interference alignment with asymmetric complex signaling settling the host madsen nosratinia conjecture it has been conjectured by ho madsen and nosratinia that complex gaussian interference channels with constant channel coefficients have only one degree of freedom regardless of the number of users while several examples are known of constant channels that achieve more than 1 degree of freedom these special cases only span a subset of measure zero in other words for almost all channel coefficient values it is not known if more than 1 degree of freedom is achievable in this paper we settle the host madsen nosratinia conjecture in the negative we show that at least 1 2 degrees of freedom are achievable for all values of complex channel coefficients except for a subset of measure zero for the class of linear beamforming and interference alignment schemes considered in this paper it is also shown that 1 2 is the maximum number of degrees of freedom achievable on the complex gaussian 3 user interference channel with constant channel coefficients for almost all values of channel coefficients to establish the achievability of 1 2 degrees of freedom we use the novel idea of asymmetric complex signaling i e the inputs are chosen to be complex but not circularly symmetric it is shown that unlike gaussian point to point multiple access and broadcast channels where circularly symmetric complex gaussian inputs are optimal for interference channels optimal inputs are in general asymmetric with asymmetric complex signaling we also show that the 2 user complex gaussian x channel with constant channel coefficients achieves the outer bound of 4 3 degrees of freedom i e the assumption of time variations frequency selectivity used in prior work to establish the same result is not needed

a kernel adaptive algorithm for quaternion valued inputs the use of quaternion data can provide benefit in applications like robotics and image recognition and particularly for performing transforms in 3 d space here we describe a kernel adaptive algorithm for quaternions a least mean square lms based method was used resulting in the derivation of the quaternion kernel lms quat klms algorithm deriving this algorithm required describing the idea of a quaternion reproducing kernel hilbert space rkhs as well as kernel functions suitable with quaternions a modified hr calculus for hilbert spaces was used to find the gradient of cost functions defined on a quaternion rkhs in addition the use of widely linear or augmented filtering is proposed to improve performance the benefit of the quat klms and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations

design of asymptotically optimal improper constellations with hexagonal packing this paper addresses the problem of designing asymptotically optimal improper constellations with a given circularity coefficient correlation coefficient between the constellation and its complex conjugate the designed constellations are optimal in the sense that at high signal to noise ratio snr and for a large number of symbols yield the lowest probability of error under an average power constraint for additive white gaussian noise channels as the number of symbols grows the optimal constellation is the intersection of the hexagonal lattice with an ellipse whose eccentricity determines the circularity coefficient based on this asymptotic result we propose an algorithm to design finite improper constellations the proposed constellations provide significant snr gains with respect to previous improper designs which were generated through a widely linear transformation of a standard m ary quadrature amplitude modulation constellation as an application example we study the use of these improper constellations by a secondary user in an underlay cognitive radio network

rate region boundary of the siso z interference channel with improper signaling this paper provides a complete characterization of the boundary of an achievable rate region called the pareto boundary of the single antenna z interference channel z ic when interference is treated as noise and users transmit complex gaussian signals that are allowed to be improper by considering the augmented complex formulation we derive a necessary and sufficient condition for improper signaling to be optimal this condition is stated as a threshold on the interference channel coefficient which is a function of the interfered user rate and which allows insightful interpretations into the behavior of the achievable rates in terms of the circularity coefficient i e degree of impropriety furthermore the optimal circularity coefficient is provided in closed form the simplicity of the obtained characterization permits interesting insights into when and how improper signaling outperforms proper signaling in the single antenna z ic we also provide an in depth discussion on the optimal strategies and the properties of the pareto boundary

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

symmetric sor method for augmented systems in this paper we develop symmetric successive overrelaxation ssor method to find solution of augmented systems these systems have appeared in many different applications of scientific computing e g the finite element approximation to solve the navier stokes equation and the constrained optimization the convergence of ssor method are studied finally we apply the new method to solve augmented systems the iteration number of this method to receive the solution is very better than sor like method

on convergence and semi convergence of ssor like methods for augmented linear systems abstract in this paper we analyze the convergence and semi convergence of a class of ssor like methods with four real functions for augmented systems the class takes most existed ssor like methods as its special cases for nonsingular systems we obtain the minimum of convergence factors of all the ssor like methods in the class and study when it can be reached by the convergence factors of methods in the class by considering the equivalence of methods we show that most of the existed ssor like methods have the same minimum of convergence factors

symmetric successive overrelaxation methods for rank deficient linear systems in this paper we develop symmetric successive overrelaxation symmetric sor or ssor methods for finding the least square solution of minimal norm to the linear system ax b where a is an mxn matrix of rank r the methods are obtained by first augmenting the system to a block 4x4 consistent system the augmented coefficient matrix is then split by a subproper ssor splitting we state and prove some theorems and by some numerical examples we show the number of iterations for ssor is less than sor and accelerated overrelaxation methods for finding the least square solution of minimal norm to the linear system

preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite linear systems for the positive semidefinite system of linear equations of a block two by two structure by making use of the hermitian skew hermitian splitting iteration technique we establish a class of preconditioned hermitian skew hermitian splitting iteration methods theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system moreover the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly numerical examples further confirm the correctness of the theory and the effectiveness of the method

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

widely linear mmse transceivers for mimo channels this paper considers the joint design of the transmitter and the receiver for linear multiple input multiple output mimo channels when the channel state information csi is available at both sides of the link assuming that the data symbols are mapped into points of fixed signal constellations a transceiver structure employing widely linear wl filters rather than linear ones is proposed in order to exploit the statistical redundancy of some constellations i e the correlation between the signals and their conjugate version wl filters linearly and independently process both the in phase and the quadrature components of the input signals and with a limited increase in the computational complexity allows one to improve the system performances it is shown that by representing the basic system model in terms of in phase and quadrature components the proposed structure can be derived by utilizing the already existing procedure for the design of the linear transceiver according to the minimum mean square error mmse criterion the performances of the wl and linear transceivers are compared in terms of mean square error symbol error rate and achieved multiplexing gain

on generalized symmetric sor method for augmented systems in this paper we establish the generalized symmetric sor method gssor for solving the large sparse augmented systems of linear equations which is the extension of the ssor iteration method the convergence of the gssor method for augmented systems is studied numerical resume shows that this method is effective

improper signaling for symbol error rate minimization in k user interference channel the rate maximization for the k user interference channels ics has been investigated extensively in the literature however the practical problem of minimizing the error probability with given signal modulations and or data rates of the users is less studied in this paper by utilizing additional degrees of freedom from the improper signaling versus the conventional proper signaling we seek to optimize the precoding matrices for the k user single input single output siso ics to minimize pair wise error probability pep and symbol error rate ser with two proposed algorithms respectively compared with conventional proper signaling and other state of the art improper signaling designs our proposed improper signaling schemes achieve notable error rate improvement in siso ics under both the additive white gaussian noise awgn and cellular system setups with or without channel coding our study provides another viewpoint for optimizing transmissions in ics and further justifies the practical benefit of improper signaling in interference limited communication systems

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

improper complex valued multiple model adaptive estimation motivated by the problem of estimating the discrete and continuous states of an improper complex valued stochastic hybrid system the paper proposes a class of widely linear augmented multiple model adaptive estimation algorithms referred to as the c mmae we show that for an improper complex valued signal pseudo covariance of the innovation sequence is not zero and therefore carries useful statistical information regarding the unknown behaviour mode of the hybrid system a new bayesian law is therefore derived as a function of the pseudo covariance of the innovation sequence and used to compute the probability that a hypothesized model is in effect at a certain time we show that the c mmae which uses the new bayesian law and utilizes the complete second order statistical characterization of the complex valued innovation sequence convergences faster than its counterpart which only uses the conventional covariance of the innovation sequence in order to simplify the computational complexity we develop two circularized versions of the c mmae using a preprocessing step referred to as the circularizing filter cf the cf is incorporated to convert the improper observations innovations into the proper ones in order to reduce the computational complexity of the hypothesis testing step finally an interacting version of the c mmae referred to as c imm is developed for improper complex valued systems with markovian switching coefficients simulation results indicate that the proposed hybrid estimators provide improved performance and convergence properties over their traditional counterparts

class of widely linear complex kalman filters recently a class of widely linear augmented complex valued kalman filters kfs that make use of augmented complex statistics have been proposed for sequential state space estimation of the generality of complex signals this was achieved in the context of neural network training and has allowed for a unified treatment of both second order circular and noncircular signals that is both those with rotation invariant and rotation dependent distributions in this paper we revisit the augmented complex kf augmented complex extended kf and augmented complex unscented kf in a more general context and analyze their performances for different degrees of noncircularity of input and the state and measurement noises for rigor a theoretical bound for the performance advantage of widely linear kfs over their strictly linear counterparts is provided the analysis also addresses the duality with bivariate real valued kfs together with several issues of implementation simulations using both synthetic and real world proper and improper signals support the analysis

preconditioning for the steady state navier stokes equations with low viscosity we introduce a preconditioner for the linearized navier stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero for constant coefficient problems with periodic boundary conditions we show that the preconditioning yields a system with a single eigenvalue equal to 1 so that performance is independent of both viscosity and mesh size for other boundary conditions we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon we also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration with virtually no degradation of performance

receivers with widely linear processing for frequency selective channels we propose several equalization schemes based on widely linear processing wlp the received signal and its complex conjugate are separately filtered and the results are linearly combined it is shown that wlp yields a gain in performance if the noiseless received signal can be interpreted as the convolution of a real valued data sequence and an equivalent complex valued intersymbol interference channel impulse response such a model applies to e g amplitude shift keying offset quadrature amplitude modulation and binary minimum shift keying type modulation we consider receivers without and with decision feedback finite impulse response filters are derived for these structures which are optimum with respect to the zero forcing and minimum mean squared error mmse criteria respectively in the mmse case adaptive algorithms for filter adjustment are given infinite filter orders are investigated in order to obtain analytical performance results furthermore suboptimum trellis based detection with widely linear preprocessing is briefly discussed it is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly depending on the considered application

generating function of the gel fand basis for the representation of unitary groups constructs the generating function of the gel fand basis for unitary groups as well as representation matrix elements from these functions the author obtains via simple calculations both the basis vectors and the representation matrix elements in the gel fand basis the generating functions are obtained by two different methods the first takes advantage of a property of the generating function shown and the second one uses recurrence relations for the chain gl 1 c contained in implied by gl 2 c contained in implied by contained in implied by gl n c

a study on the optimal double parameters for steepest descent with momentum this letter presents the stability analysis for two steepest descent algorithms with momentum for quadratic functions the corresponding local optimal parameters in torii and hagan 2002 and zhang 2013 are extended to the global optimal parameters that is both the optimal learning rates and the optimal momentum factors are obtained simultaneously which make for the fastest convergence

a solution to the su n external state labelling problem based upon a u n 1 n 1 group ii recursion relations for the su 2 and su 3 wigner coefficients for pt i see ibid vol 20 p 769 84 1987 the new solution to the su n external state labelling problem proposed in the first paper of this series is analysed in detail in the su 3 case in terms of the two complementary chains u 3 u 3 contains implies u 3 and u 2 2 contains implies u 2 u 2 the classification of su 3 coupled states is completed by the labels of an intermediate u 2 irreducible representation hs hs1hs2 directly related to king s branching rule for u 3 u 3 u 3 for pedagogical purposes the su 2 coupled state construction based upon the complementary chains u 2 u 2 contains implies u 2 and u 1 1 contains implies u 1 u 1 is considered first for both su 2 and su 3 it is proved that in addition to the standard recursion relations the corresponding wigner coefficients satisfy recursion relations of a different type arising from the action of the u 1 1 or u 2 2 complementary group generators a detailed example shows that such complementary recursion relations are quite useful for numerical purposes

detection and estimation of improper complex random signals nonstationary complex random signals are in general improper not circularly symmetric which means that their complementary covariance is nonzero since the karhunen loeve k l expansion in its known form is only valid for proper processes we derive the improper version of this expansion it produces two sets of eigenvalues and improper observable coordinates we then use the k l expansion to solve the problems of detection and estimation of improper complex random signals in additive white gaussian noise we derive a general result comparing the performance of conventional processing which ignores complementary covariances with processing that takes these into account in particular for the detection and estimation problems considered we find that the performance gain as measured by deflection and mean squared error mse respectively can be as large as a factor of 2 in a communications example we show how this finding generalizes the result that coherent processing enjoys a 3 db gain over noncoherent processing

on parameterized inexact uzawa methods for generalized saddle point problems abstract for the large sparse saddle point problems bai et al recently studied a class of parameterized inexact uzawa piu methods z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 for a special case that the 1 1 block is solved exactly they determined the convergence domain and computed the optimal iteration parameters and the corresponding optimal convergence factor for the induced method in this paper we develop these methods to the large sparse generalized saddle point problems for the obtained parameterized inexact uzawa method we prove its convergence under suitable restrictions on the iteration parameters in particular we determine its quasi optimal iteration parameters and the corresponding quasi optimal convergence factor for the saddle point problems furthermore this piu method is generalized to obtain a framework of accelerated variants of the parameterized inexact uzawa methods for solving both symmetric and nonsymmetric generalized saddle point problems by using the techniques of vector extrapolation matrix relaxation and inexact iteration

complex support vector machines for regression and quaternary classification the paper presents a new framework for complex support vector regression svr as well as support vector machines svm for quaternary classification the method exploits the notion of widely linear estimation to model the input out relation for complex valued data and considers two cases 1 the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and 2 a pure complex kernel is used to directly map the data to the induced complex feature space the recently developed wirtinger s calculus on complex reproducing kernel hilbert spaces is employed to compute the lagrangian and derive the dual optimization problem as one of our major results we prove that any complex svm svr task is equivalent with solving two real svm svr tasks exploiting a specific real kernel which is generated by the chosen complex kernel in particular the case of pure complex kernels leads to the generation of new kernels which have not been considered before in the classification case the proposed framework inherently splits the complex space into four parts this leads naturally to solving the four class task quaternary classification instead of the typical two classes of the real svm in turn this rationale can be used in a multiclass problem as a split class scenario based on four classes as opposed to the one versus all method this can lead to significant computational savings experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data

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

on generalized successive overrelaxation methods for augmented linear systems for the augmented system of linear equations golub wu and yuan recently studied an sor like method bit 41 2001 71 85 by further accelerating it with another parameter in this paper we present a generalized sor gsor method for the augmented linear system we prove its convergence under suitable restrictions on the iteration parameters and determine its optimal iteration parameters and the corresponding optimal convergence factor theoretical analyses show that the gsor method has faster asymptotic convergence rate than the sor like method also numerical results show that the gsor method is more effective than the sor like method when they are applied to solve the augmented linear system this gsor method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation matrix relaxation and inexact iteration besides we also demonstrate a complete version about the convergence theory of the sor like method

coexisting linear and widely linear transceivers in the mimo interference channel recent results have shown the benefits of widely linear precoding wlp in the mimo interference channel mimo ic assuming that all transmitters can follow the same strategy motivated by a transitional scenario where legacy linear transmitters coexist with widely linear ones this work investigates the general k user mimo ic in a heterogeneous linear and widely linear transmitter deployment in particular we address the maximization of the weighted sum rate wsr for widely linear transmit filters design through the use of the complex valued formulation since the maximum wsr problem is non convex and thus difficult to be solved we formulate an equivalent minimum weighted mean square error problem that allows deriving closed form expressions for widely linear transceivers then an iterative procedure is proposed which is proven to reach a stationary point of the maximum wsr problem simulations show that the proposed procedure allows increasing the sum rate as compared to coordinated linear transceiver schemes the gains are larger and significant in two different nonexclusive conditions as the interference level increases or when the number of antennas is low

on semi convergence of a class of uzawa methods for singular saddle point problems in this paper a class of uzawa methods are presented for singular saddle point problems these methods contain the recently proposed uzawa aor and uzawa saor methods as special cases the 1 1 block of the corresponding uzawa preconditioner is positive definite both nonsingular and singular preconditioning matrices are considered the semi convergence of these methods is analyzed by using the techniques of singular value decomposition and moore penrose inverse numerical results show that they need less workload per iteration step comparing with the gsor and piu methods in some situations so they are feasible and effective for singular saddle point problems in some situations

a modified ssor iterative method for augmented systems golub wu and yuan g h golub x wu j y yuan sor like methods for augmented systems bit 41 2001 71 85 have presented the sor like algorithm to solve augmented systems in this paper we present the modified symmetric successive overrelaxation mssor method for solving augmented systems which is based on darvishi and hessari s work above we derive its convergence under suitable restrictions on the iteration parameter determine its optimal iteration parameter and the corresponding optimal convergence factor under certain conditions finally we apply the mssor method to solve augmented systems

3jm and 6j tables for some bases of su6 and su3 tables of 6j symbols for su6 and su3 and tables of 3jm factors for su6 contains implies su2 su3 su3 contains implies u1 su2 and su3 contains implies so3 are presented the tables are computer produced using a program that implements the building up principle in a general form these tables are useful for calculations in high energy nuclear and solid state physics some other tabulations contain errors and none uses all the symmetries available the n independence of sun results is discussed by using the various symmetric group unitary group duality relations

canonical orthonormal basis for su 3 contains implies so 3 iii complete set of su 3 tensor operators for pt ii see ibid vol 18 p 1905 1985 a complete set of tensor operators for su 3 is given in a model space generated by two bargmann vectors use is made of modified operator patterns to classify these tensors their tensorial properties are then discussed in the context of the su 3 tensor algebra developed by biedenharn and collaborators 1957 the authors also given analytical semi analytical expressions for important classes of wigner coefficients in gel fand rotational basis

convergence of a generalized mssor method for augmented systems recently wu et al s l wu t z huang x l zhao a modified ssor iterative method for augmented systems j comput appl math 228 1 2009 424 433 introduced a modified ssor mssor method for augmented systems in this paper we establish a generalized mssor gmssor method for solving the large sparse augmented systems of linear equations which is the extension of the mssor method furthermore the convergence of the gmssor method for augmented systems is analyzed and numerical experiments are carried out which show that the gmssor method with appropriate parameters has a faster convergence rate than the mssor method with optimal parameters

determination of the weyl invariants and calculation of the coupling coefficients for unitary groups the author presents a new approach for determining the weyl invariants of unitary groups such an approach is based on the generating function of the basis of the representation for unitary groups built in an earlier work hage hassan 1983 the author obtains two expressions for the weyl invariants both including the parameters involved in the generating function coupling coefficients appear in one of the expressions the comparison of the development of the two expressions allows the calculation of the coupling coefficients the application of this approach to the calculation of the coupling coefficients for the direct product lambda 10 x lambda 2 mu 2 of su 3 leads to an expression of the isoscalar factor where no summation occurs in contradistinction with the known expression for the coupling coefficients which involve five summations

optimal parameters of the generalized symmetric sor method for augmented systems for the augmented system of linear equations zhang and lu 2008 recently studied the generalized symmetric sor method gssor with two parameters in this note the optimal parameters of the gssor method are obtained and numerical examples are given to illustrate the corresponding results

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

complex valued random vectors and channels entropy divergence and capacity recent research has demonstrated significant achievable performance gains by exploiting circularity noncircularity or properness improperness of complex valued signals in this paper we investigate the influence of these properties on important information theoretic quantities such as entropy divergence and capacity we prove two maximum entropy theorems that strengthen previously known results the proof of the first maximum entropy theorem is based on the so called circular analog of a given complex valued random vector the introduction of the circular analog is additionally supported by a characterization theorem that employs a minimum kullback leibler divergence criterion in the proof of the second maximum entropy theorem results about the second order structure of complex valued random vectors are exploited furthermore we address the capacity of multiple input multiple output mimo channels regardless of the specific distribution of the channel parameters noise vector and channel matrix if modeled as random we show that the capacity achieving input vector is circular for a broad range of mimo channels including coherent and noncoherent scenarios finally we investigate the situation of an improper and gaussian distributed noise vector we compute both capacity and capacity achieving input vector and show that improperness increases capacity provided that the complementary covariance matrix is exploited otherwise a capacity loss occurs for which we derive an explicit expression

structured preconditioners for nonsingular matrices of block two by two structures for the large sparse block two by two real nonsingular matrices we establish a general framework of practical and efficient structured preconditioners through matrix transformation and matrix approximations for the specific versions such as modified block jacobi type modified block gauss seidel type and modified block unsymmetric symmetric gauss seidel type preconditioners we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices also we show that when these structured preconditioners are employed to precondition the krylov subspace methods such as gmres and restarted gmres fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two by two coefficient matrices in particular these structured preconditioners can lead to efficient and high quality preconditioning matrices for some typical matrices from the real world applications

generating function of isoscalar factors of unitary groups the author introduces a new schematisation of the elements of the bases of the fundamental representations of the unitary groups using this schematisation as well as two rules which will be established in this work the author is able to find by an elementary calculation the generating function of coupling coefficients of this basis this last generating function permits the author to find the one corresponding to su n isoscalar factors the approach gives in the general case i e for every n the algebraic expressions of these factors the author shows that to find the elements of the irreducible representation of the direct product of n representations and gives the details of this method in the special case n 2 a priori the method can be easily applied to other classical groups

semi convergence analysis of uzawa methods for singular saddle point problems recently zheng bai and yang studied the parameterized uzawa method for solving singular saddle point problems b zheng z z bai x yang on semi convergence of parameterized uzawa methods for singular saddle point problems linear algebra appl 431 2009 808 817 in this paper we discuss the inexact uzawa method which covers the uzawa method the preconditioned uzawa method and the parameterized uzawa method to solve the singular saddle point problems we prove the semi convergence result under restrictions by verifying two necessary and sufficient conditions that is all elementary divisors associated with the eigenvalue 1 of its iterative matrix are linear and the pseudo spectral radius of the iterative matrix is less than 1 sufficient conditions for the semi convergence of several uzawa type methods are also provided in addition numerical examples are given to demonstrate the semi convergence of uzawa type methods

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

new preconditioners for saddle point problems we present new preconditioners based on matrix splittings for the saddle point problems the spectral property of one of the preconditioned matrix is studied in detail numerical examples are used to illustrate the efficiency of the new preconditioners

optimal parameter in hermitian and skew hermitian splitting method for certain two by two block matrices the optimal parameter of the hermitian skew hermitian splitting hss iteration method for a real two by two linear system is obtained the result is used to determine the optimal parameters for linear systems associated with certain two by two block matrices and to estimate the optimal parameters of the hss iteration method for linear systems with n by n real coefficient matrices numerical examples are given to illustrate the results

convergence of relaxation iterative methods for saddle point problem in this paper we first provide convergence results of three relaxation iterative methods for solving saddle point problem next we propose how to find near optimal parameters for which preconditioned krylov subspace method performs nearly best when the relaxation iterative methods are applied to the preconditioners of krylov subspace method lastly we provide efficient implementation for the relaxation iterative methods and efficient computation for the preconditioner solvers numerical experiments show that the miaor method and the bicgstab with maor preconditioner using near optimal parameters perform more than twice faster than the gsor method

complex valued filtering based on the minimization of complex error entropy in this paper we consider the training of complex valued filter based on the information theoretic method we first generalize the error entropy criterion to complex domain to present the complex error entropy criterion ceec due to the difficulty in estimating the entropy of complex valued error directly the entropy bound minimization ebm method is used to compute the upper bounds of the entropy of the complex valued error and the tightest bound selected by the ebm algorithm is used as the estimator of the complex error entropy then based on the minimization of complex error entropy mcee and the complex gradient descent approach complex valued learning algorithms for both the linear transverse filter and the nonlinear neural network are derived the algorithms are applied to complex valued linear filtering and complex valued nonlinear channel equalization to demonstrate their effectiveness and advantages

high snr asymptotics of mutual information for discrete constellations with applications to bicm asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white gaussian noise channel are presented in the limit as the signal to noise ratio snr tends to infinity asymptotic expressions of the symbol error probability sep and the minimum mean square error mmse achieved by estimating the channel input given the channel output are also developed it is shown that for any input distribution the conditional entropy of the channel input given the output mmse and sep have an asymptotic behavior proportional to the gaussian q function the argument of the q function depends only on the minimum euclidean distance med of the constellation and the snr and the proportionality constants are functions of the med and the probabilities of the pairs of constellation points at med the developed expressions are then generalized to study the high snr behavior of the generalized mutual information gmi for bit interleaved coded modulation bicm by means of these asymptotic expressions the long standing conjecture that gray codes are the binary labelings that maximize the bicm gmi at high snr is proven it is further shown that for any equally spaced constellation whose size is a power of two there always exists an anti gray code giving the lowest bicm gmi at high snr

wigner s d matrix elements for su 3 a generating function approach using our calculus for su 3 a generating function for wigner d matrix elements is derived for the first time from this an explicit expression for the individual matrix elements in an arbitrary irreducible representation is obtained also for the first time in terms of polynomials in the matrix elements of the defining representation of su 3 this expression does not depend on any particular parametrization of the group

a unifying discussion of correlation analysis for complex random vectors the assessment of multivariate association between two complex random vectors is considered a number of correlation coefficients based on three popular correlation analysis techniques namely canonical correlation analysis multivariate linear regression and partial least squares are reviewed and connected to performance measures in signal processing and communications such as mean squared estimation error mutual information and signal to noise ratio snr for complex data there are three types of correlation coefficients which account for rotational reflectional and total i e rotational and reflectional dependencies between two random vectors these three types are defined and analyzed for different correlation coefficients and a numerical example is given it is often required to compare two complex random vectors in a lower dimensional subspace for the large class of increasing schur convex correlation coefficients it is shown that the low rank approximations of two random vectors maximizing a particular correlation coefficient are determined only by the constraints imposed on the correlation analysis technique in this context the correlation spread is defined as a normalized measure of how much of the overall correlation is contained in a low dimensional subspace

cyclic wiener filtering theory and method conventional time and space filtering of stationary random signals which amounts to forming linear combinations of time translates and space translates exploits the temporal and spatial coherence of the signals by including frequency translates as well the spectral coherence that is characteristic of cyclostationary signals can also be exploited some of the theoretical concepts underlying this generalized type of filtering called frequency shift fresh filtering are developed the theory of optimum fresh filtering which is a generalization of wiener filtering called cyclic wiener filtering is summarized and the theory is illustrated with specific examples of separating temporally and spectrally overlapping communications signals including am bpsk and qpsk the structures and performances of optimum fresh filters are presented and adaptive adjustment of the weights in these structures is discussed also specific results on the number of digital qam signals that can be separated as a function of excess bandwidth are obtained

arma prediction of widely linear systems by using the innovations algorithm a new autoregressive moving average arma predictor for widely linear systems is presented by using the innovations algorithm and under an improper treatment the main characteristics of this predictor are its facility of implementation from a practical standpoint and a better performance with respect to the conventional predictor obtained from a proper processing

a modified symmetric successive overrelaxation method for augmented systems in this paper we establish a modified symmetric successive overrelaxation mssor method to solve augmented systems of linear equations which uses two relaxation parameters this method is an extension of the symmetric sor ssor iterative method the convergence of the mssor method for augmented systems is studied numerical examples show that the new method is an efficient method

a generalization of the inexact parameterized uzawa methods for saddle point problems abstract for large sparse saddle point problems bai and wang recently studied a class of parameterized inexact uzawa methods see z z bai z q wang on paramaterized inexact uzawa methods for generalized saddle point problems linear algebra appl 428 2008 2900 2932 in this paper we generalize these methods and propose a class of generalized inexact parameterized iterative schemes for solving the saddle point problems we derive conditions for guaranteeing the convergence of these iterative methods with different choices of the parameter matrices the generalized iterative methods lead to a series of existing and new iterative methods including the classical uzawa method the inexact uzawa method the gsor method and the giaor method

on parameter acceleration methods for saddle point problems for solving saddle point problems parameter acceleration methods which include uzawa type methods are investigated by many researchers in the literature in this paper we introduce the inexact uzawa method with another parameter acceleration that is the so called momentum acceleration method for solving saddle point problems we discuss the convergence conditions of the inexact uzawa iteration with momentum acceleration and give the optimal momentum factors which minimize the spectral radii of the associated iteration matrices numerical results demonstrate the effectiveness of the inexact uzawa method with momentum acceleration and the mixed parameter acceleration methods for solving saddle point problems