bayesian beamforming for doa uncertainty theory and implementation a bayesian approach to adaptive narrowband beamforming for uncertain source direction of arrival doa is presented the doa is modeled as a random variable with prior statistics that describe its level of uncertainty the bayesian beamformer is the corresponding minimum mean square error mmse estimator which can be viewed as a mixture of directional beamformers combined according to the posterior distribution of the doa given the data under a deterministic doa the mean square error mse of the bayesian beamformer becomes as low as that of the directional beamformer equipped with the doa candidate in the prior set that is the closest to the true doa at exponential rate where closeness is defined in the kullback leibler sense two efficient algorithms using a uniform linear array ula are presented the first method utilizes the efficiency of the fast fourier transform fft to compute the posterior distribution on a large number of doa candidates the second method approximates the posterior distribution by a gaussian distribution which leads to a directional beamformer incorporated with a particular spreading matrix and an adjusted doa numerical simulations show that the proposed beamformer outperforms other related blind or robust beamforming algorithms over a wide range of signal to noise ratios snrs

categorifications and cyclotomic rational double affine hecke algebras varagnolo and vasserot conjectured an equivalence between the category mathcal o for crdaha s and a subcategory of an affine parabolic category o of type a we prove this conjecture as applications we prove a conjecture of rouquier on the dimension of simple modules of crdaha s and a conjecture of chuang miyachi on the koszul duality for the category mathcal o of crdaha s

quasidiagonal morphisms and homotopy abstract adapting certain methods of voiculescu we show that the quasidiagonality of c algebras is invariant under completely positive deformations coming from asymptotic morphisms we define a notion of quasidiagonal morphism the quasidiagonality of morphisms from exact separable c algebras is shown to be invariant under completely positive deformations

stability of group relations under small hilbert schmidt perturbations abstract if matrices almost satisfying a group relation are close to matrices exactly satisfying the relation then we say that a group is matricially stable here almost and close are in terms of the hilbert schmidt norm using tracial 2 norm on i i 1 factors we similarly define i i 1 factor stability for groups our main result is that all 1 relator groups with non trivial center are i i 1 factor stable many of them are also matricially stable and rfd for amenable groups we give a complete characterization of matricial stability in terms of the following approximation property for characters each character must be a pointwise limit of traces of finite dimensional representations this allows us to prove matricial stability for the discrete heisenberg group h 3 and for all virtually abelian groups for non amenable groups the same approximation property is a necessary condition for being matricially stable we study this approximation property and show that rf groups with character rigidity have it

projection decomposition in multiplier algebras in this paper we present new structural information about the multiplier algebra mathcal m mathcal a of a unital purely infinite simple c algebra mathcal a by characterizing the positive elements a in mathcal m mathcal a that are strict sums of projections belonging to mathcal a if a not in mathcal a and a itself is not a projection then the necessary and sufficient condition for a to be a strict sum of projections belonging to mathcal a is that a 1 and that the essential norm a ess geq 1 based on a generalization of the perera rordam weak divisibility of separable simple c algebras of real rank zero to all unital simple c algebras of real rank zero we show that every positive element of mathcal a with norm 1 can be approximated by finite sums of projections based on block tri diagonal approximations we decompose any positive element a in mathcal m mathcal a with a 1 and a ess geq 1 into a strictly converging sum of positive elements in mathcal a with norm 1

extensions of c x by simple c algebras of real rank zero let ext c x a be the set of unitarily equivalence classes of essential c algebra exten sions of the following form 0 a e c x 0 where a is a nonunital separable simple c algebra of real rank zero stable rank one with unique normalized trace and x is a finite cw complex we show that there is a bijection ext c x a kk c x m a a where m a is the multiplier algebra of a in particular we determine when an extension is actually splitting we also in a more general setting give a condition when an essential extension is quasidiagonal 0 introduction we study essential extensions of the following form 0 a f c x 0 where a is a j unital nonunital simple c algebra of real rank zero and stable rank one and x is finite cw complex the brown douglas fillmore bdf theory bdf1 and bdf2 gives a classification of these extensions up to unitary equivalence in the case that a k the c algebra of compact operators on an infinite dimensional separable hubert space since then the theory of c algebra extensions developed rapidly it is very difficult to give a complete list we refer the reader to bl for references while using of theory ext c x a have been computed for the most interesting cases however ext c x a does not provide enough information in general to classify extensions up to unitary equivalence in fact as shown in ln6 and lnl2 there are usually many different unitary equivalence classes of trivial extensions and an extension r with r 0 in ext c x a may not be trivial we will only consider simple c algebras that share some properties with c we consider only those with real rank zero stable rank one and unique quasi trace up to scalar multiples there is an additional property that c has namely its corona algebra m k k the calkin algebra is simple we also as sume that m a a is simple it has been studied when a nonunital but cr unital simple c algebra a has the property that m a a is simple see lnl rrl and zh2 etc it is shown in lnl that a simple c algebra a has the property that m a a is simple if and only if a has continuous scale

theory and multipliers of stable algebras the main theorem is that if a is a c algebra with a countable approximate identity consisting of projections then the unitary group of m a k is contractible this gives a realization via the index map of ko a as components in the set of fredholm operators on ha for a c algebra a let ha ai i ai e a and eai ai converges in norm then ha becomes a right a module under the action ai b aib with the a valued inner product ai b1 ea bi ha is a hilbert a module y ha is the c algebra of operators on ha that have an adjoint k ha is an ideal of y ha called the compact operators on ha set 11 2 definition 4 operators in ha invertible modulo 3f ha are called fredholm and have an index that takes its values in ko a the paper is divided into two parts in part 1 we show that index a ko a is an isomorphism where t denotes the set of path components of the set of fredholm operators in part 2 we show that the unitary group of m a k is contractible when a has a countable approximate identity consisting of projections as 2 ha m a k this in particular implies that the unitary group of s ha is connected when a is unital this latter result is used to prove the isomorphism mentioned above the results of this paper were announced in 14 see remark 2 5 2 this research is based on the author s doctoral work done at dalhousie university under the supervision of professor p a fillmore the author also wishes to thank w j phillips for many useful suggestions part 1 the index of a fredholm operator 1 1 we describe the index map from fredholm operators on hilbert c modules to the corresponding k groups the principal ingredients of this construction have been discussed by several authors kasparov 12 miscenko and fomenko 15 and pimsner popa and voiculescu 17 however as we shall need refinements and variations of these constructions we will give a detailed account of the index map throughout this paper k or y h will denote the c algebra of compact operators on a separable infinite dimensional hilbert space h for any two c algebras a and b a b will denote the completion of the algebraic tensor product aob in the spatial or minimal c norm see e g effros and lance 8 2 received by the editors july 28 1983 and in revised form december 27 1985 1980 mathematics subject classification 1985 revision primary 46l05 46m20 01987 american mathematical society 0002 9947 87 1 00 25 per page

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

extensions of exchange rings we define non unital exchange rings and we prove that ifiis an ideal of a ringr thenris an exchange ring if and only ifiandr iare exchange rings and idempotents can be lifted moduloi we also show that we can replace the condition on liftability of idempotents with the condition that the canonical mapk0 r k0 r i be surjective

performance analysis of the minimum variance beamformer we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer the analysis is based on the assumption that the signals and noise are gaussian and that the number of samples is large compared to the array size and it yields an explicit expression for the sinr in terms of the different parameters affecting the performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between the desired signal and the interference array size and shape correlation between the desired signal and the interference and finite sample size

symmetries of the car algebra a automorphism of period two of the uhf c algebra of type 2 is constructed for which the fixed point algebra is not approximately finite dimensional the construction also yields a diagonal maximal commutative c subalgebra whose spectrum is not totally disconnected variations and consequences of the construction are discussed

an analogue of row removal for diagrammatic cherednik algebras we prove an analogue of james donkin row removal theorems for diagrammatic cherednik algebras this is one of the first results concerning the graded decomposition numbers of these algebras over fields of arbitrary characteristic as a special case our results yield a new reduction theorem for graded decomposition numbers and extension groups for cyclotomic q schur algebras

the generalized berg theorem and bdf theorem let a be a separable simple af algebra with finitely many extreme traces we give a necessary and sufficient condition for an essentially normal element x e m a i e ir x is normal r m a m a a is the quotient map having the form y a for some normal element y c m a and a e a we also show that a normal element x e m a can be quasidiagonalized if and only if the fredholm index ind a x 0 for all a 0 sp 7r x in the case that a is a simple c algebra of real rank zero with stable rank one and with continuous scale k1 a 0 and ko a has countable rank we show that a normal element x e m a with zero fredholm index can be written as

convergence analysis of finite alphabet beamformers for digital cochannel signals in this paper we examine the convergence behavior of finite alphabet fa beamformers the two most popular implementations of fa beamformers for digital communication signals are the iterative least squares with projection ilsp and the minimum mean square error mmse beamformer to facilitate the analysis for the binary communications case we derive closed form expressions for the mean weight vector signal to noise ratio and signal to interference ratio for both the ilsp and mmse beamformers in terms of the bit error rate ber performance at each iteration next we generalize the analysis for the m ary pulse amplitude modulation and m ary phase shift keying cases we show that both ilsp and mmse beamformers have previously unreported bias terms in the array response vectors which are functions of the ber for each iteration furthermore as the ber becomes arbitrarily small we show that our solutions converge to the well known asymptotic expressions widely published in the literature next we provide a geometric interpretation of the effects of the noise bias vector in terms of angles between subspaces based on our analysis we were able to develop necessary and sufficient conditions for convergence in the mean we conclude with monte carlo simulations to validate our analysis

weakly clean rings abstract we study the class of weakly clean rings which were introduced in 15 it is known that weakly clean rings are a subclass of exchange rings and that they contain clean rings as a proper subclass in this paper we prove that weakly clean rings also contain some other important examples of exchange rings such as regular rings and c algebras of real rank zero further we prove that many classes of weakly clean rings can be viewed as corners of clean rings this for example implies that every regular ring and every c algebra of real rank zero is a corner of a clean ring lastly we study the question when the ideal extension of weakly clean rings is weakly clean and we give an example of a non weakly clean exchange ring answering the question in 15

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

the corona algebra of the stabilized jiang su algebra abstract let z be the jiang su algebra and k the c algebra of compact operators on an infinite dimensional separable hilbert space we prove that the corona algebra m z k z k has real rank zero we actually prove a more general result

geodesics in the space of singular kahler potentials motivated by the results of b berndtsson in this memoir we use the new estimates developed by w he to extend a theorem of the second author on the existence of weak c 1 1 geodesics between two smooth non degenerate kahler potentials to the case where the metrics on the end points may have singularities on some analytic set and may be positive semi definite

approximations of c algebras and the ideal property we introduce several classes of c algebras using for this local approximations by nice c algebras that generalize the ah algebras among others we initiate their study proving mainly results about the ideal property but also about the ideals generated by their projections the real rank zero the weak projection property minimal tensor products extensions quasidiagonal extensions ideal structure the largest ideal with the ideal property and short exact sequences some of the previous results of the second named author are generalized 2007 elsevier inc all rights reserved

diagonality inc algebras soit a une c algebre et a sa les elements hermitiens soit i un ideal ferme separable dans une c algebre a et on suppose que les elements de a sa de spectres finis sont denses dans a sa si a a sa et e 0 alors il existe b a sa diagonal relativement a i et il existe x i sa tel que x e et a b x

performance analysis for finite sample mvdr beamformer with forward backward processing the employment of forward backward fb processing to both batch and adaptive beamformers provides a superior performance than the forward only fo algorithm based on the finite sample minimum variance distortionless response mvdr beamformer a set of closed form expressions for the variance of the weight vector the output signal to interference plus noise ratio sinr and the mean square error mse is derived for both fb and fo algorithms as shown in our analysis all errors of the fb algorithm are only approximately half of the fo case

corrigendum to classifying c algebras with both finite and infinite subquotients j funct anal 265 2013 449 468 abstract as recently pointed out by gabe a fundamental paper by elliott and kucerovsky concerning the absorption theory for c algebras contains an error and as a consequence we must report that lemma 4 5 in 3 is not true as stated in this corrigendum we prove an adjusted statement and explain why the error has no consequences to the main results of 3 in particular it is noted that all the authors claims concerning morita equivalence or stable isomorphism of graph c algebras remain correct as stated

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest diagonal loading is one of the most popular techniques to improve robustness in this paper we present a theoretical analysis of the signal to interference plus noise ratio sinr for the class of beamformers based on generalized i e not necessarily diagonal loading of the covariance matrix in the presence of random steering vector errors a closed form expression for the sinr is derived that is shown to accurately predict the sinr obtained in simulations this theoretical formula is valid for any loading matrix it provides insights into the influence of the loading matrix and can serve as a helpful guide to select it finally the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal sinr

approximating macroscopic observables in quantum spin systems with commuting matrices abstract macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements 1 2 n 1 j n n j a i n n i 1 m in a uhf algebra one of their properties is that they commute asymptotically as n goes to infinity it is not true that any given set of asymptotically commuting matrices can be approximated by commuting ones in the norm topology in this paper we show that for macroscopic observables this is true

on the structure of simple c algebras tensored with a uhf algebra ii let d be a simple unital c algebra let b be a uhf algebra and put a b d it is proved that if p q a are projections and p q for all quasitraces on a then p q in the sense of murray and von neumann a more general result involving positive operators in a is also proved if d has finitely many extremal quasi traces and the projections in d k separate these then it is proved that a has real rank zero finally it is proved that provided d is stably finite then each positive state on k0 d lifts to a quasi trace

abelian strict approximation in aw algebras and weyl von neumann type theorems in this paper for a c algebra a with m m a an aw algebra or equivalently for an essential norm closed two sided ideal a of an aw algebra m we investigate the strict approximability of the elements of m from commutative c subalgebras of a in the relevant case of the norm closed linear span a of all finite projections in a semi finite aw algebra m we shall give a complete description of the strict closure in m of any maximal abelian self adjoint subalgebra masa of a we shall see that the situation is completely different for discrete respectively continuous m in the discrete case for any masa c of a the strict closure of c is equal to the relative commutant c m while in the continuous case under certain conditions concerning the center valued quasitrace of the finite reduced algebras of m satisfied by all von neumann algebras c is already strictly closed thus in the continu ous case no elements of m which are not already belonging to a can be strictly approximated from commutative c subalgebras of a in spite of this pathology of the strict topology in the case of the norm closed linear span of all finite projections of a continuous semi finite aw algebra we shall prove that in general situations including also this case any normal y 2 m is equal modulo a to some x 2 m which belongs to an order theoretical closure of an appropriate commutative c subalgebra of a in other words if we replace the strict topology with order theoretical approximation weyl von neumann berg sikonia type theo rems will hold in substantially greater generality

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

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

dimension and stable rank in the k theory of c algebras in topological k theory which can be viewed as the algebraic side of the theory of vector bundles some of the interesting properties which one investigates are for example the conditions under which bundles must possess trivial direct summands or the extent to which the cancellation property for direct whitney sums of bundles holds such properties turn out to be controlled in part by the dimension of the base space and results describing the nature of this control are among what are frequently called stability results 17 during the past few years there has been a sudden flowering of a theory for c algebras see surveys 35 36 37 since c algebras are profitably thought of as non commutative locally compact spaces with the finitely generated projective modules being the appropriate generalization of vector bundles according to swan s theorem 40 it would be natural to look for stability results for c algebras but until now the theory has been focussed on the c groups of c algebras and there has been little discussion of stability properties presumably in part for lack of an appropriate concept of dimension for c algebras one of the main objectives of this paper is to introduce a concept of dimension for c algebras which directly generalizes the classical concept of dimension for compact spaces 16 20 22 and to develop some techniques for calculating it notably for c algebras which are obtained as crossed product algebras for an action of the group of integers in algebraic k theory which is the generalization of topological c theory to rings a substantial number of stability properties have been discovered 2 39 42 48 within that theory the concept which has played a role most analogous to that of dimension is the bass stable rank but despite its many successes the bass stable rank has often been difficult to calculate even for relatively uncomplicated rings another main objective of the present paper is to make accessible for application to c algebras some of the stability results from algebraic c theory this comes about from the fact that the concept of dimension which we introduce dominates the bass stable rank i was led to seek stability results for c algebras by my desire to determine whether the cancellation property for projective modules holds for the irrational rotation c algebras discussed in 30 which as elliott 11 has suggested can appropriately be called 2 dimensional non commutative tori in more concrete terms the question is whether two projections in such an algebra which have the same trace must be unitarily equivalent the present paper provides the general theory which is needed for the affirmative answer which i obtained in a subsequent paper i will derive the

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

moore penrose inverse in rings with involution abstract we study the moore penrose inverse mp inverse in the setting of rings with involution the results include the relation between regular mp invertible and well supported elements we present an algebraic proof of the reverse order rule for the mp inverse valid under certain conditions on mp invertible elements applications to c algebras are given

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

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

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

trivial k1 flow of af algebras and finite von neumann algebras abstract a c algebra is said to have a trivial k1 flow if k1 b 0 for any hereditary c subalgebra b of m a we prove that if a is a unital af algebra then a has a trivial k1 flow and that if a is a finite von neumann algebra then a k has a trivial k1 flow moreover we prove that if the multiplier algebra of a has fs then the unitary group of b is connected for any hereditary c subalgebra b of m a in addition we prove that if a is either a unital nonunital purely infinite simple c algebra or a nonunital c algebra stably isomorphic to a bunce deddens algebra then k1 b 0 for any hereditary c subalgebra b of m a not contained in a

almost commuting unitary elements in purely infinite simple c algebras we consider the problem whether a pair of almost commuting unitaries selfadjoints is close to a pair of commuting unitaries selfadjoints it is an old problem see hi psh bo v1 v2 d bd ch lorl exli exl2 de lin4 etc dan voiculescu showed in v2 that there is a positive number d and a sequence of commuting unitary matrices un and v with i u v v u ji o

groups quasidiagonality and interpolation by multiplier projections we relate the following conditions on a a unital c algebra a with the fs property a k1 a 0 b every projection in m a a lifts c the general weyl von neumann theorem holds in m a any selfadjoint element h in m a can be written as h a lpi a for some selfadjoint element a in a some bounded real sequence ai and some mutually orthogonal projections pi in a with ez1 pi 1 d m a has fs and e interpolation by multiplier projections holds for any closed projections p and q in a with pq o there is a projection r in m a such that p b 4 a and that a x b if in addition a is stable combining the above results we obtain counterexamples to the conjecture of g k pedersen a has fs m a has fs for example the stabilized buncededdens algebras hence the generalized weyl von neumann theorem does not generally hold in l ha for a unital c algebras with fs

performance analysis of the minimum variance beamformer in the presence of steering vector errors we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer in the presence of steering vector errors the analysis yields an explicit expression for the sinr in terms of the variance of the steering vector errors and the other parameters affecting performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between desired signal and interference array size and shape correlation between desired signal and interference and finite sample size

when almost multiplicative morphisms are close to homomorphisms absrract it is shown that approximately multiplicative contractive positive morphisms from c x with dim x 2 into a simple c algebra a of real rank zero and of stable rank one are close to homomorphisms provided that certain k theoretical obstacles vanish as a corollary we show that a homomorphism h c x a is approximated by homomorphisms with finite dimensional range if h gives no k theoretical obstacle

an infinite family of non isomorphic c algebras with identical k theory we exhibit a countably infinite family of simple separable nuclear and mutually non isomorphic c algebras which agree on k theory and traces the algebras do not absorb the jiang su algebra z tensorially answering a question of n c phillips they are also pairwise shape and morita equivalent confirming a conjecture from our earlier work the distinguishing invariant is the radius of comparison a non stable invariant of the cuntz semigroup

sign sequences and decomposition numbers we obtain a closed formula for the v decomposition numbers d v arising from the canonical basis of the fock space representation of uv le where the partition is obtained from by moving some nodes in its young diagram all of which having the same e residue we also show that when these v decomposition numbers are evaluated at v 1 we obtain the corresponding decomposition numbers for the schur algebras and symmetric groups

sinr analysis of the subtraction based smi beamformer the sample matrix inversion smi beamformer suffers from performance degradation due to the finite sample size effect and the arrival angle mismatch problem a simple technique to provide robustness to the conventional smi beamformer is to block the desired signal from the received data before calculating the beamformer s weight vector which leads to the subtraction based smi s smi beamformer in this correspondence closed form approximations of the expected value of the signal to interference plus noise ratio sinr for the s smi beamformer and the smi beamformer are derived where the effect of both finite sample size and arrival angle mismatch are considered simulations show that the derived approximations are close enough to represent the true values of the sinr when the sample size is small and the arrival direction mismatch exists

exponential rank and exponential length of operators on hilbert c modules in this article we consider unitary operators on the hilbert c module ha associated with a large class of c algebras let l x denote the algebra consisting of all bounded linear operators on a separable hilbert space 7 and let k denote the algebra of all compact operators on r halmos and kakutani proved that every unitary operator on r is a product of four symmetries cf ha 143 haka for the case when x is a compact hausdorff space ringrose r recently considered the c algebra c x l q consisting of all norm continuous maps from x to l x and proved that every unitary element of c x l x can be written as a product of at most three exponentials in other words a norm continuous map u from x to the unitary group of l x forms a product of three norm continuous maps written as exp ihi exp ih2 exp ih3 where hl h2 and h3 are maps from x to the space of self adjoint operators in l x phillips and ringrose phr conjectured that every unitary of c x l x can even be approximated in the norm by products of two exponentials using techniques in the theory of c algebras but by a different approach we generalized ringrose s result to hilbert c modules associated with all a unital in particular all unital c algebras cf z8 we also proved in z8 similar results for the c algebra consisting of norm continuous maps from x to a purely infinite simple c algebra the purpose of this article is to settle the phillips ringrose conjecture in the affirmative and to prove a generalized version of the halmos kakutani theorem in haka we consider the group of unitary operators on hilbert c modules associated with the following two specific classes which together comprise the majority of interesting c algebras

kleshchev s decomposition numbers for diagrammatic cherednik algebras we construct a family of graded isomorphisms between certain subquotients of diagrammatic cherednik algebras as the quantum characteristic multicharge level degree and weighting are allowed to vary this provides new structural information even in the case of the classical q schur algebra this also allows us to prove some of the first results concerning the graded decomposition numbers of these algebras over fields of arbitrary characteristic