accommodates a penalty function within the cross power spectrum based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization this leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient based descent algorithm using this approach not only can the degenerate solution induced by a null unmixing matrix and the effect of large errors within the elements of covariance matrices at low frequency bins be automatically removed but in addition a unifying view to joint diagonalization with unitary or nonunitary constraint is provided numerical experiments are presented to verify the performance of the new method which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals in particular in terms of shape preservation and amplitude ambiguity reduction as compared with the conventional second order based algorithms for convolutive mixtures that exploit signal nonstationarity

a bayesian framework for blind adaptive beamforming in this work the problem of blind adaptive beamforming in the presence of steering vector uncertainty is addressed within a bayesian estimation framework we express the single input multiple output simo observation model in the short time fourier transform stft domain and employ a variational formulation to obtain iterative closed form learning rules for inferring approximate posteriors on the steering vector and the target signal by varying the a priori belief in the top level statistical model i e modeling a quantity as a random process or an unknown deterministic entity it is shown that the considered framework yields a variety of beamforming algorithms including the celebrated minimum variance distortionless response mvdr beamformer we highlight these interconnections and show by means of simulation results that the bayesian approach alleviates signal distortion in noisy and uncertain environments as compared to the conventional mvdr beamformer by adaptively learning and incorporating uncertainty pertaining to the steering vector

robust minimum ell_ 1 norm adaptive beamformer against intermittent sensor failure and steering vector error a robust adaptive beamformer is described to mitigate against steering vector error and intermittent sensor s failure which exists in the form of impulsive noise in the received signal of failed sensor s this new beamformer iteratively minimizes the l 1 norm of the beamformer s output subject to a prespecified set of quadratic constraints which target on attenuating the influence caused by steering vector error to solve the proposed optimization problem gradient descent algorithm is adopted the choice of the lagrange multiplier as well as the adaptive step size k are derived in detail simulation results verify validity and advantages of the proposed algorithms over some existing methods

doubly constrained robust capon beamformer with ellipsoidal uncertainty sets the doubly constrained robust dcr capon beamformer with a spherical uncertainty set was introduced and studied by stoica and wang here we consider the generalized dcr problem gdcr in which the uncertainty set is an ellipsoid rather than a sphere although as noted previously by stoica and wang this problem is nonconvex and appears to be intractable we show that it can be solved efficiently in fact we prove that the gdcr beamformer can be obtained as a solution to a convex optimization problem to this end we first derive a strong duality result for nonconvex quadratic programs with two quadratic constraints over the complex domain specializing the results to our context leads to a semidefinite programming formulation of the gdcr beamformer

on the nonlinear complementarity problem abstract we consider and study an algorithm for a new class of complementarity problems of finding u such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a diagonally nonlinear mapping from r n into itself furthermore it is proved that the approximate solution obtained by the iterative scheme converges to the exact solution special cases are also discussed

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

three step iterative algorithms for multivalued quasi variational inclusions in this paper we suggest and analyze some new classes of three step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique new iterative algorithms include the ishikawa mann and noor iterations for solving variational inclusions inequalities and optimization problems as special cases the results obtained in this paper represent an improvement and a significant refinement of previously known results

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

on multivalued complementarity problems in banach spaces in this paper we prove a new existence result for multivalued complementarity problems in banach spaces our result represents a refinement and improvement of the previously known results

a recursive least squares implementation for lcmp beamforming under quadratic constraint quadratic constraints on the weight vector of an adaptive linearly constrained minimum power lcmp beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters we propose a technique for implementing a quadratic inequality constraint with recursive least squares rls updating a variable diagonal loading term is added at each step where the amount of loading has a closed form solution simulations under different scenarios demonstrate that this algorithm has better interference suppression than both the rls beamformer with no quadratic constraint and the rls beamformer using the scaled projection technique as well as faster convergence than lms beamformers

reformulation of time convolutionless mode coupling theory near the glass transition abstract the time convolutionless mode coupling theory tmct recently proposed is reformulated under the condition that one of two approximations which have been used to formulate the original tmct in addition to the mct approximations done on a derivation of nonlinear memory function in terms of the intermediate scattering function is not employed because it causes unphysical results for intermediate times the improved tmct equation is then derived consistently under another approximation it is first checked that the ergodic to non ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long time dynamics of both equations coincides with each other however it is emphasized that a difference between them appears in the intermediate time dynamics of physical quantities such a difference is explored numerically in the dynamics of a non gaussian parameter by employing the percus yevick static structure factor to calculate the nonlinear memory function

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

mean field theory of glass transitions abstract the experimental and the simulation results for the mean square displacements in various systems are analyzed near glass transitions by employing the mean field theory recently proposed by comparing different glass transitions with each other from a unified point view it is then shown that the mean square displacements obey a logarithmic growth followed by a power law growth of a super diffusion type in relaxation stage it is also shown that although the long time self diffusion coefficients are approximately described by a singular function of a control parameter with the same critical exponent for different systems where the singular point depends on the system no divergence of any characteristic times such as a relaxation time is found near the singular point nor the glass transition point a crossover point over which the supercooled liquid phase appears is also predicted theoretically it is thus suggested that the present theory provides an useful tool to understand phenomena near the glass transition within the framework of the mean square displacements

a coordinate descent algorithm for complex joint diagonalization under hermitian and transpose congruences abstract this paper deals with the problem of joint complexmatrix diagonalization by considering both the hermitian andtranspose congruences we address the general case where thesearched diagonalizing matrix is apriori nonunitary based onthe minimization of a quadratic criterion we propose a ex ible algorithm in the sense that it allows to directly consider arectangular diagonalizing matrix and to take into considerationboth the hermitian and transpose congruences within the sameframework the proposed algorithm is a coordinate descentalgorithm that is based on an approximate criterion leading to theanalytical derivation of the minima arguments computer simu lations are drawn to illustrate the usefulness and performancesof the algorithm and a comparison to state of the art algorithmsis presented finally an application to independent componentanalysis based on fourth order statistics is also presented index terms blind source separation complex symmetric ma trices hermitian matrices independent component analysis jointdiagonalization

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

robust adaptive beamformers based on worst case optimization and constraints on magnitude response in this paper novel robust adaptive beamformers are proposed with constraints on array magnitude response with the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight the optimization of an adaptive beamformer which is often described as a quadratic optimization problem in conventional beamforming methods is then reformulated as a linear programming lp problem unlike conventional robust beamformers the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple in practice an array has many imperfections besides steering direction error in order to make the adaptive beamformer robust against all kinds of imperfections worst case optimization is exploited to reconstruct the robust beamformer by minimizing array output power with the existence of the worst case array imperfections the robust beamforming can be expressed as a second order cone programming socp problem the resultant beamformer possesses superior robustness against arbitrary array imperfections with the proposed methods a large robust response region and a high signal to interference plus noise ratio sinr enhancement can be achieved readily simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed methods

response vector constrained robust lcmv beamforming based on semidefinite programming although linearly constrained minimum variance lcmv beamforming is robust against imprecise target information it usually leads to relatively high sidelobe and distorted mainlobe which would induce a high false alarm probability to circumvent this problem this work devises a novel robust lcmv beamforming approach by utilizing response vector optimization it intends to find the optimal response vector in lieu of the all one response vector in traditional lcmv beamformer the proposed robust beamformer is first formulated as a nonconvex quadratically constrained quadratic programming problem and then transformed into a semidefinite programming problem which can be efficiently and exactly solved the proposed beamformer not only improves the performance in terms of signal to interference plus noise ratio substantially but also possesses low sidelobe and well maintained mainlobe moreover since the response vector is quite small in size the complexity of calculating the optimal response vector is negligible additionally the proposed beamformer is also extended to two dimensional space time adaptive processing simulation results are presented to demonstrate the superiority of the proposed approach

robust adaptive beamforming for general rank signal model with positive semi definite constraint via potdc the robust adaptive beamforming rab problem for general rank signal model with an additional positive semi definite constraint is considered using the principle of the worst case performance optimization such rab problem leads to a difference of convex functions dc optimization problem the existing approaches for solving the resulted non convex dc problem are based on approximations and find only suboptimal solutions here we aim at finding the globally optimal solution for the non convex dc problem and clarify the conditions under which the solution is guaranteed to be globally optimal particularly we rewrite the problem as the minimization of a one dimensional optimal value function ovf then the ovf is replaced with another equivalent one for which the corresponding optimization problem is convex the new one dimensional ovf is minimized iteratively via polynomial time dc potdc algorithm we show that the potdc converges to a point that satisfies karush kuhn tucker kkt optimality conditions and such point is the global optimum under certain conditions towards this conclusion we prove that the proposed algorithm finds the globally optimal solution if the presumed norm of the mismatch matrix that corresponds to the desired signal covariance matrix is sufficiently small the new rab method shows superior performance compared to the other state of the art general rank rab methods

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction