estimating the covariance matrix by signal subspace averaging an efficient algorithm is presented for estimating a covariance matrix consisting of a low rank signal term and a full rank noise term known apart from a scalar factor for each sample of the vector of sensor outputs the algorithm approximates in the least squares sense a rank one update of the covariance matrix under the side condition that the rank of the signal term remains bounded if the model noise is spatially colored the least squares approximation is preceded by spatial prewhitening it is shown that if the rank of the signal term is small compared to the number of sensors then the proposed algorithm requires substantially less computational work than conventional averaging some simulation results are included indicating that the proposed algorithm reduces the variance of some commonly used spectral estimators in off target directions without impairing their detection and resolution properties

design and analysis of a 2 d eigenspace based interference canceller this paper deals with the problem of eigenspace based interference cancellation using a two dimensional 2 d rectangular array an efficient 2 d signal blocking technique is presented to remove the desired signal from the received array data in conjunction with the 2 d signal blocking technique a positive definite matrix is further constructed and used to compensate the effect of the signal blocking operation on the sensor noise received by a 2 d eigenspace based interference canceller eic therefore the interference subspace required for computing the optimal weight vector of the designed 2 d eic can be obtained by simply using conventional eigenvalue decomposition methods instead of any complicated generalized eigenvalue decomposition methods the performances of the designed 2 d eic under finite samples and steering angle error are also evaluated the developed theoretical results are confirmed by several simulation examples

a formal power series expansion regularization approach for levy stable distributions the symmetric case with m positive integer in practice the levy stable distribution is usually expressed in terms of the fourier integral of its characteristic function indeed known closed form expressions are relatively scarce given the huge parameters space and hence systematic efforts have been made towards the development of proper methods for analytically solving the mentioned integral as a further contribution in this direction here we propose a new way to tackle the problem we consider an approach in which one first solves the fourier integral through a formal thus not necessarily convergent series representation then one uses if necessary a pertinent sum regularization procedure to the resulting divergent series so as to obtain an exact formula for the distribution which is amenable to direct numerical calculations as a concrete study we address the centered symmetric unshifted and unscaled distribution with conceivably the present protocol could be applied to other sets of parameter values

analysis of the performance and sensitivity of an eigenspace based interference canceler eigenspace based interference cancelers eics possess the advantages of providing maximal suppression of interference with fast convergence over conventional adaptive beamformers however the performance and sensitivity to steering angle error of eics have not been analyzed due to the use of a signal blocking matrix we first present a technique to construct a positive definite matrix based on the signal blocking matrix and then use this matrix to compensate the effect of the signal blocking matrix on the sensor noise received by an eic therefore the interference subspace required for finding the optimal weight vector can be obtained using conventional eigenvalue decomposition evd moreover the performance and sensitivity to the steering angle error of the eic can be analyzed simulation examples are provided for confirming the theoretical results

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

algebraic shift equivalence and primitive matrices motivated by symbolic dynamics we study the problem given a unital subring s of the reals when is a matrix a algebraically shift equivalent over s to a primitive matrix we conjecture that simple necessary conditions on the nonzero spectrum of a are sufficient and establish the conjecture in many cases if s is the integers we give some lower bounds on sizes of realizing primitive matrices for dedekind domains we prove that algebraic shift equivalence implies algebraic strong shift equivalence

a signal subspace method for adaptive interference cancellation an interference cancellation technique that combines a signal subspace approach with adaptive adjustment of the weight vector is derived the weight vector is constrained to lie in a signal subspace computed by eigendecomposition of the covariance matrix of the array outputs the weight vector is rotated to maximize the output signal to interference ratio the technique does not require array calibration as in other subspace methods this technique applies to receiver arrays for digital communication signals the case of a bpsk signal modulating an am transmitter is analyzed in some detail numerical examples illustrate the behavior of the algorithm

on the summation of some divergent hypergeometric series and related perturbation expansions abstract divergent hypergeometric series 2 f 0 1 occur frequently in poincare type asymptotic expansions of special functions these divergent series 2 f 0 can be used for the evaluation of the corresponding special functions if suitable summation technique are applied there is considerable evidence that levin s sequence transformation 1973 and in particular also some closely related sequence transformations weniger 1989 which were derived recently sum divergent series 2 f 0 much more efficiently than pade approximants similar summation problems occur also in the case of divergent rayleigh schrodinger perturbation expansions of elementary quantum mechanical systems a comparison of the perturbation series for the quartic anharmonic oscillator with the closely related asymptotic series for the complementary error function shows that levin s sequence transformation and the recently derived new sequence transformations are again more efficient than pade approximants however the superiority of levin s sequence transformation and of the new sequence transformations is less pronounced in the case of the perturbation expansion

auxiliary antenna assisted interference mitigation for radio astronomy arrays interferometric image synthesis in radio astronomy is plagued by signal corruption from man made sources the very weak signals of interest can be overwhelmed by such interference recent work has proposed using array signal processing techniques of adaptive beamforming adaptive filtering and subspace projection to remove interference prior to image synthesis in some practical scenarios we have found poor cancellation performance when using such methods because signal of interest levels in radio astronomy ra are usually well below the noise even interference to noise ratios inr less than unity can affect signal estimation at these low inrs it is difficult to estimate interference parameters or statistics with sufficient accuracy for high performance adaptive cancellation or subspace projection by adding a few one to three low gain relative to the primary telescope dishes auxiliary antennas to an array it is possible to overcome this problem this paper will show that using such antennas e g commercial grade 3 m dishes with an existing array can significantly improve interference rejection new extensions to subspace projection spatial filtering methods are presented along with analytical and simulated results for performance comparison

the spectra of nonnegative integer matrices via formal power series an old problem in matrix theory is to determine the n tuples of complex numbers which can occur as the spectrum of a matrix with nonnegative entries see bp94 chapter 4 or min88 chapter vii authors have studied the case where the ntuple is comprised of real numbers bor95 cia68 fri78 kel71 per53 sal72 sou83 sul49 the case where the matrices under consideration are symmetric fie74 jll96 and the general problem joh81 lm99 ll79 rea94 rea96 wuw97 various necessary conditions and sufficient conditions have been provided but a complete characterization is known for real n tuples only for n 4 kel71 sul49 and for complex n tuples only for n 3 ll79 motivated by symbolic dynamics boyle and handelman refocused attention on the nonzero part of the spectrum by making the following spectral conjecture bh91 bh93 see also boy93 8 and lm95 chapter 11 below a matrix a is primitive if all entries of a are nonnegative and for some n all entries of a are strictly positive also

a characterization of trace zero nonnegative 5 5 matrices let 1 2 3 4 5 be a list of complex numbers with 1 2 3 4 5 0 necessary and sufficient conditions for the existence of an entry wise nonnegative 5 5 matrix a with spectrum are presented

implementation of adaptive array algorithms some new efficient and numerically stable algorithms for the recursive solution of matrix problems arising in optimal beam forming and direction finding are described and analyzed the matrix problems considered are systems of linear equations and spectral decomposition while recursive solution procedures based on the matrix inversion lemma may be unstable ours are stable furthermore these algorithms are extremely fast

levy stable two sided distributions exact and explicit densities for asymmetric case we investigate functions g ensuremath alpha ensuremath beta x which are heavy tailed l evy stable probability distributions of index 0l ensuremath alpha ensuremath leqslant 2 and appropriate asymmetry parameter ensuremath beta they are of central importance in physics of amorphous and disordered systems econophysics geology hydrology internet traffic dynamics of human relations etc we present an ensemble of exact and explicit solutions of g ensuremath alpha ensuremath beta x for all admissible rational values of ensuremath alpha and ensuremath beta we reproduce all the previously known cases and furnish distributions for values ensuremath alpha and ensuremath beta which were previously inaccessible we point out many instances of experimental and statistical data that could be described by our results

model based subspace projection beamforming for deep interference nulling this paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments in many practical scenarios the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace we address the particularly troublesome cases of low interference to noise ratio inr relatively rapid interference motion and correlated noise across the receiving array a polynomial based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time mitigate interference subspace estimation errors and improve canceler performance the application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution here even weak residual interference after cancellation may obscure a signal of interest so very deep beampattern nulls are required performance for conventional subspace projection sp is compared with polynomial augmented sp using simulated and real experimental data showing null depth improvement of 6 to 30 db

an efficient technique for eigenspace based adaptive interference cancellation this paper presents a technique for the computation of the interference subspace for eigenspace based interference cancellation using a subarray partitioning scheme we construct the interference subspace from the subarray interference subspaces in the case of uniform linear arrays the proposed technique has the advantages of reclaiming the lost degrees of freedom due to signal blocking and reduced computational burden over existing techniques the proposed technique also possesses the capabilities to cope with the case of using nonuniform linear arrays in the environment of partially correlated signals a computer simulation example is provided for illustration and comparison

generalized eigenspace based beamformers the generalized eigenspace based beamformer geib is presented here which utilizes the eigenstructure of the correlation matrix to enhance the performance of the linearly constrained minimum variance beamformer lcmvb the weight vector of the geib is found by projecting the lcmvb weight vector onto a vector subspace constructed from the eigenstructure of the correlation matrix the geib and the lcmvb have the same responses to the desired signal and the interferers however the weight vector of the geib has a smaller norm and generates a lower output noise power an additional advantage of the geib is that the linear constraints can be treated flexibly i e each linear constraint can be chosen to be preserved or not preserved the cost of preserving a linear constraint is to get more output noise power in addition to developing the geib we discuss the effects of imposing linear constraints on the output noise powers of the geib and the lcmvb computer simulations are also presented that demonstrate the merits of the geib

small polynomial matrix presentations of nonnegative matrices we investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior

on positive matrices abstract we relate several results on positive matrices due to soittola 1976 handelman 1981 1987 and lind 1984 giving conditions for the existence of some positive matrix to represent a linear map the result of soittola concerns finite automata and those of handelman and lind concern symbolic dynamics

levy flights exact results and asymptotics beyond all orders a comprehensive study of the symmetric levy stable probability density function is presented this is performed for orders both less than 2 and greater than 2 the latter class of functions are traditionally neglected because of a failure to satisfy non negativity the complete asymptotic expansions of the symmetric levy stable densities of order greater than 2 are constructed and shown to exhibit intricate series of transcendentally small terms asymptotics beyond all orders it is demonstrated that the symmetric levy stable densities of any arbitrary rational order can be written in terms of generalized hypergeometric functions and a number of new special cases are given representations in terms of special functions a link is shown between the symmetric levy stable density of order 4 and pearcey s integral which is used widely in problems of optical diffraction and wave propagation this suggests the existence of applications for the symmetric levy stable densities of order greater than 2 despite their failure to define a probability density function