a semi blind channel estimation technique based on second order blind method for cdma systems this paper aims at studying a semi blind channel estimation scheme based on the subspace method or a carefully weighted linear prediction approach the corresponding composite semi blind cost functions result from a linear combination of the training based cost function and a blind cost function for each blind method we show how to calculate the asymptotic estimation error therefore by minimizing this error we can properly tune the k dimensional regularizing vector introduced in the composite semi blind criterion for k active users in the uplink the asymptotic estimation error minimization is a k variable minimization problem which is a complex issue with which to deal we explicitly show under what conditions this problem boils down to k single variable minimization problems our discussion is not limited to theoretical analyses simulation results performed in a realistic context universal mobile telecommunication system time division duplex umts tdd mode are provided in particular we conclude about the potential of the proposed approach in real communication systems

weightless cohomology of algebraic varieties abstract using morel s weight truncations in categories of mixed sheaves we attach to varieties over finite fields or the complex numbers a series of groups called the weightless cohomology groups these lie between the usual cohomology and intersection cohomology have natural ring structures and are functorial for certain morphisms

geometry of sets of quantum maps a generic positive map acting on a high dimensional system is not completely positive we investigate the set a of positive trace preserving maps acting on density matrices of size n and a sequence of its nested subsets the sets of maps which are b decomposable c completely positive and d extended by identity impose positive partial transpose and e are superpositive working with the hilbert schmidt euclidean measure we derive tight explicit two sided bounds for the volumes of all five sets a sample consequence is the fact that as n increases a generic positive map becomes not decomposable and a fortiori not completely positive due to the jamiolkowski isomorphism the results obtained for quantum maps are closely connected to similar relations between the volume of the set of quantum states and the volumes of its subsets such as states with positive partial transpose or separable states or supersets our approach depends on the systematic use of duality to derive quantitative estimates and on various tools of classical convexity high dimensional probability and geometry of banach spaces some of which are not standard

motivic weightless complex and the relative artin motive abstract we construct a motivic analogue of the weightless cohomology groups 18 and demonstrate several expected properties ring structure kunneth functoriality for certain morphisms etc we also demonstrate the expected relationship with the motivic intersection complex of wildeshaus 26 25 whenever it exists the methods also give another construction of the weightless cohomology groups over any base field in characteristic 0 this motive coincides with the motive e x of ayoub zucker 3 and recovers the motivic construction of the reductive borel serre compactification of shimura varieties

idempotent completion of triangulated categories we show that the idempotent completion of a triangulated category has a natural structure of a triangulated category the idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion in particular the derived category of an idempotent complete exact category is idempotent complete

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

a signal perturbation free whitening rotation based semiblind approach for mimo channel estimation it was shown in our previous work that in the noise free case the whitening rotation wr based mimo channel estimation algorithm is subject to a signal perturbation error justifying that the wr based method is efficient only in the low signal to noise ratio snr case in this paper a very efficient signal perturbation free wr based approach is proposed for semiblind channel estimation of mimo systems a novel transmit scheme is developed based on the eigenvalue decomposition of the correlation matrix of the transmitted signal the new scheme is to send a small volume of data bearing the information of the correlation matrix to the receiver for the cancellation of the signal perturbation error so as to improve the performance of the wr based method in the case of high snrs then a perturbation analysis of the proposed wr based semiblind method with the new transmit scheme is conducted leading to a closed form expression for the mean square error mse of the channel estimate computer simulations show that the proposed approach significantly outperforms the original wr based method as well as some other channel estimation methods for all snr levels

triangulated categories of relative 1 motives abstract the category da 1 s of relative cohomological 1 motives is the localizing subcategory of the triangulated category da s da e t s q of relative voevodsky motives with rational coefficients over a scheme s which is generated by cohomological motives of curves over s we construct and study a candidate for the standard motivic t structure on da 1 s for s noetherian finite dimensional and excellent we show this t structure is non degenerate and relate its heart mm 1 s with deligne 1 motives over s in particular when s is regular the category of deligne 1 motives embeds in mm 1 s fully faithfully we also study the inclusion of da 1 s into the larger category da coh s of relative cohomological motives on s and prove that its right adjoint 1 preserves compact objects

spectral properties of entanglement witnesses entanglement witnesses are observables which when measured detect entanglement in a measured composed system it is shown what kind of relations between eigenvectors of an observable should be fulfilled to allow an observable to be an entanglement witness some restrictions on the signature of entanglement witnesses based on an algebraic geometrical theorem will be given the set of entanglement witnesses is linearly isomorphic to the set of maps between matrix algebras which are positive but not completely positive a translation of the results to the language of positive maps is also given the properties of entanglement witnesses and positive maps are expressed as special cases of general theorems for k schmidt witnesses and k positive maps the results are therefore presented in a general framework

relative artin motives and the reductive borel serre compactification of a locally symmetric variety we introduce the notion of artin motives and cohomological motives over a scheme x given a cohomological motive m over x we consider the universal artin motive mapping to m and denote it omega 0 x m we use this to define a motive mathbb e x over x which is an invariant of the singularities of x the first half of the paper is devoted to the study of the functors omega 0 x and the computation of the motives mathbb e x

realisation l adique des motifs triangules geometriques ii for geometrical triangulated motives with rational coefficients over a ground field of characteristic zero which is embeddable into mathbb c huber j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 has constructed a realization functor with values in the category of mixed realization of huber mixed motives and their realization in derived categories lecture notes in mathematics vol 1604 springer berlin 1995 in this sequel to ivorra doc math 12 607 671 2007 we prove that the l adic realization functor obtained in theorem 4 3 of ivorra doc math 12 607 671 2007 is the same up to a canonical isomorphism as the l adic component of a huber s construction in this way ivorra in doc math 12 607 671 2007 might be viewed as an integral generalization to all noetherian separed schemes of the work huber in j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 as far as the l adic setting is concerned we also prove a comparison theorem with the classical l adic cycle class map over a perfect field using a naive motivic cycle class map

toroidal and reductive borel serre compactifications of locally symmetric spaces by hermitian locally symmetric space we mean an arithmetic quotient of a bounded symmetric domain both the toroidal and the reductive borel serre compactifications of such a space come equipped with canonical mappings to the baily borel satake compactification in this article we show that there is a mapping from the toroidal compactification to the reductive borel serre compactification whose composition with the projection to the baily borel compactification agrees with the canonical projection up to an arbitrarily small homotopy we also consider arithmetic quotients of a self adjoint homogeneous cone there is a canonical mapping from the reductive borel serre compactification to the standard compactification of such a locally symmetric cone we show that this projection when restricted to the closure of a polyhedral cone has contractible fibers

a family of norms with applications in quantum information theory we consider a family of vector and operator norms defined by the schmidt decomposition theorem for quantum states we use these norms to tackle two fundamental problems in quantum information theory the classification problem for k positive linear maps and entanglement witnesses and the existence problem for nonpositive partial transpose bound entangled states we begin with an analysis of the norms showing that the vector norms can be explicitly calculated and we derive several inequalities in order to bound the operator norms and compute them in special cases we then use the norms to establish what appears to be the most general spectral test for k positivity currently available showing how it implies several other known tests as well as some new ones building on this work we frame the nonpositive partial transpose bound entangled problem as a concrete problem on a specific limit specifically that a particular entangled werner state is bound entangled if and only if a certain norm inequality ho

on the performance of semi blind subspace based channel estimation this paper is devoted to the analysis of a semi blind estimation framework in which the standard least squares estimator based on a known training sequence is enhanced by using the statistical structure of the observations more specifically we consider the case of a general time division multiple access tdma frame based receiver equipped with multiple sensors and restrict our attention to second order based subspace methods that are suitable for most standard communication applications due to their moderate computational cost the semi blind channel estimator is obtained as a regularized least squares solution where a blind subspace criterion plays the role of the regularization constraint the main contribution of the paper consists of showing by asymptotic analysis how to optimally tune the balance between the blind criterion and the least squares fit depending on the design parameters of the system simulations show that the proposed solutions are robust and significantly improve the efficiency of the equalization

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

an inverse eigenvalue problem for symmetrical tridiagonal matrices we consider the following inverse eigenvalue problem to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices we give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix our results are constructive in the sense that they generate an algorithmic procedure to construct the matrix

on weight truncations in the motivic setting abstract using punctual gluing of t structures we construct an analogue of s morel s weight truncation functors for certain weight profiles in the setting of motivic sheaves as an application we construct a canonical motivic analogue of the intersection complex for an arbitrary threefold over any field k we are also able to recover certain invariants of singularities motivically

the nonnegative inverse eigenvalue problem abstract let 1 n be a list of complex numbers the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix our purpose is to give an overview of the niep its history modern results and subproblems with particular emphasis on symmetric realizing matrices a substantial bibliography is included

asymptotic analysis of blind multiuser detection with blind channel estimation the analytical performance of the subspace based blind linear minimum mean square error mmse multiuser detection algorithm in general multipath multi antenna code division multiple access cdma systems is investigated in blind multiuser detection the linear mmse detector of a given user is estimated from the received signals based on the knowledge of only the spreading sequence of that user typically the channel of that user must be estimated first based on the orthogonality between the signal and noise subspaces an asymptotic limit theorem for the estimate of the blind linear detector when the received signal sample size is large is obtained based on which approximate expressions of the average output signal to inference plus noise ratios sinrs and bit error rates bers for both binary phase shift keying bpsk and quaternary phase shift keying qpsk modulations are given corresponding results for group blind multiuser detectors are also obtained examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results

blind channel estimation using the second order statistics algorithms most second order moment based blind channel estimators belong to two categories i optimal correlation spectral fitting techniques and ii eigenstructure based techniques these two classes of algorithms have complementary advantages and disadvantages a new optimization criterion referred to as the joint optimization with subspace constraints josc is proposed to unify the two types of approaches based on this criterion a new algorithm is developed to combine the strength of the two classes of blind channel estimators among a number of attractive features the josc algorithm does not require the accurate detection of the channel order when compared with existing eigenstructure based techniques the josc performs better especially when the channel is close to being unidentifiable when compared with correlation spectral fitting schemes the josc is less affected by the presence of local minima

generalized lqr control and kalman filtering with relations to computations of inner outer and spectral factorizations we investigate the generalized linear quadratic regulator lqr control where the dimension of the control input is strictly greater than the dimension of the controlled output and the weighting matrix on the control signal is singular the dual problem is the generalized kalman filtering where the dimension of the input noise process is strictly smaller than the dimension of the output measurement and the covariance of the observation noise is singular these two problems are intimately related to inner outer factorizations for nonsquare stable transfer matrices with square inners of the smaller size such inner outer factorizations are in turn related to spectral factorizations for power spectral density psd matrices whose normal ranks are not full we propose iterative algorithms and establish their convergence for inner outer and spectral factorizations which in turn solve the generalized lqr control and kalman filtering

a semiblind channel estimation approach for mimo ofdm systems in this paper a very efficient semiblind approach that uses a training based least square criterion along with a blind constraint is proposed for multiple input multiple output orthogonal frequency division multiplexing mimo ofdm channel estimation the blind constraint is derived from the linear prediction of the received mimo ofdm signal and is used in conjunction with a weighting factor in the semiblind cost function an appealing scheme for the determination of the weighting factor is presented as a part of the proposed approach a perturbation analysis of the proposed method is conducted to justify the superiority of the semiblind solution and to obtain a closed form expression for the mean square error mse of the blind constraint further facilitating the calculation of the weighting factor the proposed method is validated through computer simulation based experimentations showing a very high estimation accuracy of the semiblind solution in terms of the mse of the channel estimate

the inverse eigenvalue problem for entanglement witnesses abstract we consider the inverse eigenvalue problem for entanglement witnesses which asks for a characterization of their possible spectra or equivalently of the possible spectra resulting from positive linear maps of matrices we completely solve this problem in the two qubit case and we derive a large family of new necessary conditions on the spectra in arbitrary dimensions we also establish a natural duality relationship with the set of absolutely separable states and we completely characterize witnesses i e separating hyperplanes of that set when one of the local dimensions is 2

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

intermediate extension of chow motives of abelian type abstract in this article we give an unconditional construction of a motivic analogue of the intermediate extension in the context of chow motives of abelian type our main application concerns intermediate extensions of chow motives associated to kuga families to the baily borel compactification of a shimura variety

equalization and semi blind channel estimation for space time block coded signals over a frequency selective fading channel in this paper we investigate the equalization and channel identification for space time block coded signals over a frequency selective multiple input multiple output mimo channel the equalization has been considered by taking into account the cyclostationarity of space time block coded signals the minimum mean square error mmse solutions have been derived for the linear and decision feedback df equalizers the channel estimation is required for the equalization with known symbols as pilot symbols mimo channels can be estimated in addition due to the redundancy induced by space time block code it is possible to identify mimo channels blindly using the subspace method we consider both blind and semi blind channel estimation for mimo channels it is shown that the semi blind channel estimate has fewer estimation errors and it results in less bit error rate performance degradation of the mmse linear and df equalizers

the inverse eigenvalue problem for symmetric doubly stochastic matrices abstract for a positive integer n and for a real number s let ns denote the set of all n n real matrices whose rows and columns have sum s in this note by an explicit constructive method we prove the following i given any real n tuple 1 2 n t there exists a symmetric matrix in n 1 whose spectrum is ii for a real n tuple 1 2 n t with 1 2 n if 1 n 2 n n 1 3 n n 2 n 2 1 0 then there exists a symmetric doubly stochastic matrix whose spectrum is the second assertion enables us to show that for any 2 n 1 n 1 1 there is a symmetric doubly stochastic matrix whose spectrum is 1 2 n t and also that any number 1 1 is an eigenvalue of a symmetric positive doubly stochastic matrix of any order

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

chow groups are finite dimensional in some sense when s is a surface with pg s 0 mumford proved that its chow group a s is not finite dimensional in some sense in this paper we propose another definition of finite dimensionality for the chow groups using this new definition at least the chow group of some surface s with pg s 0 for example the product of two curves becomes finite dimensional the finite dimensionality of the chow groups follows from the finite dimensionality of the chow motives it turns out that the finite dimensionality of the chow motives is a very strong property for example we can prove bloch s conjecture representability of the chow groups of surfaces with pg s 0 under the assumption that the chow motive of s is finite dimensional

weights on cohomology invariants of singularities and dual complexes we study the weight filtration on the cohomology of a proper complex algebraic variety and obtain natural upper bounds on its size when it is the exceptional divisor of a singularity we also give bounds for the cohomology of links the invariants of singularities introduced here gives rather strong information about the topology of rational and related singularities