reliability evaluation of bc networks reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems extra connectivity determination and faulty networks structure analysis are two important aspects for the reliability evaluation of interconnection networks an n dimensional bijective connection network in brief bc network denoted by xn is an n regular graph with 2n vertices and n2n 1 edges the hypercubes mobius cubes crossed cubes and twisted cubes are some examples of the bc networks by exploring the boundary problem of the bc networks we prove that when n 4 and 0 h n 4 the h extra connectivity of an n dimensional bc network xn is kh xn n h 1 1 2h h 3 furthermore there exists a large connected component and the remaining small components have at most h vertices in total if the total number of faulty vertices is strictly less its h extra connectivity as an application the results on the h extra connectivity and structure of faulty networks on hypercubes mobius cubes crossed cubes and twisted cubes are obtained

subspace averaging and order determination for source enumeration in this paper we address the problem of subspace averaging with special emphasis placed on the question of estimating the dimension of the average the results suggest that the enumeration of sources in a multi sensor array which is a problem of estimating the dimension of the array manifold and as a consequence the number of radiating sources may be cast as a problem of averaging subspaces this point of view stands in contrast to conventional approaches which cast the problem as one of identifiying covariance models in a factor model we present a robust formulation of the proposed order fitting rule based on majorization minimization algorithms a key element of the proposed method is to construct a bootstrap procedure based on a newly proposed discrete distribution on the manifold of projection matrices for stochastically generating subspaces from a function of experimentally determined eigenvalues in this way the proposed subspace averaging sa technique determines the order based on the eigenvalues of an average projection matrix rather than on the likelihood of a covariance model penalized by functions of the model order by means of simulation examples we show that the proposed sa criterion is especially effective in high dimensional scenarios with low sample support

generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

the t k diagnosability of the bc graphs processor fault diagnosis takes an important role in fault tolerant computing on multiprocessor systems there are two classical diagnosis strategies the precise strategy and the pessimistic strategy both of which are based on the well known pmc diagnostic model nevertheless the degree of diagnosability of the system is limited under these two strategies a better method called the t k diagnosis strategy is proposed by somani and peleg in which the identified fault set is allowed to contain at most k fault free processors using this diagnosis strategy the degree of diagnosability of the hypercube increases greatly as the number of the fault free processors in the fault set increases we study the t k diagnosability of so called bc graphs that include hypercubes crossed cubes mobius cubes and twisted cubes etc we show that any n dimensional bc graph is t n k k diagnosable when n spl ges 4 and 0 spl les k spl les n where t n k k 1 n 1 2 k 1 k 2 1 therefore the crossed cube the mobius cube and the twisted cube all have the same t k diagnosability as the hypercube as a result the algorithms developed for diagnosis on the hypercube may also be used to diagnose multiprocessor systems whose network topologies are based on bc graphs

statistical characterization of the music null spectrum statistical characterization of the music sample null spectrum is presented for an arbitrary number of possibly correlated emitters observed by a general array a remarkably simple expression is developed for the spectral covariance matrix in the vicinity of the emitters the covariance result together with prior mean spectral results support a gaussian characterization in the neighborhood of the emitters for many scenarios it is shown that the sample spectrum is exactly wishart distributed in the emitter directions the results can be utilized to quantify a variety of performance metrics as an illustration models based on physical parameters are constructed for the curve of probability of resolution versus signal to noise ratio the models predict the curve with a high degree of accuracy for example scenarios

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

edge pancyclicity and path embeddability of bijective connection graphs an n dimensional bijective connection graph in brief bc graph is a regular graph with 2 n nodes and n2 n 1 edges the n dimensional hypercube crossed cube mobius cube etc are some examples of the n dimensional bc graphs in this paper we propose a general method to study the edge pancyclicity and path embeddability of the bc graphs first we prove that a path of length l with dist x n x y 2 y in x n where x n n 4 is a n dimensional bc graph satisfying the three specific conditions and v x n is the node set of x n furthermore by this result we can claim that x n is edge pancyclic lastly we show that these results can be applied to not only crossed cubes and mobius cubes but also other bc graphs except crossed cubes and mobius cubes so far the research on edge pancyclicity and path embeddability has been limited in some specific interconnection architectures such as crossed cubes mobius cubes

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

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

estimation of the directions of arrival of signals in unknown correlated noise i the map approach and its implementation the authors propose a method of direction of arrival doa estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary other than being positive definite they examine the projection of the data onto the noise subspace the conditional probability density function pdf of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed the a posteriori pdf of the signal parameters alone is then obtained by assigning a noninformative a priori pdf to the unknown noise covariance matrix and integrating out this quantity a simple criterion for the maximum a posteriori map estimate of the doas of the signals is established some properties of this criterion are discussed and an efficient numerical algorithm for the implementation of this criterion is developed the advantage of this method is that the noise covariance matrix does not have to be known nor must it be estimated

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

efficient computation of the far field of parabolic reflectors by pseudo sampling algorithm the newly developed pseudo sampling representation is applied for computing the far field of an offset parabolic reflector with a cluster feed illumination a new comb type fast fourier transform fft algorithm is used in a computer program both precision and computational time are analyzed demonstrating the excellent performance of the method

fault free hamiltonian cycles in crossed cubes with conditional link faults the crossed cube which is a variation of the hypercube possesses some properties superior to the hypercube in this paper assuming that each node is incident with at least two fault free links we show that an n dimensional crossed cube contains a fault free hamiltonian cycle even if there are up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated we also verify that the assumption is practically meaningful by evaluating its occurrence probability which is very close to 1

on the behavior of information theoretic criteria for model order selection the akaike 1974 information criterion aic and the minimum description length mdl are two well known criteria for model order selection in the additive white noise case our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eigenvalue dispersion our results are mostly qualitative and serve to explain the behavior of the aic and the mdl in some cases of great practical importance we show that when the noise eigenvalues are not clustered sufficiently closely then the aic and the mdl may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise eigenvalues for fixed number of data samples overmodeling becomes more likely for increasing the dispersion of the noise eigenvalues for fixed dispersion overmodeling becomes more likely for increasing the number of data samples undermodeling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently closely we illustrate our results by using simulations from the effective channel order determination area

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

an eigenvector technique for detecting the number of emitters in a cluster the paper introduces a new algorithm for estimating the number of sources in a cluster of closely spaced sources the algorithm is based on consideration of the eigenvectors of the sample covariance matrix and is designated as the eigenvector detection technique edt it is shown by examples that the edt can reliably detect sources that number at lower signal to noise ratios snrs than either the minimum description length mdl or akaike information criterion aic algorithms the paper also presents a performance analysis of the edt results include a theoretical expression for detection threshold snr and a theoretical curve of probability of detection versus snr for the technique all analysis results show good agreement with simulation results

the t k diagnosability for regular networks the t k diagnosis strategy can significantly enhance the system s self diagnosing capability at the expense of no more than k fault free processors vertices being mistakenly diagnosed as faulty under the pmc model it is a generalization of the precise and pessimistic diagnosis strategies of system level diagnosis on multiprocessor systems it can detect up to t faulty processors vertices which might include at most k misdiagnosed processors vertices where k is typically a small number in the case k ge 1 to our knowledge there is no known t k diagnosis algorithm for general regular networks in this paper we first propose a general t k diagnosis k ge 1 algorithm for some m regular networks these m regular networks satisfying some conditions could establish the t k diagnosis algorithm say t k g diag to determine the t k diagnosability the complexity of this algorithm is only o n log n when n ge 2 m or o nm when n where n is the number of vertices in the network second we present a complete proof that the network g is actually t k diagnosable finally we establish the t k diagnosability 1 le k le 3 of some regular networks including an n dimensional alternating group graph an n dimensional split star network a l n hypermesh and an n l star graph which are well known interconnection networks proposed for multiprocessor systems

the extra connectivity extra conditional diagnosability and t k diagnosability of the data center network dcell abstract connectivity and diagnosability are two important metrics in evaluating the fault tolerability of a network the g extra connectivity and the g extra conditional diagnosability are both defined under the restraint that every component of the network removing a faulty vertex set has at least g 1 fault free vertices the t k diagnosability is an outstanding diagnosis strategy in which the identified faulty vertex set is allowed to contain at most k fault free vertices as a well known model for a large scale data center network dcn with a server centric structure the m dimensional dcell with n port switches and t m n servers d m n has many desirable properties in this paper we first investigate the g extra connectivity of d m n for 0 g n 1 based on this we establish the g extra conditional diagnosability of d m n under the pmc model for 0 g n 1 finally we evaluate the t k diagnosability of d m n under the pmc model for 1 k n 1

the cramer rao bound on frequency estimates of signals closely spaced in frequency this paper examines the cramer rao cr lower bound on the variance of frequency estimates for the problem of n signals closely spaced in frequency the main results presented are simple analytic expressions for the cr bound in terms of the maximum frequency separation delta omega snr and the number of data vectors n that are valid for small delta omega the results are applicable to the conditional deterministic signal model the results show that the cr bound on frequency estimates is proportional to delta omega sup 2 n 1 n snr therefore the bound increases rapidly as the signal separation is reduced examples indicate that the expressions closely approximate the exact cr bounds whenever the signal separation is smaller than one resolution cell based upon the results it is argued that the threshold snr at which an unbiased estimator can resolve n closely spaced signals is at least proportional to delta omega sup 2n n the results are quite general and apply to many different types of temporal and spatial sampling grids

a fast fault identification algorithm for bijective connection graphs using the pmc model diagnosis of reliability is an important topic for interconnection networks under the classical pmc model dahura and masson 5 proposed a polynomial time algorithm with time complexity o n 2 5 to identify all faulty nodes in an n node network this paper addresses the fault diagnosis of so called bijective connection bc graphs including hypercubes twisted cubes locally twisted cubes crossed cubes and mobius cubes utilizing a helpful structure proposed by hsu and tan 20 that was called the extending star by lin et al 24 and noting the existence of a structured hamiltonian path within any bc graph we present a fast diagnostic algorithm to identify all faulty nodes in o n time where n 2 n n 4 stands for the total number of nodes in the n dimensional bc graph as a result this algorithm is significantly superior to dahura masson s algorithm when applied to bc graphs

on diagnosability of large fault sets in regular topology based computer systems the classical diagnosability approach has its limitation when dealing with large fault sets in large multiprocessor systems this is due to limited diagnosability of large multiprocessor systems connected using regular interconnection structures we propose an alternative approach to system diagnosis by allowing a few upper bounded number of units to be diagnosed incorrectly this measure is called t k diagnosability using this new measure it is possible to increase the degree of diagnosability of large system considerably the t k diagnosis guarantees that all the faulty units processors in a system are detected provided the number of faulty units does not exceed t while at most k units are incorrectly diagnosed we provide necessary and sufficient conditions for t k diagnosability and discuss their implication to demonstrate the power of this approach we analyze the diagnosability of large systems connected as hypercube star graph and meshes it is shown that a substantial increase in the degree of diagnosability of these structures is achieved compared with the degree of diagnosability achieved using the classic diagnosability approach at the cost of a comparably small number of incorrectly diagnosed units

a lower bound on the size of k neighborhood in generalized cubes abstract the determination of the minimum size of a k neighborhood i e a neighborhood of a set of k nodes in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems the generalized cubes include the hypercube and most hypercube variants as special cases in this paper we present a lower bound on the size of a k neighborhood in n dimensional generalized cubes where 2 n 1 k 3 n 2 this lower bound is tight in that it is met by the n dimensional hypercube our result is an extension of two previously known results

remarks on certain criteria for detection of number of signals in this paper we derive the asymptotic distribution of the logarithm of the likelihood ratio statistic for testing the hypothesis that the number of signals is equal to q against the alternative that it is equal to k specified for a special case this distribution is not chi square the above statistic also rises in studying consistency property of the mdl criterion and aic for detection of the number of signals

quantification of the difference between detection and resolution thresholds for multiple closely spaced emitters the problem of estimating the parameters of multiple signals closely spaced in either space or frequency has been much researched because it is a difficult case for modern spectral analysis techniques based on empirical evidence it has been noted by others that signal to noise ratio snr detection thresholds typically are lower than resolution thresholds that is one can detect the occurrence of n closely spaced signals at snrs lower than those at which one can resolve the signals and reliably estimate their parameters the difference between detection and resolution thresholds is quantified for the direction finding problem in which source locations are specified by a single angular coordinate e g azimuth

complex polynomial phase integration a previously published integration algorithm applicable to the numerical computation of integrals with rapidly oscillating integrands is generalized the previous algorithm involved quadratic approximation of the phase function which was assumed to be real the present generalization concerns approximation of a complex phase function by a polynomial of arbitrary degree as before the integrand is then written without approximation as a slowly varying function multiplied by the polynomial phase exponential and the slowly varying factor is approximated by a finite sum of chebyshev polynomials the integral is thus expressed as a sum of constituent integrals which are computed recursively via lu decomposition applied to a system of linear equations with a banded coefficients matrix examples are presented comparing various degree phase approximants

reduced rank processing for oversampled arrays in this paper we study array processing techniques for oversampled passive arrays oversampling occurs when an array contains sensors that are closely spaced relative to the operational wavelength or when the sources are known a priori to be confined to a limited angular range we examine here the application of the recently introduced reduced rank processing rrp approach to several widely used array processing methods for source detection and bearing estimation such as maximum likelihood and music and show how when an array is oversampled rrp can be used to reduce their computational load furthermore we use asymptotic performance analysis to show that rrp for oversampled arrays can significantly enhance the performance of signal subspace based methods

source enumeration for high resolution array processing using improved gerschgorin radii without eigendecomposition accurate detection of sources with low complexity is of considerable interest in practical applications of high resolution array processing this paper addresses a new computationally efficient method for source enumeration by using enhanced gerschgorin radii without eigendecompositofion the proposed method can calculate the gerschgorin radii in a more efficient manner in which the additive background noise can be efficiently suppressed and the computational complexity can be considerably reduced therefore the method is more accurate and computationally attractive furthermore the method does not rely on the eigenvalues of a covariance matrix or the signal noise power making it robust against deviations from the assumption of spatially white noise model numerical results are presented to demonstrate the performance of the method

on the t k diagnosability of bc networks to increase the degree of the diagnosability of a system under system level diagnosis strategies somani and peleg introduced a measure so called t k diagnosis strategy in which the identified fault set is allowed to contain at most k fault free processors using this diagnosis strategy the degree of diagnosability of the bc graphs include hypercubes crossed cubes mobius cubes and twisted cubes etc as the subfamily increases greatly as the number of the fault free processors in the fault set increases for 1 5 and n 1

on the performance of signal subspace processing part i narrow band systems this paper presents an analytical evaluation of detection determination of the number of sources and estimation performances of narrow band signal subspace processing for multiple source direction finding the probabilities of underestimating and overestimating the number of sources are derived under asymptotic conditions and around the threshold regions in terms of the choice of a penalty function and signal noise and array parameters for the cases of at most two closely spaced sources in the spatially white noise a scalar measure is introduced for the evaluation of the quality of the estimated signal subspace based on the statistics of this measure performance thresholds are demonstrated for the signal to noise ratio angle separation and correlation between two equipowered sources

eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency the eigenstructures of common covariance matrices are identified for the general case of m closely spaced signals it is shown that the largest signal space eigenvalue is relatively insensitive to signal separation by contrast the ith largest eigenvalue is proportional to delta omega sup 2 i 1 or delta omega sup 4 i 1 where delta omega is a measure of signal separation therefore matrix conditioning degrades rapidly as signal separation is reduced it is also shown that the limiting eigenvectors have remarkably simple structures the results are very general and apply to planar far field direction finding problems involving almost arbitrary scenarios and also to time series analysis of sinusoids exponentials and other signals

efficient unicast in bijective connection networks with the restricted faulty node set the connectivity is an important criteria to measure the fault tolerant performance of a graph however the connectivity based on the condition of the set of arbitrary faulty nodes is generally lower in this paper in order to heighten this measure we introduce the restricted connectivity into bijective connection networks first we prove that the probability that all the neighbors of an arbitrary node becomes faulty in any n dimensional bijective connection network x n is very low when n becomes sufficient large then we give a constructive proof that under the condition that each node of an n dimensional bijective connection network x n has at least one fault free neighbor its restricted connectivity is 2n 2 about half of the connectivity of x n finally by our constructive proof we give an o n algorithm to get a reliable path of length at most n 3 log 2 f 1 between any two fault free nodes in an n dimensional bijective connection network in particular since the family of bc networks contains hypercubes crossed cubes mobius cubes etc our algorithm is appropriate for these cubes

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

correction to a new integration algorithm and its application to the analysis of symmetrical cassegrain microwave antennas an efficient numerical algorithm for physical optics po analysis of reflectors is presented cylindrical symmetry of the reflector is not essential but is assumed for purposes of illustration and this leads to the use of fourier representation in the azimuthal variable the algorithm is based on quadratic approximation of the phase and polynomial approximation of the remaining portion of the integrand the necessary integrals are generated recursively and they involve the fresnel integral additional efficiency is achieved by means of an interpolation scheme therein one interpolates all but the rapidly varying edge diffraction contribution to the integral and then adds the explicitly calculated edge contribution at each far field point a few illustrative examples are included

statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing the performances of the akaike 1974 information criterion and the minimum descriptive length criterion methods are examined the events which lead to erroneous decisions are considered and on the basis of these events the probabilities of error for the two criteria are derived the probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated hermitian matrix it is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation although the derivation of the probabilities of error is based on an asymptotic analysis the results are confirmed to be in very close agreement with computer simulation results

quadratic phase integration using a chebyshev expansion an integration algorithm is described which is particularly effective in the numerical treatment of integrands having rapidly varying phase and slowly varying amplitude the algorithm involves approximating the phase function by a quadratic polynomial and rewriting the integrand without approximation as a slowly varying function multiplied by this quadratic phase exponential the slowly varying function is then approximated by chebyshev expansion and the desired integral is thus expressed as a sum of constituent integrals with integrands containing a chebyshev polynomial multiplied by the quadratic phase factor these constituent integrals are computed by means of lu decomposition applied to a system of linear equations with a banded coefficients matrix example results are presented indicating that a substantial reduction in computation time may be realized by means of this approach

the g extra connectivity and diagnosability of crossed cubes abstract connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network g in 1996 fabrega and fiol proposed the g extra connectivity of g in 2016 zhang et al proposed the g extra diagnosability of g that requires every component of g s has at least g 1 vertices the g extra connectivity of g is necessary for g extra diagnosability of g in this paper we show that the g extra connectivity of the crossed cube cq n is n g 1 1 2 g g 3 for n 5 0 g n 2 and the g extra diagnosability of cq n is n 1 2 g g 1 under the pmc model for n 5 0 g n 2 and the mm model for n 7 0 g n 2

an efficient fault tolerant routing algorithm in bijective connection networks with restricted faulty edges in this paper we study fault tolerant routing in bijective connection networks with restricted faulty edges first we prove that the probability that all the incident edges of an arbitrary node become faulty in an n dimensional bijective connection network denoted by x n is extremely low when n becomes sufficient large then we give an o n algorithm to find a fault free path of length at most email protected log 2 f 1 between any two different nodes in x n if each node of x n has at least one fault free incident edge and the number of faulty edges is not more than 2n 3 in fact we also for the first time provide an upper bound of the fault diameter of all the bijective connection networks with the restricted faulty edges since the family of bc networks contains hypercubes crossed cubes mobius cubes etc all the results are appropriate for these cubes

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

reflector antenna fields an exact aperture like approach a new computational approach is presented which allows fast analysis of radiation from large reflector antennas for an aperture a fourier transform ft relationship does exist between far field and aperture distribution accordingly the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe shannon whittaker theorem applied at nyquist rate the finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a ft in order to overcome this difficulty a new pseudosampling expansion which explicitly takes into account the extra factor is developed for parabolic reflector the sampling functions are related to the fresnel integrals and the far field can be exactly reconstructed in terms of aperture far field samples which can be computed using the fast fourier transform fft numerical computations and error analysis show the excellent performance of the method which can be generalized to deal with arbitrary reflector surfaces and near field evaluation

svd based information theoretic criteria for detection of the number of damped undamped sinusoids and their performance analysis following the information theoretic approach to model selection the authors develop criteria for detection of the number of damped undamped sinusoids these criteria are matched to the singular value decomposition svd based methods such as modified forward backward and forward backward linear prediction so well that the extra computations needed over and above those required for computing the svd are marginal next an analytical framework for analyzing the performance of these criteria is developed in the development of the analysis some approximations which become better for large signal to noise ratio are made simulations are used to verify the usefulness of the analysis and to compare the performance of the method with that of j j fuchs 1988

simplified technique for evaluating the radiation integrals a simplified numerical method is described for computing the radiation integral of a reflector antenna which is associated with either the aperture field method afm or the induced current method icm the method involves linear approximation of the phase function and absorption of the approximation error into amplitude function then the integrand is rewritten as a slowly varying function multiplied by the phase exponential the slowly varying function is expanded in terms of a polynomial for the radial direction and trigonometric functions for the circumferential direction expansion coefficients are determined by matching at points on the aperture the matching points are chosen in a manner similar to that of a two dimensional numerical integration scheme

reliability evaluation of bc networks in terms of the extra vertex and edge connectivity reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems the extra connectivity and the extra edge connectivity are two important parameters for the reliability evaluation of interconnection networks the mbi n dimensional bijective connection network in brief bc network includes several well known network models such as hypercubes mobius cubes crossed cubes and twisted cubes in this paper we explore the extra connectivity and the extra edge connectivity of bc networks and discuss the structure of bc networks with many faults we obtain a sharp lower bound of g extra edge connectivity of an mbi n dimensional bc network for n geq 4 and 1 leq g leq 2 n over 2 we also obtain a sharp lower bound of g extra connectivity of an n dimensional bc network for n geq 4 and 1 leq g leq 2 n which improves the result in reliability evaluation of bc networks ieee trans computers doi 10 1109 tc 2012 106 for 1 leq g leq n 3 furthermore we give a remark about exploring the g extra edge connectivity of bc networks for the more general mbi g and we also characterize the structure of bc networks with many faulty nodes or links as an application we obtain several results on the mbi g extra edge connectivity and the structure of faulty networks on hypercubes mobius cubes crossed cubes and twisted cubes