blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

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

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

asymptotic properties of the algebraic constant modulus algorithm the algebraic constant modulus algorithm acma is a noniterative blind source separation algorithm it computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem we analyze its asymptotic properties and show that unlike cma it converges to the wiener beamformer when the number of samples or the signal to noise ratio snr goes to infinity we also sketch its connection to the related jade algorithm and derive a version of acma that converges to a zero forcing beamformer this gives improved performance in applications that use the estimated mixing matrix such as in direction finding

a hyperplane based algorithm for the digital co channel communications problem the relationship between the blind digital co channel communications problem and the problem of finding a separating hyperplane in ir sup d is explored a simple model for the blind digital co channel communications problem is x as where x is a known ir sup d spl times n matrix a is an unknown full rank ir sup d spl times d matrix and s is an unknown full rank d spl times n matrix with elements drawn from a multiple amplitude shift keying m ask alphabet s an algorithm with proof is given that solves for a and s up to a simple matrix factor the algorithm is extended to the complex quadrature amplitude modulation qam alphabet the key step in this algorithm involves finding a separating hyperplane parallel to one of the hyperplanes defining the received signal vectors the geometric interpretation of this relationship is discussed examples with noisy data are presented and refinements to the algorithm are discussed

a class of bounded component analysis algorithms for the separation of both independent and dependent sources bounded component analysis bca is a recent approach which enables the separation of both dependent and independent signals from their mixtures in this approach under the practical source boundedness assumption the widely used statistical independence assumption is replaced by a more generic domain separability assumption this article introduces a geometric framework for the development of bounded component analysis algorithms two main geometric objects related to the separator output samples namely principal hyper ellipsoid and bounding hyper rectangle are introduced the maximization of the volume ratio of these objects and its extensions are introduced as relevant optimization problems for bounded component analysis the article also provides corresponding iterative algorithms for both real and complex sources the numerical examples illustrate the potential advantage of the proposed bca framework in terms of correlated source separation capability as well as performance improvement for short data records

biased random walk on the trace of biased random walk on the trace of we study the behaviour of a sequence of biased random walks x scriptscriptstyle i i ge 0 on a sequence of random graphs where the initial graph is mathbb z d and otherwise the graph for the ith walk is the trace of the i 1 st walk the sequence of bias vectors is chosen so that each walk is transient we prove the aforementioned transience and a law of large numbers and provide criteria for ballisticity and sub ballisticity we give examples of sequences of biases for which each x scriptscriptstyle i i ge 1 is transient but not ballistic and the limiting graph is an infinite simple self avoiding path we also give examples for which each x scriptscriptstyle i i ge 1 is ballistic but the limiting graph is not a simple path

joint angle and delay estimation using shift invariance techniques in a multipath communication scenario it is often relevant to estimate the directions and relative delays of each multipath ray we derive a closed form subspace based method for the simultaneous estimation of these parameters from an estimated channel impulse response using knowledge of the transmitted pulse shape function the algorithm uses a two dimensional 2 d esprit like shift invariance technique to separate and estimate the phase shifts due to delay and direction of incidence with automatic pairing of the two parameter sets improved resolution is obtained by enlarging the data matrix with shifted and conjugated copies of itself

time delay estimation from low rate samples a union of subspaces approach time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel previous methods for time delay recovery either operate on the analog received signal or require sampling at the nyquist rate of the transmitted pulse in this paper we develop a unified approach to time delay estimation from low rate samples this problem can be formulated in the broader context of sampling over an infinite union of subspaces although sampling over unions of subspaces has been receiving growing interest previous results either focus on unions of finite dimensional subspaces or finite unions the framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate even in the presence of overlapping transmitted pulses and allows for a variety of different sampling methods the sampling rate depends only on the number of multipath components and the transmission rate but not on the bandwidth of the probing signal this result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces by properly manipulating the low rate samples we show that the time delays can be recovered using the well known esprit algorithm combining results from sampling theory with those obtained in the context of direction of arrival estimation we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate

the procrustes problem for orthogonal kronecker products the procrustes problem for orthogonal kronecker products is considered given matrices a in mathbb r n 2 times k 2 t in mathbb r n 2 times n 2 n ge k we minimize the frobenius norm t q otimes q a for all orthogonal stiefel matrices q in mathbb r n times k q tq i k we introduce and implement left and right relaxation methods for minimization numerical results for the data in general and kronecker product form are given to illustrate convergence of both methods

adaptive blind source separation and equalization for multiple input multiple output systems in this paper we investigate adaptive blind source separation and equalization for multiple input multiple output mimo systems we first analyze the convergence of the constant modulus algorithm cma used in mimo systems mimo cma our analysis reveals that the mimo cma equalizer is able to recover one of the input signals remove the intersymbol interference isi and suppress the other input signals furthermore for the mimo finite impulse response fir systems satisfying certain conditions the mimo cma fir equalizers are able to perfectly recover one of the system inputs regardless of the initial settings we then propose a novel algorithm for blind source separation and equalization for mimo systems our theoretical analysis proves that the new blind algorithm is able to recover all system inputs simultaneously regardless of the initial settings finally computer simulation examples are presented to confirm our analysis and illustrate the effectiveness of blind source separation and equalization for mimo systems

blind detection of synchronous cdma in non gaussian channels most blind source separation algorithms assume the channel noise to be gaussian this paper considers the problem of noncooperative blind detection of synchronous direct sequence code division multiple access communications no knowledge of the spreading sequences or training data in non gaussian channels three iterative algorithms with different performance and complexity tradeoffs are proposed simulation results show that they significantly outperform gaussian optimal blind source separation algorithms in non gaussian channels the cramer rao lower bound for this problem is computed and the performance of the proposed algorithms is shown to approach this bound for moderate signal to noise ratios

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

on regularity and identifiability of blind source separation under constant modulus constraints we investigate the information regularity and identifiability of the blind source separation bss problem with constant modulus cm constraints on the sources we establish for this problem the connection between the information regularity existence of a finite crame spl acute r rao bound crb and local identifiability sufficient and necessary conditions for local identifiability are derived we also study the conditions under which unique global identifiability is guaranteed within the inherently unresolvable ambiguities on phase rotation and source permutation both sufficient and necessary conditions are obtained

blind high resolution localization and tracking of multiple frequency hopped signals this paper considers the problem of blind localization and tracking of multiple frequency hopped spread spectrum signals using a uniform linear antenna array without knowledge of hopping patterns or directions of arrival as a preprocessing step we propose to identify a hop free subset of data by discarding high entropy spectral slices from the spectrogram high resolution localization is then achieved via either quadrilinear regression of four way data generated by capitalizing on both spatial and temporal shift invariance or a new maximum likelihood ml based two dimensional 2 d harmonic retrieval algorithm the latter option achieves the best known model identifiability bound while remaining close to the cramer rao bound even at low signal to noise ratios snrs following beamforming using the recovered directions a dynamic programming approach is developed for joint ml estimation of signal frequencies and hop instants in single user tracking the efficacy of the proposed algorithms is illustrated in pertinent simulations

on the existence of moments for the busy period in a single server queue we obtain sufficient conditions for the finiteness of the moments of the single server queue busy period in discrete and continuous time in the cases of power and exponential moments the conditions found coincide with the known necessary ones

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a compact cramer rao bound expression for parametric estimation of superimposed signals the problem of parameter estimation of superimposed signals in white gaussian noise is considered closed form expressions of the cramer rao bound for real or complex signals with vector parameters are derived extending recent results by p stoica and a nehorai 1989

a block component model based blind ds cdma receiver in this paper we consider the problem of blind multiuser separation equalization in the uplink of a wideband ds cdma system in a multipath propagation environment with intersymbol interference isi to solve this problem we propose a multilinear algebraic receiver that relies on a new third order tensor decomposition and generalizes the parallel factor parafac model our method is deterministic and exploits the temporal spatial and spectral diversities to collect the received data in a third order tensor the specific algebraic structure of this tensor is then used to decompose it in a sum of user s contributions the so called block component model bcm receiver does not require knowledge of the spreading codes the propagation parameters nor statistical independence of the sources but relies instead on a fundamental uniqueness condition of the decomposition that guarantees identifiability of every user s contribution the development of fast and reliable techniques to calculate this decomposition is important we propose a blind receiver based either on an alternating least squares als algorithm or on a levenberg marquardt lm algorithm simulations illustrate the performance of the algorithms

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

analysis of joint angle frequency estimation using esprit high resolution parameter estimation techniques have been applied to jointly estimate multiple signal parameters we consider the problem of determining the directions and center frequencies of a number of narrowband sources in a band of interest we present a joint angle frequency estimation method based on the multidimensional esprit algorithm a perturbation error analysis gives bounds on the parameter estimates and provides optimal values for the temporal and spatial smoothing parameters the analysis is shown to be consistent with simulation results

determination of the dimension of a signal subspace from short data records a nested sequence of constant false alarm rate cfar hypothesis tests is presented for rank determination over short data records the procedure is based on the interpretation of sum of squares of singular values as energy in a particular subspace the cfar thresholds are set up based on distributions derived from matrix perturbation ideas expressions for probability of overestimation and underestimation are presented

fri sampling on structured nonuniform grids application to super resolved optical imaging the annihilating filter forms the core of many state of the art techniques for finite rate of innovation fri signal reconstruction and spectral estimation in its standard manifestation the annihilating filter is setup in the discrete time domain with uniform sampling and is used to estimate the parameters of a signal that is expressible as a sum of exponentials in this paper we consider annihilation in the continuous domain using translation operators codenamed opera and show that fri signals can be reconstructed using measurements taken on a structured nonuniform sampling sns grid the parameters are estimable uniquely under certain conditions the transition from uniform sampling to sns comes with specific advantages the measurements could be made in bursts from high signal to noise ratio snr regions which directly enhances parameter estimation accuracy the sampling interval could be made larger than in the uniform case which leads to a reduction in the mean squared error mse and closely spaced exponential parameters could be resolved better we present theoretical developments related to the sns grid and demonstrate accurate parameter estimation monte carlo performance analysis in the presence of noise shows that the opera with the sns approach yields a significant decrease in mse up to 10 to 20 db for certain snr ranges compared with the uniform sampling scenario considering an application to frequency domain optical coherence tomography we show that the proposed methodology results in higher resolution and higher reconstruction accuracy than the standard techniques

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

nonorthogonal joint diagonalization free of degenerate solution the problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications for nonorthogonal joint diagonalization based on the weighted least squares wls criterion the trivial zero solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms however the resultant algorithms may converge to some undesired degenerate solutions nonzero but singular or ill conditioned solutions this paper discusses and analyzes the problem of degenerate solutions in detail to solve this problem a novel nonleast squares criterion for approximate nonorthogonal joint diagonalization is proposed and an efficient algorithm called fast approximate joint diagonalization fajd is developed as compared with the existing nonorthogonal diagonalization algorithms the new algorithm can not only avoid the trivial solution but also any degenerate solutions theoretical analysis shows that the fajd algorithm has some advantages over the existing nonorthogonal diagonalization algorithms simulation results are presented to demonstrate the efficiency of this paper s algorithm

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

on the asymptotic behaviour of first passage times for transient random walk let x denote the time at which a random walk with finite positive mean first passes into x wherex 0 this paper establishes the asymptotic behaviour of pr x n asn for fixedx in two cases in the first case the left hand tail of the step distribution is regularly varying and in the second the step distribution satisfies a one sided cramer type condition as a corollary it follows that in the first case mathop lim limits n to infty pr x n pr 0 n coincides with the limit of the same quantity for recurrent random walk satisfying spitzer s condition but in the second case the limit is more complicated

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

direction of arrival estimation for constant modulus signals in many cases where direction finding is of interest the signals impinging on an antenna array are known to be phase modulated and hence to have a constant modulus cm this is a strong property by itself it is already sufficient for source separation and can be used to construct improved direction finding algorithms we first derive the relevant cramer rao bounds crbs for arbitrary array configurations and specialize to uniform linear arrays we then propose a simple suboptimal direction estimation algorithm in which the signals are separated using the cm property followed by direction finding on the decoupled signals compared with the esprit algorithm and the crb for arbitrary signals the algorithm shows good results

complex field coding for ofdm over fading wireless channels orthogonal frequency division multiplexing ofdm converts a time dispersive channel into parallel subchannels and thus facilitates equalization and de coding but when the channel has nulls close to or on the fast fourier transform fft grid uncoded ofdm faces serious symbol recovery problems as an alternative to various error control coding techniques that have been proposed to ameliorate the problem we perform complex field coding cfc before the symbols are multiplexed we quantify the maximum achievable diversity order for independent and identically distributed i i d or correlated rayleigh fading channels and also provide design rules for achieving the maximum diversity order the maximum coding gain is given and the encoder enabling the maximum coding gain is also found simulated performance comparisons of cfc ofdm with existing block and convolutionally coded ofdm alternatives favor cfc ofdm for the code rates used in a hiperlan2 experiment

blind separation of synchronous co channel digital signals using an antenna array ii performance analysis we have recently proposed a blind maximum likelihood approach for demodulating multiple co channel digital signals received synchronously at an antenna array this approach exploits the finite alphabet fa property of digital signals to simultaneously estimate the array response and symbol sequence for each signal we have presented two computationally efficient block algorithms for computing the array response and signal estimates iterative least squares with projection ilsp and iterative least squares with enumeration ilse in this paper we study the performance of these algorithms using both analysis and simulation we derive the probability of error in detecting the signals under the assumption that the array responses are known we use this probability to estimate the probability of error in the algorithms simulation results confirm that the detection error probability yields a good approximation to the performance of the blind algorithms

blind source separation the location of local minima in the case of finitely many samples cost functions used in blind source separation are often defined in terms of expectations i e an infinite number of samples is assumed an open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case to answer this question we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions in particular we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix the method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function this shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function we also answer a long standing problem of the mean squared error mse behavior of the finite sample least squares constant modulus algorithm ls cma namely whether there exist ls cma receivers with good mse performance we demonstrate how the proposed techniques can be used to determine the required number of samples for ls cma to exceed a specified performance the paper concludes with simulations that validate the results

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

independent component analysis over galois fields of prime order we consider the framework of independent component analysis ica for the case where the independent sources and their linear mixtures all reside in a galois field of prime order p similarities and differences from the classical ica framework over the real field are explored we show that a necessary and sufficient identifiability condition is that none of the sources should have a uniform distribution we also show that pairwise independence of the mixtures implies their full mutual independence namely a nonmixing condition in the binary p 2 and ternary p 3 cases but not necessarily in higher order p 3 cases we propose two different iterative separation or identification algorithms one is based on sequential identification of the smallest entropy linear combinations of the mixtures and is shown to be equivariant with respect to the mixing matrix the other is based on sequential minimization of the pairwise mutual information measures we provide some basic performance analysis for the binary p 2 case supplemented by simulation results for higher orders demonstrating advantages and disadvantages of the proposed separation approaches

notes on random walks in the cauchy domain of attraction the goal of these notes is to fill some gaps in the literature about random walks in the cauchy domain of attraction which has been in many cases left aside because of its additional technical difficulties we prove here several results in that case a fuk nagaev inequality and a local version of it a large deviation theorem two types of local large deviation theorems we also derive two important applications of these results a sharp estimate of the tail of the first ladder epochs and renewal theorems extending standard renewal theorems to the case of random walks most of our techniques carry through to the case of random walks in the domain of attraction of an alpha stable law with alpha in 0 2 so we also present results in that case since many of them seem to be missing in the literature

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

blind identification of fir systems excited by discrete alphabet inputs an algorithm for the identification of finite impulse response fir system parameters from output measurements for systems excited by discrete alphabet inputs is described the approach taken is algebraic it does not rely directly on the statistical properties of the measurements but rather it essentially solves the nonlinear equations appearing in the problem by converting them to equivalent linear equations using the discrete alphabet property of the input signal the proposed algorithm was tested by computer simulations and some of these simulations are illustrated

on blind beamforming for multiple non gaussian signals and the constant modulus algorithm a new method for blindly separating multiple cochannel non gaussian signals received by a sensor array is presented the method is based on a cumulant based least squares criterion that for identically distributed negative kurtosis signals is proven to be identical to the 2 2 constant modulus cm cost function commonly used by cm algorithms a computationally simple algorithm is proposed to minimize the criterion the algorithm performs well even when the number of samples is small thus allowing its application in dynamic environments e g moving emitters for the special case of two signals only the minimization is obtained analytically simulation results are included

the distribution and moments of the smallest eigenvalue of a random matrix of wishart type abstract given a random rectangular m n matrix with elements from a normal distribution what is the distribution of the smallest singular value to pose an equivalent question in the language of multivariate statistics what is the distribution of the smallest eigenvalue of a matrix from the central wishart distribution in the null case we give new results giving the distribution as a simple recursion this includes the more difficult case when n m is an even integer without resorting to zonal polynomials and hypergeometric functions of matrix arguments with the recursion one can obtain exact expressions for the density and the moments of the distribution in terms of functions usually no more complicated than polynomials exponentials and at worst ordinary hypergeometric functions we further elaborate on the special cases when n m 0 1 2 and 3 and give a numerical table of the expected values for 2 m 25 and 0 n m 25

blind identification of underdetermined mixtures by simultaneous matrix diagonalization in this paper we study simultaneous matrix diagonalization based techniques for the estimation of the mixing matrix in underdetermined independent component analysis ica this includes a generalization to underdetermined mixtures of the well known sobi algorithm the problem is reformulated in terms of the parallel factor decomposition parafac of a higher order tensor we present conditions under which the mixing matrix is unique and discuss several algorithms for its computation

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

globally convergent blind source separation based on a multiuser kurtosis maximization criterion we consider the problem of recovering blindly i e without the use of training sequences a number of independent and identically distributed source user signals that are transmitted simultaneously through a linear instantaneous mixing channel the received signals are hence corrupted by interuser interference iui and we can model them as the outputs of a linear multiple input multiple output mimo memoryless system assuming the transmitted signals to be mutually independent i i d and to share the same non gaussian distribution a set of necessary and sufficient conditions for the perfect blind recovery up to scalar phase ambiguities of all the signals exists and involves the kurtosis as well as the covariance of the output signals we focus on a straightforward blind constrained criterion stemming from these conditions from this criterion we derive an adaptive algorithm for blind source separation which we call the multiuser kurtosis muk algorithm at each iteration the algorithm combines a stochastic gradient update and a gram schmidt orthogonalization procedure in order to satisfy the criterion s whiteness constraints a performance analysis of its stationary points reveals that the muk algorithm is free of any stable undesired local stationary points for any number of sources hence it is globally convergent to a setting that recovers them all

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

a low complexity blind estimator of narrowband polynomial phase signals consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array in practice it is difficult to maintain a precisely calibrated array the array manifold is then assumed to be unknown and the estimation is referred to as blind estimation to date only an approximated maximum likelihood estimator amle was suggested for blindly estimating the polynomial coefficients of each signal however this estimator requires a multidimensional search over the entire coefficient space instead we propose an estimation approach which is based on two steps first the signals are separated using a blind source separation technique which exploits the constant modulus property of the signals then the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal this estimator does not involve any search in the coefficient spaces the computational complexity of the proposed estimator increases linearly with respect to the polynomial order whereas that of the amle increases exponentially simulation results show that the proposed estimator achieves the cramer rao lower bound at moderate or high signal to noise ratio

sensor array signal processing via a procrustes rotations based eigenanalysis of the esprit data pencil the authors propose the procrustes rotation based esprit algorithm pro esprit for estimating characteristic parameters associated with a scene of radiating sources given data derived from two identical sensor arrays the x and y arrays which are displaced relative to one another pro esprit uses the inherent redundancy built into the esprit array system to compensate for deviations from the ideal array model this redundancy is manifested by two fundamental properties of the noiseless x and y data matrices comprising the esprit data pencil a they have the same row space the signal subspace and 2 they have the same column space the source subspace these properties are utilized by invoking two primary tools 1 the solution to the procrustes problem for optimally approximating an invariant subspace rotation and 2 the total least squares method for perturbing each of two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same

analysis of a nonlinear least squares procedure used in global positioning systems iterated least squares ils is a widely used parameter estimation algorithm for nonlinear least squares problems the ils estimation error covariance is usually written gtr 1g 1 where g is the jacobian matrix at the solution and r is the noise covariance using a first order expansion of the gain matrix in ils we provide a rigorous justification for the covariance formula the analysis includes uncertainty in the initial estimate and is capable of modeling the transient performance of the algorithm given convergence the usual ils covariance is obtained asymptotically the analysis makes use of matrix differential calculus to obtain the first differential of the ils gain matrix and includes as a special case the r i case where the gain matrix is the pseudoinverse of the jacobian matrix the results are harnessed to obtain a sensitivity analysis of the ils algorithm to additional random parametric variations the analysis is then applied to a global positioning system problem to characterize the effect of ephemeris errors on the ils position estimates results from a comparative monte carlo simulation demonstrate the approach s effectiveness

estimating frequencies of exponentials in noise using joint diagonalization the problem of estimating frequencies of superimposed exponentials in white noise collected by a single sensor is considered we discuss a solution based on a modification of an analytic algorithm that was proposed for separation of constant modulus signals received by an antenna array by van der veen and paulraj see ibid vol vol 44 p 1136 55 1996 we show that with an appropriate implementation of certain constraints the algorithm produces excellent super resolution results an advantage of the algorithm is that it does not require multidimensional search and therefore it is free from problems associated with search algorithms like convergence to local extremum or proper initialization another advantage is its applicability in nonuniform sampling conditions where methods based on linear prediction cannot be applied we carry out a detailed performance analysis under the assumption of long data record and derive conditions for estimating all the frequencies the performance of the proposed algorithm compares favorably with the performance of the tufts kumaresan method 1982

paley wiener characterization of kernels for finite rate of innovation sampling exact reconstruction of finite rate of innovation signals can be achieved by employing customized sampling kernels that satisfy certain frequency domain properties we impose compact support in time as an additional constraint considering frequency domain reconstruction we derive conditions for admissible sampling kernels and corresponding sampling rates our constructive kernel design methodology is based on the paley wiener theorem for compactly supported functions the new kernels satisfy generalized strang fix conditions and have specific polynomial modulated exponential reproducing properties unlike exponential splines which have a support that is directly proportional to the number of exponentials they can generate the proposed kernels have a support that is independent of that number to analyze noise robustness we consider a special member of the class that has a sum of modulated splines sms form in the time domain and optimize its parameters to minimize the noise variance the sum of sincs sos kernel reported in the literature is an instance of this construction in noise robustness analysis sms kernels show improvement in mean squared error mse compared with the state of the art alternatives in continuous time noise the improvement in mse is about 2 db for low signal to noise ratio snr and 7 db for high snr in the case of discrete white gaussian noise the mse is lower by as much as 25 db by using a higher order sms kernel compared with the sos kernel for snrs in the range of 10 15 db

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

blind mimo eigenmode transmission based on the algebraic power method identification of the channel matrix is of main concern in wireless multiple input multiple output mimo systems to maximize the snr the best way to utilize a mimo system is to communicate on the top singular vectors of the channel matrix here we present a new approach for direct blind identification of the main independent singular modes without estimating the channel matrix itself the right and left singular vectors with maximum corresponding singular values are determined using payload data and are continuously updated while at the same time being used for communication the feasibility of the approach is demonstrated by simulating the performance over a noisy fading time varying channel mathematically the technique is related to the iterative numerical power method for finding eigenvalues of a matrix as well as the time reversal mirror technique developed within acoustics

analytical method for blind binary signal separation the blind separation of multiple co channel binary digital signals using an antenna array involves finding a factorization of a data matrix x into x as where all entries of s are 1 or 1 it is shown that this problem can be solved exactly and noniteratively via a certain generalized eigenvalue decomposition as indicated by simulations the algorithm is robust in the presence of noise an interesting implication is that certain cluster segmentation problems can be solved using eigenvalue techniques

asymmetric pulse modeling for fri sampling we consider sampling and reconstruction of finite rate of innovation fri signals such as a train of pulses where the pulses have varying degrees of asymmetry we address the problem of asymmetry modeling starting from a given symmetric prototype we show that among the class of unitary operators that are linear and invariant to translation and scale the fractional hilbert frh operator is unique for parametrically modeling pulse asymmetry the frh operator is obtained by a trigonometric interpolation between the standard hilbert and identity operators where the interpolation weights are determined by the degree of asymmetry the frh operators are also steerable which allows for estimation of the asymmetry factors in addition to the delays and amplitudes using the high resolution spectral estimation techniques that are used for solving standard fri problems we also develop the discrete counterpart using discrete frh operators and show that all the desirable properties carry over smoothly to the discrete setting as well we derive closed form expressions for the cramer rao bounds and hammersley chapman robbins bound on the variances of the estimators for continuous and discrete parameters respectively experimental results show that the proposed estimators have variances that meet the lower bounds we demonstrate an application of the proposed discrete frh methodology on real electrocardiogram ecg signals in the presence of noise specifically we show how the asymmetry of qrs complexes in various channels of an ecg signal could be modeled accurately

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

bounded component analysis of linear mixtures a criterion of minimum convex perimeter this study presents a blind and geometric technique which pursues the linear decomposition of the observations in bounded component signals the bounded component analysis of the observations relies on the hypotheses of compactness and cartesian decomposition of the convex support of the vector of component signals and in the invertibility of the mixture assumptions which in absence of noise are able to guarantee the identifiability of the mixture and separability of the components up to permutation scaling and phase ambiguities under these conditions the convex perimeter of the normalized linear combination of the observations is shown to be a global contrast function whose minima correspond with the extraction of bounded components of the observations practical extraction and separation algorithms based on the minimization of this criterion are given the experimental results with communications signals serve to illustrate the good performance of the proposed method in high snr scenarios even for a small number of samples

on the schur decomposition of a matrix for parallel computation an algorithm to solve the eigenproblem for nonsymmetric matrices on an n n array of mesh connected processors isomorphic to the architecture described by brent and luk for symmetric matrices is presented this algorithm is a generalization of the classical jacobi method and as such holds promise for parallel architectures the rotational parameters for the nonsymmetric case are carefully analyzed many examples of a working program simulating the parallel architecture are given with experimental evidence of quadratic convergence

algebraic joint zero diagonalization and blind sources separation this paper adresses the problem of the joint zero diagonalization of a given set of matrices we establish the identiflability conditions of the zero diagonalizer and we propose a new algebraical algorithm based on the reformulation of the initial problem into a joint diagonalization problem the zero diagonalizer is not constrained to be unitary computer simulations illustrate the behavior of the algorithm moreover as an application we show that the blind separation of correlated sources can be performed applying this algorithm to a particular set of spatial quadratic time frequency distribution matrices in this case computer simulations are also provided in order to illustrate the performances of the proposed algorithm and to compare it with other existing ones

non symmetrical joint zero diagonalization and mimo zero division multiple access this paper addresses the problem of non symmetrical joint zero diagonalization nsjzd of a given set of matrices and its use in user interference cancellation for a new multiple access multiple input multiple output mimo wireless transmission scheme first sufficient conditions for uniqueness of the non symmetrical zero diagonalizer are described and we propose a non iterative efficient algorithm termed non symmetrical joint algebraic zero diagonalization nsjaz based on the reformulation of the initial problem into a joint generalized eigendecomposition problem second we define the new concept of mimo zero division multiple access zdma allowing training sequence free and simultaneous multiple access to a wireless receiver base station over a single frequency channel each zdma emitter combines two types of modulation fsk am the multiple antenna zdma access point performs an nsjaz based blind separation of the different accesses assuming a flat fading channel computer simulations of such a system are presented both in analog and digital cases finally to demonstrate that our multiple access scheme is technically feasible and works in a real environment we present some preliminary results obtained with a full analog zdma based hardware prototype system that we have developed

blind digital signal separation using successive interference cancellation iterative least squares blind separation of instantaneous linear mixtures of digital signals is a basic problem in communications when little or nothing can be assumed about the mixing matrix signal separation may be achieved by exploiting structural properties of the transmitted signals e g finite alphabet or coding constraints we propose a monotonically convergent and computationally efficient iterative least squares ils blind separation algorithm based on an optimal scaling lemma the signal estimation step of the proposed algorithm is reminiscent of successive interference cancellation sic ideas for well conditioned data and moderate snr the proposed sic ils algorithm provides a better performance complexity tradeoff than competing ils algorithms coupled with blind algebraic digital signal separation methods sic ils offers a computationally inexpensive true least squares refinement option we also point out that a widely used ils finite alphabet blind separation algorithm can exhibit limit cycle behavior

estimation of sparse mimo channels with common support we consider the problem of estimating sparse communication channels in the mimo context in small to medium bandwidth communications as in the current standards for ofdm and cdma communication systems with bandwidth up to 20 mhz such channels are individually sparse and at the same time share a common support set since the underlying physical channels are inherently continuous time we propose a parametric sparse estimation technique based on finite rate of innovation fri principles parametric estimation is especially relevant to mimo communications as it allows for a robust estimation and concise description of the channels the core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support we show the application of our technique for channel estimation in ofdm uniformly contiguous dft pilots and cdma downlink walsh hadamard coded schemes in the presence of additive white gaussian noise theoretical lower bounds on the estimation of sparse common support scs channel parameters in rayleigh fading conditions are derived finally an analytical spatial channel model is derived and simulations on this model in the ofdm setting show the symbol error rate ser is reduced by a factor 2 0 db of snr to 5 high snr compared to standard non parametric methods e g lowpass interpolation

conditioned local limit theorems for random walks defined on finite markov chains let x n n geqslant 0 be a markov chain with values in a finite state space mathbb x starting at x 0 x in mathbb x and let f be a real function defined on mathbb x set s n sum k 1 n f x k n geqslant 1 for any y in mathbb r denote by tau y the first time when y s n becomes non positive we study the asymptotic behaviour of the probability mathbb p x left y s n in z z a tau y n right as n rightarrow infty we first establish for this probability a conditional version of the local limit theorem of stone then we find for it an asymptotic equivalent of order n 3 2 and give a generalization which is useful in applications we also describe the asymptotic behaviour of the probability mathbb p x left tau y n right as n rightarrow infty

a continuous jacobi like approach to the simultaneous reduction of real matrices abstract the problem of simultaneous reduction of real matrices by either orthogonal similarity or orthogonal equivalence transformations is considered based on the jacobi idea of minimizing the sum of squares of the complementary part of the desired form to which matrices are reduced the projected gradient method is used in this paper it is shown that the projected gradient of the objective function can be formulated explicitly this gives rise to a system of ordinary differential equations that can be readily solved by numerical software the advantages of this approach are that the desired form to which matrices are reduced can be almost arbitrary and that if a desired form is not attainable then the limit point of the corresponding differential equation gives a way of measuring the distance from the best reduced matrices to the nearest matrices that have the desired form the general procedure for deriving these differential equations is discussed the framework can be generalized to the complex valued case some applications are given

blind separation of synchronous co channel digital signals using an antenna array i algorithms we propose a maximum likelihood ml approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site the spatial response of the array is assumed to be known imprecisely or unknown we exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal uniqueness of the estimates is established for bpsk signals we introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner computationally efficient algorithms for both block and recursive estimation of the signals are presented this new approach is applicable to an unknown array geometry and propagation environment which is particularly useful in wireless communication systems simulation results demonstrate its promising performance

fast subspace decomposition many recent signal processing techniques in various areas e g array signal processing system identification and spectrum estimation require a step of extracting the low dimensional subspace from a large space this step is usually called subspace decomposition which is conventionally accomplished by an eigendecomposition ed since an ed requires o m sup 3 flops for an m spl times m matrix it may represent a barrier to the real time implementation of these algorithms the authors present a fast algorithm for signal subspace decomposition which is termed fsd that exploits the special matrix structure low rank plus identity associated with signal subspace algorithms and requires only o m sup 2 d flops where d often spl lt m denotes the signal subspace dimension unlike most of alternatives the dimension of the signal subspace is not assumed known apriori and is estimated as part of the procedure moreover theoretical analysis has been conducted and its results show the strong consistency of the new detection scheme and the asymptotic equivalence between fsd and ed in estimating the signal subspace their new approach can also exploit other matrix structure common in signal processing areas e g toeplitz or hankel and thus achieve another order of computational reduction moreover it can be easily implemented in parallel to reduce further the computation time to as little as o md using o m simple processors

joint channel and carrier offset estimation in cdma communications this paper addresses the problem of cdma multiuser detection in the presence of unknown multipath channels and residual carriers an analytic algorithm that provides closed form channel and carrier offset estimates is proposed the algorithm first converts the multiuser estimation problem into single user problems and then analytically solves the resulting nonlinear multivariate optimization problems using a polynomial matrix projection property the performance of the proposed algorithm is investigated through first order perturbation analysis we also calculate the cramer rao bound crb to illustrate the efficiency of the new algorithm the analyzes are supported by computer simulations

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