determination of number of sources with multiple arrays in correlated noise fields a detection scheme for signals in a noise field is considered the information theoretic criterion is derived and it gives a consistent estimation of the number of signals comparison of this multiarray estimation and those of the two array systems is given through simulations

the twisted xxz chain at roots of unity revisited the twisted xxz chain alias the six vertex model is investigated at roots of unity it is shown that when the twist parameter is chosen to depend on the total spin an infinite dimensional non abelian symmetry algebra can be explicitly constructed in all spin sectors this symmetry algebra can be identified with the upper or lower borel subalgebra of the sl2 loop algebra the proof uses only the intertwining property of the six vertex monodromy matrix and the familiar relations of the six vertex yang baxter algebra

algebraic tensegrity form finding abstract this paper concerns the form finding problem for general and symmetric tensegrity structures with shape constraints a number of different geometries are treated and several fundamental properties of tensegrity structures are identified that simplify the form finding problem the concept of a tensegrity invariance similarity transformation is defined and it is shown that tensegrity equilibrium is preserved under affine node position transformations this result provides the basis for a new tensegrity form finding tool the generality of the problem formulation makes it suitable for the automated generation of the equations and their derivatives state of the art numerical algorithms are applied to solve several example problems examples are given for tensegrity plates shell class symmetric tensegrity structures and structures generated by applying similarity transformation

multiantenna glr detection of rank one signals with known power spectrum in white noise with unknown spatial correlation multiple antenna detection of a gaussian signal with spatial rank one in temporally white gaussian noise with arbitrary and unknown spatial covariance is considered this is motivated by spectrum sensing problems in the context of dynamic spectrum access in which several secondary networks coexist but do not cooperate creating a background of spatially correlated broadband interference when the temporal correlation of the signal of interest is assumed known up to a scale factor the corresponding generalized likelihood ratio test is shown to yield a scalar optimization problem closed form expressions of the test are obtained for the general signal spectrum case in the low signal to noise ratio snr regime as well as for signals with binary valued power spectrum in arbitrary snr the two resulting detectors turn out to be equivalent an asymptotic approximation to the test distribution for the low snr regime is derived closely matching empirical results from spectrum sensing simulation experiments

on a nonparametric detection method for array signal processing in correlated noise fields the correct derivation of maximization of the likelihood function is presented and the correct form of information theoretic criteria itc for the determination of the number of signals in an unknown correlated noise field is shown the possible pitfalls of using itc under the circumstances are briefly considered

a monte carlo form finding method for large scale regular and irregular tensegrity structures we propose a monte carlo form finding method that employs a stochastic procedure to determine equilibrium configurations of a tensegrity structure this method does not involve complicated matrix operations or symmetry analysis works for arbitrary initial configurations and can handle large scale regular or irregular tensegrity structures with or without material geometrical constraints

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

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

matrix analysis of statically and kinematically indeterminate frameworks abstract the paper is concerned with the structural mechanics of assemblies of bars and pinjoints particularly where they are simultaneously statically and kinematically indeterminate the physical significance of the four linear algebraic vector subspaces of the equilibrium matrix is examined and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces in particular this algorithm gives full details of any states of self stress and modes of inextensional deformation which an assembly may possess a scheme is devised for the segregation of inextensional modes into rigid body modes up to six of these may be allowed by the foundation constraints and internal mechanisms in some circumstances a state of self stress may impart first order stiffness to an inextensional mode a matrix method for detecting this effect is devised and it is shown that if there is no state of self stress which imparts first order stiffness to a given mode then that mode can undergo rather large distortion which involves either zero change in length of the bars or possibly changes in length of third or higher order in the displacements the significance of negative stiffness as indicated by the matrix method is discussed the paper contains simple examples which illustrate all of the main points of the work

cyclic monodromy matrices for sl n trigonometric r matrices the algebra of monodromy matrices forsl n trigonometricr matrix is studied it is shown that a generic finite dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product ofl operators cocommutativity of representations is discussed and intertwiners for factorizable representations are written through the boltzmann weights of thesl n chiral potts model

a new aspect of representations of uq sl2 root of unity case abstract the structure of the tensor product representation v 1 x v 2 y of uq sl2 is investigated at roots of unity a polynomial identity is derived as an outcome also new bases of v 1 x v 2 y are established under certain conditions

t increasing paths on the bruhat graph of affine weyl groups are self avoiding abstract let w s be a coxeter system t wsw 1 s s w w its set of reflections any total reflection order and the undirected bruhat graph we consider the natural labeling of the edges of which assigns to the edge v w the reflection vw 1 a path on i e a sequence v 1 v k such that v i v 1 i 1 t for i 1 k 1 is called t increasing if v 1 v 1 2 v k 1 v 1 k t increasing paths play an important role in the computation of both the kazhdan lusztig and the r polynomials of w we prove that if w is finite or is an affine weyl group then any t increasing path is self avoiding i e it has no self intersection points

nilpotent orbits and commutative elements abstract let w be a simply laced coxeter group with generating set s and let w c denote the subset consisting of those elements whose reduced expressions have no substrings of the form sts for any non commuting s t s we give a root system characterization of w c and in the case where w corresponds to a finite weyl group show that w c is a union of spaltenstein springer steinberg cells the latter is valid also for affine weyl groups of type a but not for type d or e

convex orderings in affine root systems ii abstract this paper contains several results concerning convex orderings in root systems these results complete the analysis developed in earlier papers by the author we obtain in the finite case a combinatorial characterization of reflections longest elements in standard parabolic subgroups of the weyl group of the root system and of coxeter elements in the affine case a refinement of the main construction done earlier by the author j algebra 172 1995 613 623 is described moreover infinite periodic compatible sets are classified

the maximum cardinality of minimal inversion complete sets in finite reflection groups abstract we compute for reflection groups of type a b d f 4 h 3 and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect to this property we also provide lower bounds for the e types that we conjecture to be the exact value of our statistic

abelian ideals of borel subalgebras and affine weyl groups abstract this paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a borel subalgebra our main result is a nice uniform formula for the dimension of maximal ideals in these posets we also obtain results on ad nilpotent ideals which complete the analysis started in j algebra 225 2000 130 258 2002 112

evaluation representations of quantum affine algebras at roots of unity the purpose of this paper is to compute the drinfel d polynomials for two types of evaluation representations of quantum affine algebras at roots of unity and construct those representations as the submodules of evaluation schnizer modules moreover we obtain the necessary and sufficient condition for that the two types of evaluation representations are isomorphic to each other

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

symmetric prismatic tensegrity structures part i configuration and stability this paper presents a simple and efficient method to determine the self equilibrated configurations of prismatic tensegrity structures nodes and members of which have dihedral symmetry it is demonstrated that stability of this class of structures is not only directly related to the connectivity of members but is also sensitive to their geometry height radius ratio and is also dependent on the level of self stress and stiffness of members a catalogue of the structures with relatively small number of members is presented based on the stability investigations

twisted filtrations of soergel bimodules and linear rouquier complexes abstract we consider twisted standard filtrations of soergel bimodules associated to arbitrary coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the hecke algebra this corresponds to the positivity of the polynomials occurring when expressing an element of the canonical basis in a generalized standard basis twisted by a biclosed set of roots in the sense of dyer and comes as a corollary of soergel s conjecture we then show the positivity of the corresponding inverse polynomials in the case where the biclosed set is an inversion set of an element or its complement by generalizing a result of elias and williamson on the linearity of the rouquier complexes associated to lifts of these basis elements in the artin tits group these lifts turn out to be generalizations of mikado braids as introduced in a joint work with digne this second positivity property generalizes a result of dyer and lehrer from finite to arbitrary coxeter groups

topology design of tensegrity structures via mixed integer programming this paper presents a numerical method for finding a tensegrity structure based on the ground structure method we first solve a mixed integer programming mip problem which maximizes the number of struts over the self equilibrium condition of axial forces and the discontinuity condition of struts subsequently we solve the minimization problem of the number of cables in order to remove redundant self equilibrium modes which is also formulated as an mip it is regarded to be advantageous that our method does not require any connectivity information of cables and struts to be known in advance while the obtained tensegrity structure is guaranteed to satisfy the discontinuity condition of struts rigorously

finite dimensional representations of quantum affine algebras at roots of unity we describe explicitly the canonical map x spec ue b spec ze where u b is a quantum loop algebra at an odd root of unity e here ze is the center of ue g and spec r stands for the set of all finite dimensional irreducible representations of an algebra r we show that spec z is a poisson proalgebraic group which is essentially the group of points of g over the regular adeles concentrated at 0 and oo our main result is that the image under x of spec u b is the subgroup of principal adeles department of mathematics harvard university cambridge massachusetts 02138 e mail address beckfmath harvard edu department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address kacimath mit edu this content downloaded from 207 46 13 124 on wed 22 jun 2016 06 11 29 utc all use subject to http about jstor org terms

infinite reduced words lattice property and braid graph of affine weyl groups abstract in this paper we establish a bijection between the infinite reduced words of an affine weyl group and certain biclosed sets of its positive system and determine all finitely generated biclosed sets in the positive system of an affine weyl group using these results we show firstly that the biclosed sets in the standard positive system of rank 3 affine weyl groups when ordered by inclusion form a complete algebraic ortholattice and secondly that the generalized braid graphs of those coxeter groups are connected which can be thought of as an infinite version of tit s solution to the word problem

information theoretic criteria for the determination of the number of signals in spatially correlated noise the problem of determining the number of signals in high resolution array processing when the noise is spatially correlated having an unknown covariance matrix is examined by considering a model in which two sensor arrays are well separated such that their noise outputs are uncorrelated the authors develop a likelihood function whose maximum can be expressed in a very simple form involving the canonical correlation coefficients this likelihood function and a choice of penalty functions constitute a number of new information theoretic criteria suitable for the determination of the number of signals in an unknown correlated noise environment furthermore it is demonstrated that the new criteria are applicable in the case when only one sensor array is available

on the combinatorics of b b orbits on group compactifications abstract it is shown that there is an order isomorphism from the poset v of b b orbits on the wonderful compactification of a semi simple adjoint group g with weyl group w to an interval in reverse chevalley bruhat order on a non canonically associated coxeter group w in general neither finite nor affine moreover preserves the corresponding kazhdan lusztig polynomials springer s partly conjectural construction of kazhdan lusztig polynomials for the analogues of v for general coxeter groups w is completed by reducing it by a similar order isomorphism to known results involving a twisted chevalley bruhat order on w

ad nilpotent ideals of a borel subalgebra ii we provide an explicit bijection between the ad nilpotent ideals of a borel subalgebra of a simple lie algebra g and the orbits of q h 1 q under the weyl group q being the coroot lattice and h the coxeter number of g from this result we deduce in a uniform way a counting formula for the ad nilpotent ideals

on the singularities of a constrained incompressible like tensegrity cytoskeleton model under equitriaxial loading singularity theory is applied for the study of the characteristic three dimensional tensegrity cytoskeleton model after adopting an incompressibility constraint the model comprises six elastic bars interconnected with 24 elastic string members previous studies have already been performed on non constrained systems however the present one allows for general non symmetric equilibrium configurations critical conditions for branching of the equilibrium are derived and post critical behaviour is discussed classification of the simple and compound singularities of the total potential energy function is effected the theory is implemented into the cusp catastrophe for the case of one dimensional branching of the buckling allowed tensegrity model and an elliptic umbilic singularity for compound branching of a rigid bar model it is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints

dual affine quantum groups let hat mathfrak g be an untwisted affine kac moody algebra with its sklyanin drinfel d structure of lie bialgebra and let hat mathfrak h be the dual lie bialgebra by dualizing the quantum double construction via formal hopf algebras we construct a new quantum group u q hat mathfrak h dual of u q hat mathfrak g studying its specializations at roots of 1 in particular its semi classical limits we prove that it yields quantizations of hat mathfrak g and widehat g infty the formal poisson group attached to hat mathfrak g and we construct new quantum frobenius morphisms the whole picture extends to the untwisted affine case the results known for quantum groups of finite type

geometry of the analytic loop group abstract we introduce and study a notion of analytic loop group with a riemann hilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity u g with non trivial central charge we introduce a poisson structure and study properties of its poisson dual group we prove that the hopf poisson structure is isomorphic to the semi classical limit of the center of u g it is a geometric realization of the center then the symplectic leaves and corresponding equivalence classes of central characters of u g are parameterized by certain g bundles on an elliptic curve

un music and un cle an application of generalized correlation analysis to the estimation of the direction of arrival of signals in unknown correlated noise a new approach is proposed for the consistent estimation of the directions of arrival doa of signals in an unknown spatially correlated noise environment the signal and noise model used is based on the assumption that the data are received by two arrays well separated so that their noise outputs are uncorrelated the generalized correlation decomposition of the cross correlation matrix between the two arrays is then introduced of particular interest is the canonical correlation decomposition the analysis of the generalized correlation leads to various interesting geometric and asymptotic properties of the eigenspace structure two algorithms un music and un cle are developed to estimate the doa of signals in unknown spatially correlated noise based on the utilization of these properties computer simulations show that these methods are superior in performance compared to conventional methods furthermore it is demonstrated that the new methods are equally effective even when only one sensor array is employed

equilibrium conditions of a tensegrity structure this paper characterizes the necessary and sufficient conditions for tensegrity equilibria static models of tensegrity structures are reduced to linear algebra problems after first characterizing the problem in a vector space where direction cosines are not needed this is possible by describing the components of all member vectors while our approach enlarges by a factor of 3 the vector space required to describe the problem the advantage of enlarging the vector space makes the mathematical structure of the problem amenable to linear algebra treatment using the linear algebraic techniques many variables are eliminated from the final existence equations

constructing tensegrity structures from one bar elementary cells this study aimed to develop a method to construct tensegrity structures from elementary cells defined as structures consisting of only one bar connected with a few strings comparison of various elementary cells leads to the further selection of the so called z shaped cell which contains one bar and three interconnected strings as the elementary module to assemble the z based spatial tensegrity structures the graph theory is utilized to analyse the topology of strings required to construct this type of tensegrity structures it is shown that a string net can be used to construct a z based tensegrity structure if and only if its topology is a simple and bridgeless cubic graph once the topology of strings has been determined one can easily design the associated tensegrity structure by adding a deterministic number of bars two schemes are suggested for this design strategy one is to enumerate all possible topologies of z based tensegrity for a specified number of bars or cells and the other is to determine the tensegrity structure from a vertex truncated polyhedron the method developed in this paper allows us to construct various types of novel tensegrity structures

auxiliary matrices for the six vertex model at qn 1 and a geometric interpretation of its symmetries the construction of auxiliary matrices for the six vertex model at a root of unity is investigated from a quantum group theoretic point of view employing the concept of intertwiners associated with the quantum loop algebra uq 2 at qn 1 a three parameter family of auxiliary matrices is constructed the elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the bethe ansatz equations this functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters because of this dependence on additional parameters the auxiliary matrices break in general the finite symmetries of the six vertex model such as spin reversal or spin conservation more importantly they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values the extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged centre z of the algebra uq 2 at qn 1 this connection provides a geometric interpretation of the enhanced symmetry of the six vertex model at rational coupling the parameters labelling the auxiliary matrices can be interpreted as coordinates on a hypersurface spec z 4 which remains invariant under the action of an infinite dimensional group g of analytic transformations called the quantum coadjoint action

on the universalr matrix of u_q widehat sl _2 at roots of unityat roots of unity we show that the action of the universalr matrix of the affine u q widehat sl 2 quantum algebra whenq is a root of unity can be renormalized by some scalar factor to give a well defined nonsingular expression satisfying the yang baxter equation it can be reduced to intertwining operators of representations corresponding to chiral potts if the parameters of these representations lie on the well known algebraic curve

the structure of total reflection orders in affine root systems abstract we analyze the structure of total reflection orders in affine root systems we obtain a complete characterization of the finite sections of these orders

optimal utilization of signal free samples for array processing in unknown colored noise fields many algorithms for direction of arrival doa estimation require the noise covariance matrix to be known or to possess a known structure in many cases the noise covariance is in fact estimated from separate measurements this paper addresses the combined effects of finite sample sizes both in the estimated noise covariance matrix and in the data with signals present it is assumed that a batch of signal free samples is available in addition to the signal containing samples no assumption is made on the structure of the noise covariance in this paper the asymptotic covariance of the weighted subspace fitting wsf algorithm is derived for the case in which the data are whitened using an estimated noise covariance the expression obtained suggests an optimal weighting that improves performance compared to the standard choice in addition a new method based on covariance matching is proposed both methods are asymptotically statistically efficient the cramer rao lower bound crb on the covariance of the estimate for the data model is also derived monte carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results

representations of ueres sl2 via restricted q fock spaces two restricted c q q 1 forms of the well known q boson algebra are introduced and the corresponding restricted q fock spaces defined all of the irreducible highest weight representations including the infinite dimensional ones of ueres sl2 of type 1 are constructed through the restricted q fock spaces

the prestressability problem of tensegrity structures some analytical solutions in this paper we formulate the general prestressability conditions for tensegrity structures these conditions are expressed as a set of nonlinear equations and inequalities on the tendon tensions several examples of tensegrity structures for which the prestressability conditions can be analytically solved are then presented

static and dynamic characterization of regular truncated icosahedral and dodecahedral tensegrity modules static and dynamic properties of a pair of dual spherical tensegrity modules invented by buckminster fuller are investigated they are regular truncated icosahedral and dodecahedral tensegrity modules the computation of the maxwell number and the use of calladine s relation reveal that regular truncated icosahedral and dodecahedral tensegrity modules possess 55 infinitesimal mechanism modes a reduced equilibrium matrix is presented for the initial shape finding to economically impose the existence of a pre stress mode both the initial shape and the corresponding pre stress mode are analytically obtained by using graphs of the icosahedral group and the reduced equilibrium matrix for both icosahedral and dodecahedral modules the maximum values of the cable tension is always less than the absolute value of bar compression in order to classify a large number of infinitesimal mechanism modes modal analyses are conducted infinitesimal mechanism modes have the stiffness due to pre stress and are associated with lowest natural frequencies their natural frequencies increase proportionally to the square root of the amplitude of pre stress it is found that there are only 15 distinct natural frequencies associated with the infinitesimal mechanism modes

on demazure polynomials abstract the dimension of the demazure module e w for an affine kac moody algebra is a polynomial in called a demazure polynomial in this article we prove that it is harmonic for the algebra sl n we define a subset e of w of non null density we calculate explicitly all the demazure polynomials for this subset

minimal inversion complete sets and maximal abelian ideals abstract let g be a simple lie algebra b a fixed borel subalgebra and w the weyl group of g in this article we study a relationship between the maximal abelian ideals of b and the minimal inversion complete sets of w the latter have been recently defined by malvenuto et al 2015 10

on determination of the number of signals in spatially correlated noise a method for determining the number of signals in a correlated noise field using two well separated linear arrays of receivers was given by zhang and wong 1993 in this paper we improve on this method with the use of new penalty functions three criteria are given and it is proved that for a large class of penalty functions the probability of incorrect detections by each of the new criteria is exponentially decreasing when the moment generating function of the squared euclidean norm of the observation vector is finite at some point it is also proved that with these new criteria the estimates of the number of signals are strongly consistent randomized penalty functions for the three criteria based on samples are presented and their uses are then shown to give consistent estimation of the number of signals the finite sample behavior of the proposed approaches are studied by monte carte simulation

maximum likelihood parameter and rank estimation in reduced rank multivariate linear regressions this paper considers the problem of maximum likelihood ml estimation for reduced rank linear regression equations with noise of arbitrary covariance the rank reduced matrix of regression coefficients is parameterized as the product of two full rank factor matrices this parameterization is essentially constraint free but it is not unique which renders the associated ml estimation problem rather nonstandard nevertheless the problem turns out to be tractable and the following results are obtained an explicit expression is derived for the ml estimate of the regression matrix in terms of the data covariances and their eigenelements furthermore a detailed analysis of the statistical properties of the ml parameter estimate is performed additionally a generalized likelihood ratio test glrt is proposed for estimating the rank of the regression matrix the paper also presents the results of some simulation exercises which lend empirical support to the theoretical findings

optimization of tensegrity structures this paper concerns the design of tensegrity structures with optimal mass to stiffness ratio starting from an initial layout that defines the largest set of allowed element connections the procedure seeks the topology geometry and prestress of the structure that yields optimal designs for different loading scenarios the design constraints include strength constraints for all elements of the structure buckling constraints for bars and shape constraints the problem formulation accommodates different symmetry constraints for structure parameters and shape the static response of the structure is computed by using the nonlinear large displacement model the problem is cast in the form of a nonlinear program examples show layouts of 2d and 3d asymmetric and symmetric structures the influence of the material parameters on the optimal shape of the structure is investigated

some remarkable degenerations of quantum groups we show that an irreducible representation of a quantized enveloping algebraue at a lth root of 1 has maximal dimension l n if the corresponding symplectic leaf has maximal dimension 2n the method of the proof consists of a construction of a sequence of degenerations ofue the last one being aq commutative algebrau e 2n this allows us to reduce many problems concerningue to that concerningu e 2n

the q characters at roots of unity abstract we consider various specializations of the untwisted quantum affine algebras at roots of unity we define and study the q characters of their finite dimensional representations

quantum superalgebras at roots of unity and non abelian symmetries of integrable models we consider integrable vertex models whose boltzmann weights r matrices are trigonometric solutions to the graded yang baxter equation as is well known the latter can be generically constructed from quantum affine superalgebras uq these algebras do not form a symmetry algebra of the model for generic values of the deformation parameter q when periodic boundary conditions are imposed if q is evaluated at a root of unity we demonstrate that in certain commensurate sectors one can construct non abelian subalgebras which are translation invariant and commute with the transfer matrix and therefore with all charges of the model in the line of argument we introduce the restricted quantum superalgebra uresq and investigate its root of unity limit we prove several new formulae involving supercommutators of arbitrary powers of the chevalley serre generators and derive higher order quantum serre relations as well as an analogue of lustzig s quantum frobenius theorem for superalgebras

passive detection of correlated subspace signals in two mimo channels in this paper we consider a two channel multiple input multiple output passive detection problem in which there is a surveillance array and a reference array the reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension but unknown basis the question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension but unknown basis which is correlated with the subspace signal in the reference channel we consider a second order detection problem where these subspace signals are structured by an unknown but common p dimensional random vector of symbols transmitted from sources of opportunity and then received through unknown m times p matrices at each of the m element arrays the noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances we provide a unified framework to derive the generalized likelihood ratio test for these different noise models in the most general case of arbitrary noise covariance matrices the test statistic is a monotone function of canonical correlations between the reference and surveillance channels