improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates the problem of estimating the eigenvalues and eigenvectors of the covariance matrix associated with a multivariate stochastic process is considered the focus is on finite sample size situations whereby the number of observations is limited and comparable in magnitude to the observation dimension using tools from random matrix theory and assuming a certain eigenvalue splitting condition new estimators of the eigenvalues and eigenvectors of the covariance matrix are derived that are shown to be consistent in a more general asymptotic setting than the traditional one indeed these estimators are proven to be consistent not only when the sample size increases without bound for a fixed observation dimension but also when the observation dimension increases to infinity at the same rate as the sample size numerical evaluations indicate that the estimators have an excellent performance in small sample size scenarios where the observation dimension and the sample size are comparable in magnitude

homogenization of two phase fluid flow in porous media via volume averaging abstract a technique of local volume averaging is employed to obtain general equations which depict mass and momentum transport of incompressible two phase flow in porous media starting from coupled navier stokes cahn hilliard equations for incompressible two phase fluid flow the averaging is performed without oversimplifying either the porous media or the fluid mechanical relations the resulting equations are darcy s law for two phase flow with medium parameters which could be evaluated by experiment the richards equation of the mixed form can be deduced from the resulting equations the differences between the resulting equations and the empirical two phase fluid flow model adopted in oil industry are discussed by several numerical examples

coherent states of the q canonical commutation relations for theq deformed canonical commutation relationsa f a g 1 q f g 1 qa g a f forf g in some hilbert space we consider representations generated from a vector satisfyinga f where we show that such a representation exists if and only if 1 moreover for 1 these representations are unitarily equivalent to the fock representation obtained for 0 on the other hand representations obtained for different unit vectors are disjoint we show that the universal c algebra for the relations has a largest proper closed two sided ideal the quotient by this ideal is a naturalq analogue of the cuntz algebra obtained forq 0 we discuss the conjecture that ford this analogue should in fact be equal to the cuntz algebra itself in the limiting casesq 1 we determine all irreducible representations of the relations and characterize those which can be obtained via coherent states

a random matrix theoretic approach to handling singular covariance estimates in many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data more specifically if we have a set of n independent identically distributed measurements of an m dimensional random vector the maximum likelihood estimate is the sample covariance matrix here we consider the case where n m such that this estimate is singular noninvertible and therefore fundamentally bad we present a radically new approach to deal with this situation based on the idea of dimensionality reduction through an ensemble of isotropically random unitary matrices we obtain two estimates cov and invcov which are estimates for the covariance matrix and the inverse covariance matrix respectively both estimates retain the original eigenvectors while altering the eigenvalues we have a closed form analytical expression for cov and invcov in terms of the eigenvector eigenvalue decomposition of the sample covariance we motivate the use of invcov through applications to linear estimation supervised learning and high resolution spectral estimation we also compare the performance of these estimators with other more conventional methods

numerical methods for a multicomponent two phase interface model with geometric mean influence parameters in this paper we consider an interface model for multicomponent two phase fluids with geometric mean influence parameters which is popularly used to model and predict surface tension in practical applications for this model there are two major challenges in theoretical analysis and numerical simulation the first one is that the influence parameter matrix is not positive definite the second one is the complicated structure of the energy function which requires us to find out a physically consistent treatment to overcome these two challenging problems we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density and furthermore we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions from this we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density for numerical simulation we propose a

the q deformation of quantum mechanics of one degree of freedom the q quantum mechanics of the one degree of freedom is studied among others the holomorphic representation of q deformed heisenberg weyl algebra and its realization by covariant berezin symbols is described

asymptotic capacity and optimal precoding in mimo multi hop relay networks a multihop relaying system is analyzed where data sent by a multi antenna source is relayed by successive multi antenna relays until it reaches a multi antenna destination assuming correlated fading at each hop each relay receives a faded version of the signal from the previous level performs linear precoding and retransmits it to the next level using free probability theory and assuming that the noise power at relays but not at destination is negligible the closed form expression of the asymptotic instantaneous end to end mutual information is derived as the number of antennas at all levels grows large the so obtained deterministic expression is independent from the channel realizations while depending only on channel statistics this expression is also shown to be equal to the asymptotic average end to end mutual information the singular vectors of the optimal precoding matrices maximizing the average mutual information with finite number of antennas at all levels are also obtained it turns out that these vectors are aligned to the eigenvectors of the channel correlation matrices thus they can be determined using only the channel statistics as the structure of the singular vectors of the optimal precoders is independent from the system size it is also optimal in the asymptotic regime

bilinear forms clifford algebras q commutation relations and quantum groups abstract constructions are described which associate algebras to arbitrary bilinear forms generalising the usual clifford and heisenberg algebras quantum groups of symmetries are discussed both as deformed enveloping algebras and as quantised function spaces a classification of the equivalence classes of bilinear forms is also given

optimal training sequences for large scale mimo ofdm systems this paper considers the optimal design of training sequences for channel estimation in large scale multiple input multiple output orthogonal frequency division multiplexing systems the application scenario of interest is when the number of transmit antennas for the downlink or the number of receive antennas for the uplink is large but not large enough to benefit the asymptotical optimality of using equipower training sequences e g due to practical constraints on deployment costs space and antenna size under the criterion of minimizing the mean square error of the channel estimate the optimal design of training sequences for such systems poses a truly large scale optimization problem to which existing optimization solvers are not applicable we develop a fast convex programming fcp procedure to find its global optimal solution in each iteration of the proposed fcp procedure a solution is found in a scalable and closed form the singularity and ill conditionedness of the channel correlation matrices are also exploited to improve the computation efficiency furthermore we also examine the design of reduced length training sequences and develop a successive quadratic programming procedure to find the solutions intensive simulation results are provided to illustrate the performance of our methods

beam division multiple access transmission for massive mimo communications we study multicarrier multiuser multiple input multiple output mu mimo systems in which the base station employs an asymptotically large number of antennas we analyze a fully correlated channel matrix and provide a beam domain channel model where the channel gains are independent of sub carriers for this model we first derive a closed form upper bound on the achievable ergodic sum rate based on which we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter furthermore we propose a beam division multiple access bdma transmission scheme that simultaneously serves multiple users via different beams by selecting users within non overlapping beams the mu mimo channels can be equivalently decomposed into multiple single user mimo channels this scheme significantly reduces the overhead of channel estimation as well as the processing complexity at transceivers for bdma transmission we work out an optimal pilot design criterion to minimize the mean square error mse and provide optimal pilot sequences by utilizing the zadoff chu sequences simulations demonstrate the near optimal performance of bdma transmission and the advantages of the proposed pilot sequences

transmit designs for the mimo broadcast channel with statistical csi we investigate the multiple input multiple output broadcast channel with statistical channel state information available at the transmitter the so called linear assignment operation is employed and necessary conditions are derived for the optimal transmit design under general fading conditions based on this we introduce an iterative algorithm to maximize the linear assignment weighted sum rate by applying a gradient descent method to reduce complexity we derive an upper bound of the linear assignment achievable rate of each receiver from which a simplified closed form expression for a near optimal linear assignment matrix is derived this reveals an interesting construction analogous to that of dirty paper coding in light of this a low complexity transmission scheme is provided numerical examples illustrate the significant performance of the proposed low complexity scheme

optimal pilot and payload power control in single cell massive mimo systems this paper considers the jointly optimal pilot and data power allocation in single cell uplink massive multiple input multiple output systems using the spectral efficiency se as performance metric and setting a total energy budget per coherence interval the power control is formulated as optimization problems for two different objective functions the weighted minimum se among the users and the weighted sum se a closed form solution for the optimal length of the pilot sequence is derived the optimal power control policy for the former problem is found by solving a simple equation with a single variable utilizing the special structure arising from imperfect channel estimation a convex reformulation is found to solve the latter problem to global optimality in polynomial time the gain of the optimal joint power control is theoretically justified and is proved to be large in the low snr regime simulation results also show the advantage of optimizing the power control over both pilot and data power as compared to the cases of using full power and of only optimizing the data powers as done in previous work

positive representations of general commutation relations allowing wick ordering we consider the problem of representing in hilbert space commutation relations of the form graphics where the tklij are essentially arbitrary scalar coefficients examples comprise the q canonical commutation relations introduced by greenberg bozejko and speicher and the twisted canonical anti commutation relations studied by pusz and woronowicz as well as the quantum group s u 2 using these relations any polynomial in the generators ai and their adjoints can uniquely be written in wick ordered form in which all starred generators are to the left of all unstarred ones in this general framework we define the fock representation as well as coherent representations we develop criteria for the natural scalar product in the associated representation spaces to be positive definite and for the relations to have representations by bounded operators in a hilbert space we characterize the relations between the generators ai not involving a i which are compatible with the basic relations the relations may also be interpreted as defining a non commutative differential calculus for generic coefficients tklij however all differential forms of degree 2 and higher vanish we exhibit conditions for this not to be the case and relate them to the ideal structure of the wick algebra and conditions of positivity we show that the differential calculus is compatible with the involution iff the coefficients t define a representation of the braid group this condition is also shown to imply improved bounds for the positivity of the fock representation finally we study the kms states of the group of gauge transformations defined by aj exp it aj

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

wavelet representations and fock space on positive matrices abstract we show that every biorthogonal wavelet determines a representation by operators on hilbert space satisfying simple identities which captures the established relationship between orthogonal wavelets and cuntz algebra representations in that special case each of these representations is shown to have tractable finite dimensional co invariant doubly cyclic subspaces further motivated by these representations we introduce a general fock space hilbert space construction which yields creation operators containing the cuntz toeplitz isometries as a special case

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

on c algebras generated by pairs of q commuting isometries we consider the c algebras and generated respectively by isometries s1 s2 satisfying the relation s 1s2 qs2s 1 with q 1 the deformed cuntz relation and by isometries s1 s2 satisfying the relation s2s1 qs1s2 with q 1 we show that is isomorphic to the cuntz toeplitz c algebra for any q 1 we further prove that if and only if either q1 q2 or in the second part of our paper we discuss the complexity of the representation theory of we show that is wild for any q in the circle q 1 and hence that is not nuclear for any q in the circle

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

endomorphisms of b h ii finitely correlated states on on we identify sets of conjugacy classes of ergodic endomorphisms of b h where h is a fixed separable hilbert space they correspond to certain equivalence classes of pure states on the cuntz algebras onwherenis the powers index these states called finitely correlated states and strongly asymptotically shift invariant states are defined and characterized the subsets of these states defining shifts will in general be identified in a later work but here an interesting cross section for the conjugacy classes of shifts called diagonalizable shifts is introduced and studied

on crossed product of algebras the concept of a crossed tensor product of algebras is studied from a few points of view some related constructions are considered crossed enveloping algebras and their representations are discussed applications to the noncommutative geometry and particle systems with generalized statistics are indicated

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

maximum modulus principle for holomorphic functions on the quantum matrix ball we describe the shilov boundary ideal for a q analog of the algebra of holomorphic functions on the unit ball in the space of n n matrices and show that its c envelope is isomorphic to the c algebra of continuous functions on the quantum unitary group u q n

the energy operator for a model with a multiparametric infinite statistics in this paper we consider an energy operator a free hamiltonian in the second quantized approach for the multiparameter quon algebras aia j qija jai ij i j i with qij i ji any hermitian matrix of deformation parameters we obtain an elegant formula for normally ordered sometimes called wick ordered series expansions of number operators which determine a free hamiltonian as a main result see theorem 1 we prove that the number operators are given with respect to a basis formed by generalized lie elements by certain normally ordered quadratic expressions with coefficients given precisely by the entries of the inverses of gram matrices of multiparticle weight spaces this settles a conjecture by meljanac s and perica a 1994 j phys a math gen 27 4737 44 these gram matrices are hermitian generalizations of the varchenko matrices associated with a quantum symmetric bilinear form of diagonal arrangements of hyperplanes the solution of the inversion problem of such matrices in meljanac s and svrtan d 1996 math commun 1 1 24 theorem 2 2 17 leads to an effective formula for the number operators studied in this paper the one parameter case in the monomial basis was studied by zagier stanciu and moller

asymptotic analysis of rzf in large scale mu mimo systems over rician channels in this paper we focus on the downlink ergodic sum rate of a single cell large scale multiuser mimo system in which the base station employs n antennas to communicate with k single antenna user equipments ues a regularized zero forcing rzf scheme is used for precoding under the assumption that each ue uses a specific power and each link forms a spatially correlated mimo rician fading channel the analysis is conducted assuming that n and k grow large with a given ratio and perfect channel state information is available at the base station new results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal to interference plus noise ratio as a function of system parameters spatial correlation matrix and rician factor numerical results are used to validate the accuracy of asymptotic approximations in the finite system regime and to evaluate the performance under different operating conditions it turns out that the asymptotic expressions provide accurate approximations even for relatively small values of n and k

wick product for commutation relations connected with yang baxter operators and new constructions of factors we analyze a certain class of von neumann algebras generated by selfadjoint elements for satisfying the general commutation relations such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors where is an orthonormal basis of a hilbert space the operator which represents the vector is denoted by and called the wick product of the operators we describe explicitly the form of this product also we estimate the operator norm of for finally we apply these two results and prove that under the assumption all the von neumann algebras considered are ii 1 factors

q gaussian processes non commutative and classical aspects we examine for 1 q 1 q gaussian processes i e families of operators non commutative random variables where the a t fulfill the q commutation relations for some covariance function equipped with the vacuum expectation state we show that there is a q analogue of the gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q gaussian processes into corresponding and much simpler questions in the underlying hilbert space in particular we use this idea to show that a large class of q gaussian processes possesses a non commutative kind of markov property which ensures that there exist classical versions of these non commutative processes this answers an old question of frisch and bourret fb

noncommutative levy processes for generalized particularly anyon statistics let t mathbb r d let a function qt 2 to mathbb c satisfy q s t overline q t s and q s t 1 a generalized statistics is described by creation operators partial t dagger and annihilation operators t t in t which satisfy the q commutation relations partial s partial dagger t q s t partial dagger t partial s delta s t partial s partial t q t s partial t partial s partial dagger s partial dagger t q t s partial dagger t partial dagger s from the point of view of physics the most important case of a generalized statistics is the anyon statistics for which q s t is equal to q if s t here q in mathbb c q 1 we start the paper with a detailed discussion of a q fock space and operators partial t dagger partial t t in t in it which satisfy the q commutation relations next we consider a noncommutative stochastic process white noise omega t partial t dagger partial t lambda partial t dagger partial t t in t here lambda in mathbb r is a fixed parameter the case 0 corresponds to a q analog of brownian motion while 0 corresponds to a centered q poisson process we study q hermite q charlier respectively polynomials of infinitely many noncommutatative variables omega t t in t the main aim of the paper is to explain the notion of independence for a generalized statistics and to derive corresponding levy processes to this end we recursively define q cumulants of a field xi t t in t this allows us to define a q levy process as a field xi t t in t whose values at different points of t are q independent and which possesses a stationarity of increments in a certain sense we present an explicit construction of a q levy process and derive a nualart schoutens type chaotic decomposition for such a process

sum capacity computation for the gaussian vector broadcast channel via dual decomposition a numerical algorithm for the computation of sum capacity for the gaussian vector broadcast channel is proposed the sum capacity computation relies on a duality between the gaussian vector broadcast channel and the sum power constrained gaussian multiple access channel the numerical algorithm is based on a lagrangian dual decomposition technique and it uses a modified iterative water filling approach for the gaussian multiple access channel the algorithm converges to the sum capacity globally and efficiently

joint spatial division and multiplexing the large scale array regime we propose joint spatial division and multiplexing jsdm an approach to multiuser mimo downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced dimensional channel state information at the transmitter csit jsdm achieves significant savings both in the downlink training and in the csit uplink feedback thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing fdd systems for which uplink downlink channel reciprocity cannot be exploited in the proposed scheme the multiuser mimo downlink precoder is obtained by concatenating a prebeamforming matrix which depends only on the channel second order statistics with a classical multiuser precoder based on the instantaneous knowledge of the resulting reduced dimensional effective channel matrix we prove a simple condition under which jsdm incurs no loss of optimality with respect to the full csit case for linear uniformly spaced arrays we show that such condition is approached in the large number of antennas limit for this case we use szego s asymptotic theory of toeplitz matrices to show that a dft based prebeamforming matrix is near optimal requiring only coarse information about the users angles of arrival and angular spread finally we extend these ideas to the case of a 2 d base station antenna array with 3 d beamforming including multiple beams in the elevation angle direction we provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max min fairness criteria showing extremely attractive performance our numerical results are obtained via asymptotic random matrix theory avoiding lengthy monte carlo simulations and providing accurate results for realistic finite number of antennas and users

no eigenvalues outside the limiting support of generally correlated gaussian matrices this paper investigates the behaviour of the spectrum of generally correlated gaussian random matrices whose columns are zero mean independent vectors but have different correlations under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace following the approach proposed by vallet et al we prove that under some mild conditions there is no eigenvalue outside the limiting support of generally correlated gaussian matrices as an outcome of this result we establish that the smallest singular value of these matrices is almost surely greater than zero from a practical perspective this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication in which this kind of matrices naturally arise

on boson algebras as hopf algebras certain types of generalized undeformed and deformed boson algebras which admit a hopf algebra structure are introduced together with their fock type representations and their corresponding r matrices it is also shown that a class of generalized heisenberg algebras including those underlying physical models such as that of calogero sutherland is isomorphic with one of the types of boson algebra proposed and can be formulated as a hopf algebra

optimal signaling schemes and capacities of non coherent correlated miso channels under per antenna power constraints this paper investigates the optimal signaling schemes and capacities of non coherent correlated multiple input single output miso channels in fast rayleigh fading we consider both channels under per antenna power constraints as well as channels under joint per antenna and sum power constraints for per antenna power constraint channels we first establish the convex and compact properties of the feasible sets and demonstrate the existence of optimal input distribution and the uniqueness of optimal effective magnitude input distribution by exploiting the solutions of a quadratic optimization problem we show that the kuhn tucker condition on the optimal inputs can be simplified to a single dimension as a result we can apply the identity theorem to show the discrete and finite nature of the optimal effective magnitude distribution with a mass point located at the origin by using this distribution we then construct a finite and discrete optimal input vector distribution the use of this input allows us to determine the capacity gain of miso over siso via the phase solutions of a constrained quadratic optimization problem on a sphere which can be obtained using a proposed penalized optimization algorithm we also extend the results to miso channels subject to the joint per antenna and sum power constraints under this consideration it is shown that not all per antenna constraints are active while the finiteness and discreteness of the optimal effective magnitude and the optimal input vector distributions still hold the optimal phases and the optimal power allocation among the transmit antennas need to be determined simultaneously via a quadratic optimization problem under inequality constraints these solutions can finally be used to obtain the miso capacity gain

degrees of freedom of generic block fading mimo channels without a priori channel state information we study the high signal to noise ratio capacity of generic multiple input multiple output mimo rayleigh block fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information but both are aware of the channel statistics in contrast to the well established constant block fading model we allow the fading to vary within each block with a temporal correlation that is generic in the sense used in the interference alignment literature we show that the number of degrees of freedom of a generic mimo rayleigh block fading channel with t transmit antennas and block length n is given by t 1 1 n provided that t n and the number of receive antennas is at least t n 1 n t a comparison with the constant block fading channel where the fading is constant within each block shows that for large block lengths generic correlation increases the number of degrees of freedom by a factor of up to four

low complexity polynomial expansion detector with deterministic equivalents of the moments of channel gram matrix for massive mimo uplink we consider a low complexity polynomial expansion pe detector in a massive multiple input multiple output mimo uplink channel in contrast to most massive mimo systems in the literature where single antenna user equipments ues are assumed multiple antenna ues are employed in this paper moreover the channel between a base station bs and a ue is a jointly correlated rician fading channel the pe detector reduces the computational complexity of the minimum mean square error mmse detector by replacing the matrix inversion with an approximate matrix polynomial the coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel gram matrix we use operator valued free probability which is a more general version of free probability to derive the deterministic equivalents in particular we use the operator valued moment cumulant formula the proposed low complexity pe detector is easy to compute simulation results show that the proposed detector can achieve performance close to the mmse detector

asymptotic and non asymptotic analysis of uplink sum rate for relay assisted mimo cellular systems we consider uplink relay assisted mimo cellular systems with multiple relays deployed in each cell that perform the amplify and forward operations we are interested in obtaining deterministic expressions for the ergodic sum rate of such systems we first consider the large mimo dimension scenario and obtain two asymptotic sum rate expressions corresponding to the cases of fixed number of users and large number of users respectively we then consider the case of arbitrary mimo dimension and large number of users and obtain an upper and lower bound that the sum rate lies in between with high probability the bounds are tight when the number of users is large both single cell and multi cell systems are considered where the latter assumes full base station cooperation numerical experiments show that these deterministic sum rate expressions match well with the monte carlo simulation results therefore they can be useful tools for the design and analysis of relay assisted mimo cellular systems

two stage beamformer design for massive mimo downlink by trace quotient formulation in this paper the problem of outer beamformer design based only on channel statistic information is considered for two stage beamforming for multi user massive mimo downlink and the problem is approached based on signal to leakage plus noise ratio slnr to eliminate the dependence on the instantaneous channel state information a lower bound on the average slnr is derived by assuming zero forcing zf inner beamforming and an outer beamformer design method that maximizes the lower bound on the average slnr is proposed it is shown that the proposed slnr based outer beamformer design problem reduces to a trace quotient problem tqp which is often encountered in the field of machine learning an iterative algorithm is presented to obtain an optimal solution to the proposed tqp the proposed method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics numerical results show that the proposed outer beamformer design method yields significant performance gain over existing methods

zero forcing methods for downlink spatial multiplexing in multiuser mimo channels the use of space division multiple access sdma in the downlink of a multiuser multiple input multiple output mimo wireless communications network can provide a substantial gain in system throughput the challenge in such multiuser systems is designing transmit vectors while considering the co channel interference of other users typical optimization problems of interest include the capacity problem maximizing the sum information rate subject to a power constraint or the power control problem minimizing transmitted power such that a certain quality of service metric for each user is met neither of these problems possess closed form solutions for the general multiuser mimo channel but the imposition of certain constraints can lead to closed form solutions this paper presents two such constrained solutions the first referred to as block diagonalization is a generalization of channel inversion when there are multiple antennas at each receiver it is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high snr the second known as successive optimization is an alternative method for solving the power minimization problem one user at a time and it yields superior results in some e g low snr situations both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined in order to accommodate more general scenarios we also propose a framework for coordinated transmitter receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas while the proposed algorithms are suboptimal they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity

asymptotic analysis of rayleigh product channels a free probability approach the rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of mimo channels in this paper such a performance degradation is investigated via the distribution of mutual information assuming the block fading channels and the uniform power transmission scheme using techniques of free probability theory the asymptotic variance of mutual information is derived when the dimensions of the channel matrices approach infinity in this asymptotic regime the mutual information is rigorously proven to be gaussian distributed using the obtained results a fundamental tradeoff between multiplexing gain and diversity gain of rayleigh product channels under the uniform power transmission can be characterized by the closed form expression at any finite signal to noise ratio numerical results are provided to compare the outage performance between the rayleigh product channels and the conventional rayleigh mimo channels

minimum ber block precoders for zero forcing equalization we determine the linear precoder that minimizes the bit error rate ber at moderate to high signal to noise ratios snrs for block transmission systems with zero forcing zf equalization and threshold detection the design is developed for the two standard schemes for eliminating inter block interference viz zero padding zp and cyclic prefix cp we show that both the zp minimum ber precoder and the cp minimum ber precoder provide substantially lower error rates than standard block transmission schemes such as orthogonal frequency division multiplexing ofdm the corresponding snr gains can be on the order of several decibels we also show that the cp minimum ber precoder can be obtained by a two stage modification of the water filling discrete multitone modulation dmt scheme in which the diagonal water filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete fourier transform dft matrix

energy efficiency scaling law of massive mimo systems massive multi input multi output mimo can support high spectral efficiency with simple linear transceivers and is expected to provide high energy efficiency ee in this paper we analyze the scaling laws of ee with respect to the number of antennas m at each base station of downlink multi cell massive mimo systems under spatially correlated channel where both transmit and circuit power consumptions channel estimation errors and pilot contamination pc are taken into account we obtain the maximal ee for the systems with maximum ratio transmission and zero forcing beamforming for given numbers of antennas and users by optimizing the transmit power subject to the minimal data rate requirement and maximal transmit power constraint the closed form expressions of approximated ee maximal transmit power and maximal ee and their scaling laws with m are derived our analysis shows that the maximal ee scales with m in mathcal o log 2 m m for the system without pc and in mathcal o 1 m for the system with pc the ee maximal transmit power scales up with m in mathcal o sqrt m ln m until reaching the maximal transmit power for the system without pc and in mathcal o 1 for the system with pc the analytical results are validated by simulations under a more realistic 3d channel model

howe duality for the quantum groups uqu m n uqu m a dual pair is defined to be a pair of mutually centralizing subgroups of the real symplectic group let g g be a dual pair of reductive groups in which g is also compact and consider the decomposition of the metaplectic representation of the symplectic group into gg irreducibles each such irreducible is a tensor product of an irreducible of g with one of g and it turns out there is a bijective correspondence between them a particular irreducible of g only occurring with a particular one of g and vice versa this so called howe duality is here generalized to the quantum group case uqu m n uqu m for q not a root of unity a metaplectic representation for this dual pair is given in terms of the q oscillator algebra and a uqu m n uqu m covariant heisenberg weyl algebra is also constructed and realized on fock space the heart of the proof lies in showing that uqu m n and uqu m are essentially mutual commutants on fock space the duality follows using the compactness of uqu m the proof is i

bdma in multicell massive mimo communications power allocation algorithms we investigate power allocation strategies for beam division multiple access transmission in multicell massive multiple input multiple output mimo communications focusing on massive mimo downlink with only statistical channel state information at serving base stations and multiantenna terminals the eigenmatrices of channel transmit covariance matrices become identical and independent of terminals utilizing these eigenmatrices as precoding matrices we consider power allocation of beam domain transmission by treating cochannel user interferences as noises the objective function of achievable ergodic sum rate of the multicell massive mimo downlink reduces to a difference of concave functions we identify the orthogonality conditions for optimal power allocation the results show that the transmit power allocated to the users should be nonoverlapping across beams defined by the channel transmit covariance matrices we present two algorithms to optimize power allocation in the beam space we also prove the convergence of the algorithms and show that the solution obtained by the algorithms satisfies the orthogonality conditions numerical results confirm the efficiency and the improved performance of the proposed algorithms

hierarchical interference mitigation for massive mimo cellular networks we propose a hierarchical interference mitigation scheme for massive mimo cellular networks the mimo precoder at each base station bs is partitioned into an inner precoder and an outer precoder the inner precoder controls the intra cell interference and is adaptive to local channel state information csi at each bs csit the outer precoder controls the inter cell interference and is adaptive to channel statistics such hierarchical precoding structure reduces the number of pilot symbols required for csi estimation in massive mimo downlink and is robust to the backhaul latency we study joint optimization of the outer precoders the user selection and the power allocation to maximize a general concave utility which has no closed form expression we first apply random matrix theory to obtain an approximated problem with closed form objective then using the hidden convexity of the problem we propose an iterative algorithm to find the optimal solution for the approximated problem we also obtain a low complexity algorithm with provable convergence simulations show that the proposed design has significant gain over various state of the art baselines

on wick algebras with additional twisted commutation relations we study the construction of the c symmetric creation and annihilation operators which form a wick algebra with some additional relations this wick algebra is an algebra of the operators which act on the associative algebra of polynomials with noncommutative variables divided by an ideal generated by quadratic relations between the variables as a result the consistency conditions for such a representation are obtained the creators and annihilator have to preserve ideal where which leads us to consistency conditions

on the amount of downlink training in correlated massive mimo channels in this paper we study the effect of downlink dl training on the achievable sum rate of multiuser massive mimo channels with spatial correlations and derive sufficient conditions of the dl channel estimation error covariance matrices that maintain the full multiplexing gain at high data signal to noise ratios snrs given the derived conditions a simple asymptotic upper bound on the average sum rate loss due to channel estimation is obtained we derive in closed form training sequences of limited duration that satisfy these conditions the training duration is variable and increases with the data snr while the sequences lie in a subspace spanned by a variable number of user spatial covariance matrices eigenvectors we additionally study the problem of sequence codebook design and find solutions to this problem for uniform linear and rectangular arrays using asymptotic results for the aforementioned training structure the designed codebooks are observed numerically to be near optimal for a moderate number of base station antennas due to their ability to identify a sufficient limited number of channel directions to train the proposed solutions can substantially reduce dl training overheads while providing achievable rates that are comparable with the rates achieved with perfect channel state information

contractivity properties of ornstein uhlenbeck semigroup for general commutation relations we study a certain class of von neumann algebras generated by selfadjoint elements i a i a i where a i a i satisfy the general commutation relations

optimal precoder design for correlated mimo communication systems using zero forcing decision feedback equalization we consider the design of the precoder for a multi input multi output mimo communication system equipped with a decision feedback equalizer dfe receiver for such design problems perfect knowledge of the channel state information csi at both the transmitter and the receiver is usually required however in the environment of wireless communications it is often difficult to provide sufficiently timely and accurate feedback of csi from the receiver to the transmitter for such designs to be practically viable in this paper we consider the optimum design of a precoder for a wireless communication link having m transmitter antennas and n receiver antennas m n in which the channels are assumed to be flat fading and may be correlated we assume that full knowledge of csi is available at the receiver at the transmitter however only the first and second order statistics of the channels are available our goal here is to come up with an efficient design of the optimal precoder for such a mimo system by minimizing the average arithmetic mean squared error mse of zero forcing zf decision feedback detection subject to a constraint on the total transmitting power applying some of the properties of the matrix parameters this nonconvex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method the performance of the mimo system equipped with this optimum precoder and a zf dfe has also been found to be comparable and in some cases superior to that of v blast which necessitates optimally ordered successive interference cancellation based on the largest postdetection signal to noise ratio snr in terms of tradeoff between performance and implementation simplicity our new system is certainly an attractive alternative

subspace identification for doa estimation in massive full dimension mimo systems bad data mitigation and automatic source enumeration in this paper the direction of arrival doa estimation problem for massive multiple input multiple output mimo systems with a two dimensional 2d array also known as full dimension mimo is investigated assuming no knowledge of path number noise power path gain correlations and bad data statistics based on the variational bayesian framework a novel iterative algorithm for subspace identification operating on tensor represented data is proposed with integrated features of effective bad data mitigation and automatic source enumeration the subspace recovered from the proposed algorithm not only enables existing 2d doa estimators to be readily applied if the number of signal paths is less than the number of horizontal antennas and vertical antennas the subspaces in elevation and azimuth domains can be separately estimated from which one dimensional 1d doa estimators can be utilized thus further lowering the complexity simulation results are presented to illustrate the excellent performance of the proposed subspace recovery method and subsequent doa estimation in terms of accuracy and robustness

secure communications for dual polarized mimo systems to enhance secure communications we deploy the dual polarized antenna arrays at communication nodes of the multi input multioutput mimo system where the base station communicates with multiple legitimate users in the presence of an eavesdropper we also adopt the dual structured precoding in which a preprocessing matrix based on the polarized array spatial correlation and a linear precoding based on the instantaneous channel state information csi are concatenated we design this dual structured multiuser linear precoding under three cases in the first case given perfect global csi the secrecy rate optimization problem is formulated and transformed into the weighted minimum mean square error mse problem which can be effectively solved by the block coordinate decent method in the second case where the eavesdropper s csi is unavailable an artificial noise is generated to confuse the eavesdropper by minimizing the information transmit power subject to a preset mse threshold for the recovered confidential signals which can be solved by an efficient iterative algorithm in the third case of imperfect global csi the robust optimization for secure communications is performed by minimizing the largest received mse among the users subject to the total transmit power constraint which can be reformulated into a biconvex semidefinite programming problem and solved by an efficient alternating convex optimization simulation results are included to demonstrate the excellent performance of our proposed designs over the conventional single polarized array based designs in terms of achievable secrecy rate minimum transmit power and the mse of recovered confidential signals

downlink training sequence design for fdd multiuser massive mimo systems we consider the problem of downlink training sequence design for frequency division duplex multiuser massive multiple input multiple output systems in the general case where users have distinct spatial correlations the training sequences leverage spatial correlations and are designed to minimize the channel estimation weighted sum mean square error mse under the assumption that users employ minimum mse estimators noting that the weighted sum mse function is invariant to unitary rotations of its argument a solution is obtained using a steepest descent method on the grassmannian manifold we extend the proposed design to scenarios with temporal correlations combined with kalman filters at the users and design sequences exploiting the multiuser spatio temporal channel structure finally we consider scenarios where only a limited number of bits b are available at the base station bs to inform the users of each chosen sequence e g sequences are chosen from a set of 2 b vectors known to the bs and users and develop a subspace version of matching pursuit techniques to choose the desired sequences simulation results using realistic channel models show that the proposed solutions improve user fairness with a proper choice of weights lead to accurate channel estimates with training durations that can be much smaller than the number of bs antennas and show substantial gains over randomly chosen sequences for even small values of b

a duality for endomorphisms of von neumann algebras we consider endomorphisms of von neumann algebras let m be a von neumann algebra represented on a hilbert space h and let m be the corresponding commutant let end m be given and suppose m has a cyclic vector in h such that the corresponding state leaves invariant then there is a dual completely positive mapping on m which we find and describe each of the two and has an associated spectral group and we show that the group for is contained in that for we consider the following three restrictions on i is a shift on m ii is strongly ergodic and iii is ergodic we give spectral theoretic conditions on using the two groups described above to fall into each of the three classes we also show that the two groups are conjugacy invariants and we discuss the case of cocycle conjugacy

amplify and forward in wireless relay networks rate diversity and network size a wireless network with fading and a single source destination pair is considered the information reaches the destination via multiple hops through a sequence of layers of single antenna relays at high signal to noise ratio snr the simple amplify and forward strategy is shown to be optimal in terms of degrees of freedom because it achieves the degrees of freedom equal to a point to point multiple input multiple output mimo system hence the lack of coordination in relay nodes does not reduce the achievable degrees of freedom the performance of this amplify and forward strategy degrades with increasing network size this phenomenon is analyzed by finding the tradeoffs between network size rate and diversity a lower bound on the diversity multiplexing tradeoff for concatenation of multiple random gaussian matrices is obtained also it is shown that achievable network size in the outage formulation short codes is a lot smaller than the ergodic formulation long codes

a finite element method for the numerical solution of the coupled cahn hilliard and navier stokes system for moving contact line problems in this paper a semi implicit finite element method is presented for the coupled cahn hilliard and navier stokes equations with the generalized navier boundary condition for the moving contact line problems in our method the system is solved in a decoupled way for the cahn hilliard equations a convex splitting scheme is used along with a p1 p1 finite element discretization the scheme is unconditionally stable a linearized semi implicit p2 p0 mixed finite element method is employed to solve the navier stokes equations with our method the generalized navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way the efficiency and capacity of the present method are well demonstrated with several numerical examples

quantum spin chains with quantum group symmetry we consider actions of quantum groups on lattice spin systems we show that if an action of a quantum group respects the local structure of a lattice system it has to be an ordinary group even allowing weakly delocalized quasi local tails of the action we find that there are no actions of a properly quantum group commuting with lattice translations the non locality arises from the ordering of factors in the quantum groupc algebra and can be made one sided thus allowing semi local actions on a half chain under such actions localized quantum group invariant elements remain localized hence the notion of interactions invariant under the quantum group and also under translations recently studied by many authors makes sense even though there is no global action of the quantum group we consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state under weak locality assumptions its gns representation carries no unitary representation of the quantum group

exclusion statistics operator algebras and fock space representations we study exclusion statistics within the second quantized approach we consider operator algebras with positive definite fock space and restrict them in a such a way that certain state vectors in fock space are forbidden ab initio we describe three characteristic examples of such exclusion namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space e g the calogero sutherland type of exclusion statistics exclusion in the single oscillator fock space where some states in single oscillator fock space are forbidden e g the gentile realization of exclusion statistics and a combination of these two exclusions e g green s realization of para fermi statistics for these types of exclusions we discuss the extended haldane statistics parameters g recently introduced by two of us in 1996 mod phys lett a 11 3081 and associated counting rules within these three types of exclusions in fock space the original haldane exclusion statistics cannot be realized

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

the spectrum of the algebra of skew differential operators and the irreducible representations of the quantum heisenberg algebra the left spectrum of a wide class of the algebras of skew differential operators is described as a sequence we determine and classify all the algebraically irreducible representations of the quantum heisenberg algebra over an arbitrary field

minimality of the data in wavelet filters abstract orthogonal wavelets or wavelet frames for l2 r are associated with quadrature mirror filters qmf a set of complex numbers which relate the dyadic scaling of functions on r to the z translates in this paper we show that generically the data in the qmf systems of wavelets are minimal in the sense that the data cannot be nontrivially reduced the minimality property is given a geometric formulation in the hilbert space l2 z and it is then shown that minimality corresponds to irreducibility of a wavelet representation of the algebra o 2 and so our result is that this family of representations of o 2 on the hilbert space l2 z is irreducible for a generic set of values of the parameters which label the wavelet representations

phase only rf precoding for massive mimo systems with limited rf chains massive mimo systems promise high spectrum efficiency by deploying m 1 antennas at the base station bs however to achieve the full gain provided by massive mimo the bs requires m radio frequency rf chains which are expensive this motivates us to consider rf chain limited massive mimo systems with m antennas but only s m rf chains we propose a two stage precoding scheme to efficiently exploit the large spatial degree of freedom dof gain in massive mimo systems with limited rf chains and reduced channel state information csi signaling overhead in this scheme the mimo precoder is partitioned into a high dimensional phase only rf precoder followed by a low dimensional baseband precoder the rf precoder is adaptive to the spatial correlation matrices for inter cluster interference mitigation the baseband precoder is adaptive to the reduced dimensional effective csi for intra cluster spatial multiplexing we formulate the two stage precoding problem such that the minimum weighted average data rate of users is maximized under the phase only constraint on the rf precoder and the limited rf chain constraint this is a combinatorial optimization problem which is in general np hard we propose a low complexity solution based on a novel bi convex approximation approach simulations show that the proposed design has significant gain over various baselines

uniform h2 regularity of solution for the 2d navier stokes cahn hilliard phase field model abstract in this paper we provide the uniform h 2 regularity results with respect to small perturbation parameter e of the solution and its time derivative for the 2d navier stokes cahn hilliard phase field model with t 0 based on sharp a priori estimates for the solution of model under weak assumptions on the initial values we show that the h 2 regularity of the solution and its time derivative depends on e 1 but is independent of time t

statistical 3 d beamforming for large scale mimo downlink systems over rician fading channels in this paper we investigate a downlink transmission algorithm for single cell multiuser systems with two dimensional 2 d large scale antenna array at the base station bs over rician fading channels we first derive some properties of the channel s line of sight los component in the large scale antenna array scenario next based on these properties and under the assumption of only statistical channel state information csi i e the los component and rician k factor at the bs we derive the optimal beamforming vector for each user in maximizing an approximation of the ergodic sum rate the main guidelines for user scheduling are also presented then a three dimensional 3 d beamforming downlink transmission algorithm exploiting only the statistical csi of each user is proposed for this algorithm we derive an exact analytical closed form expression for the achievable ergodic rate and present tractable approximations based on our analysis we gain some valuable insights the proposed algorithm is shown to perform well in achieving considerable sum rate while requiring much less csi at the bs it requires three scalar values at the bs for each user and can achieve an ergodic sum rate closer to the ergodic sum rate achieved by the matched filter precoding with perfect csi at the bs

improved subspace estimation for multivariate observations of high dimension the deterministic signals case we consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude in this context traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones it has recently been suggested that this situation where the sample size is small compared to the observation dimension can be very accurately modeled by considering the asymptotic regime where the observation dimension m and the number of snapshots n converge to at the same rate using large random matrix theory results it can be shown that traditional subspace estimates are not consistent in this asymptotic regime furthermore new consistent subspace estimate can be proposed which outperform the standard subspace methods for realistic values of m and n the work carried out so far in this area has always been based on the assumption that the observations are random independent and identically distributed in the time domain the goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals in practice this allows to use the proposed approach regardless of the statistical properties of the source signals in order to construct the proposed estimators new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of information plus noise complex gaussian models are established these results are believed to be of independent interest

on commutators of wick products on ccr and car algebras in this paper we study the q commutator of wick products on the ccr canonical commutation relation algebra and on the car canonical anticommutation relation algebra we obtain a formula on q commutator of wick products in terms of wick products of monomials of lower order moreover we give a relation of double q commutator

efficient numerical methods for simulating surface tension of multi component mixtures with the gradient theory of fluid interfaces abstract surface tension significantly impacts subsurface flow and transport and it is the main cause of capillary effect a major immiscible two phase flow mechanism for systems with a strong wettability preference in this paper we consider the numerical simulation of the surface tension of multi component mixtures with the gradient theory of fluid interfaces major numerical challenges include that the system of the euler lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite we construct a linear transformation to reduce the euler lagrange equations and naturally introduce a path function which is proven to be a monotonic function of the spatial coordinate variable by using the linear transformation and the path function we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions moreover the computation of the surface tension is also simplified the proposed methods do not need to solve the differential equation system and they are easy to be implemented in practical applications numerical examples are tested to verify the efficiency of the proposed methods

how much does transmit correlation affect the sum rate scaling of mimo gaussian broadcast channels this paper considers the effect of spatial correlation between transmit antennas on the sum rate capacity of the mimo gaussian broadcast channel i e downlink of a cellular system specifically for a system with a large number of users n we analyze the scaling laws of the sum rate for the dirty paper coding and for different types of beamforming transmission schemes when the channel is i i d it has been shown that for large n the sum rate is equal to m log log n m log p m o 1 where m is the number of transmit antennas p is the average signal to noise ratio and o 1 refers to terms that go to zero as n rarr infin when the channel exhibits some spatial correlation with a covariance matrix r non singular with tr r m we prove that the sum rate of dirty paper coding is m log log n m log p m log det r o 1 we further show that the sum rate of various beamforming schemes achieves m log log n m log p m m log c o 1 where c les 1 depends on the type of beamforming we can in fact compute c for random beamforming proposed in and more generally for random beamforming with preceding in which beams are pre multiplied by a fixed matrix simulation results are presented at the end of the paper

average sep optimal precoding for correlated massive mimo with zf detection an asymptotic analysis this paper investigates the symbol error probability sep of point to point massive multiple input multiple output mimo systems using equally likely pam psk and square qam signallings in the presence of transmitter correlation the receiver has perfect knowledge of the channel coefficients while the transmitter only knows first and second order channel statistics with a zero forcing zf detector implemented at the receiver side we design and derive closed form expressions of the optimal precoders at the transmitter that minimizes the average sep over channel statistics for various modulation schemes we then unveil some nice structures on the resulting minimum average sep expressions which naturally motivate us to explore the use of two useful mathematical tools to systematically study their asymptotic behaviors the first tool is the szego s theorem on large hermitian toeplitz matrices and the second tool is the well known limit lim x to infty 1 1 x x e the application of these two tools enables us to attain very simple expressions of the sep limits as the number of the transmitter antennas goes to infinity a major advantage of our asymptotic analysis is that the asymptotic sep converges to the true sep when the number of antennas is moderately large as such the obtained expressions can serve as an effective sep approximations for massive mimo systems even when the number of antennas is not very large for the widely used exponential correlation model we derive closed form expressions for the sep limits of both optimally precoded and uniformly precoded systems extensive simulations are provided to demonstrate the effectiveness of our asymptotic analysis and compare the performance limit of optimally precoded and uniformly precoded systems

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

network mimo with linear zero forcing beamforming large system analysis impact of channel estimation and reduced complexity scheduling we consider the downlink of a multicell system with multiantenna base stations and single antenna user terminals arbitrary base station cooperation clusters distance dependent propagation pathloss and general fairness requirements base stations in the same cooperation cluster employ joint transmission with linear zero forcing beamforming subject to sum or per base station power constraints intercluster interference is treated as noise at the user terminals analytic expressions for the system spectral efficiency are found in the large system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio in particular for the per base station power constraint we find new results in random matrix theory yielding the squared frobenius norm of submatrices of the moore penrose pseudo inverse for the structured non i i d channel matrix resulting from the cooperation cluster user distribution and path loss coefficients the analysis is extended to the case of nonideal channel state information at the transmitters obtained through explicit downlink channel training and uplink feedback specifically our results illuminate the trade off between the benefit of a larger number of cooperating antennas and the cost of estimating higher dimensional channel vectors furthermore our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large system results depending on the desired fairness criterion the proposed scheme performs close to the optimal finite dimensional opportunistic user selection while requiring significantly less channel state feedback since only a small fraction of preselected users must feed back their channel state information

adaptive mixed hybrid and penalty discontinuous galerkin method for two phase flow in heterogeneous media in this paper we present a hybrid method which consists of a mixed hybrid finite element method and a penalty discontinuous galerkin method for the approximation of a fractional flow formulation of a two phase flow problem in heterogeneous media with discontinuous capillary pressure the fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients for the wetting phase pressure equation the continuous mixed hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous while it can reduce the computational cost by using less degrees of freedom and avoiding the post processing of velocity reconstruction this method can also keep several good properties of the discontinuous galerkin method which are important to the fractional flow formulation such as the local mass balance continuous normal flux and capability of handling the discontinuous capillary pressure for the wetting phase saturation equation the penalty discontinuous galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation furthermore an adaptive algorithm for the hybrid method together with the centroidal voronoi delaunay triangulation technique is proposed five numerical examples are presented to illustrate the features of proposed numerical method such as the optimal convergence order the accurate and efficient velocity approximation and the applicability to the simulation of water flooding in oil field and the oil trapping or barrier effect phenomena