adaptive approximation of solutions to problems with multiple layers by chebyshev pseudo spectral methods we develop and analyze a family of mappings which enhance the accuracy of chebyshev pseudo spectral methods in approximating functions with multiple regions of localized rapid variation layers the mapping family depends on 3n minus 1 free parameters where n is the number of layers n parameters depend upon the locations of the layers and on the widths of the layers while the other n minus 1 parameters depend on the resolution of each layer relative to the first layer the parameters can be determined adaptively by minimizing a functional which measures the error of the approximation techniques to simplify the minimization process are developed we further demonstrate that the appropriate choice of mappings can lead to a significant reduction in the condition number of matrices associated with chebyshev pseudo spectral differentation we illustrate the effectiveness of the proposed mapping and adaptive procedure by examples in which we approximate i given functions exhibiting multiple layers and ii the solution of a system of partial differential equations modeling combustion in counterflowing jets so that two distinct flames occur 24 refs 8 figs 5 tabs

transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

linear precoding bounds for wyner type cellular networks with limited base station cooperation and dynamic clustering this work studies the achievable average data rate in the downlink of a wyner type linear cellular network with limited cooperation and linear precoders we derive upper and lower bounds on the achievable average data rate subject to an average power constraint the bounds show that even a small number of cooperating base stations applying suboptimal linear precoding can approach optimal performance and significantly increase the average user data rates as compared to those achievable with noncooperating cellular systems we highlight the importance of dynamic clustering and of base station bs silencing dynamic clustering allows the system to build clusters that benefit some users at the expense of others and then shifts the priority between the users such a scheme results in higher average rates for all users while meeting some level of fairness bs silencing is shown to be important for limited cooperation networks in the high snr regime silencing is a simple and efficient way to reduce the interference and hence increase the user rates without increasing the number of cooperating bss the theoretical analysis is accompanied by several numerical examples in selected scenarios

multi cell mimo downlink with cell cooperation and fair scheduling a large system limit analysis we consider the downlink of a cellular network with multiple cells and multi antenna base stations our model includes distance dependent pathloss arbitrary clusters of cooperating cells and general fairness requirements beyond monte carlo simulation no efficient computation method to evaluate the ergodic throughput of such systems has been presented yet furthermore for systems of practical size with tens of cells and hundreds of users per cell even simulation becomes challenging we develop an analytic framework based on the combination of results from large random matrix theory and convex optimization this allows computationally efficient calculation of the system performance in the so called large system limit i e in the limit of a large number of antennas per base station and a large number of users per cell while the ratio of antennas per user is kept constant in particular the system ergodic throughput subject to per base station power constraints and to general fairness criteria is obtained via the iterative solution of a system of fixed point equations comparisons with finite dimensional simulation results show that the large system analysis provides remarkably accurate approximations for the actual finite dimensional systems even for a small number of users and base station antennas

scaling results on the sum capacity of cellular networks with mimo links scaling results for the sum capacity of the multiple access uplink channel are provided for a flat fading environment with multiple input multiple output mimo links when there is interference from other cells the classical mimo scaling regime is considered in which the number of antennas per user and per base station grow large together utilizing the known characterizations of the limiting eigenvalue distributions of large random matrices the asymptotic behavior of the sum capacity of the system is characterized for an architecture in which the base stations cooperate in the joint decoding process of all users macrodiversity this asymptotic sum capacity is compared with that of the conventional scenario in which the base stations only decode the users in their cells for the case of base station cooperation an interesting resource pooling phenomenon is observed in some cases the limiting performance of a macrodiversity multiuser network has the same asymptotic behavior as that of a single user mimo link with an equivalent amount of pooled received power this resource pooling phenomenon allows us to derive an elegant closed form expression for the sum capacity of a new version of wyner s classical model of a cellular network in which mimo links are incorporated into the model

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

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

cellular interference alignment interference alignment promises that in gaussian interference channels each link can support half of a degree of freedom dof per pair of transmit receive antennas however in general this result requires to precode the data bearing signals over a signal space of asymptotically large diversity e g over an infinite number of dimensions for time frequency varying fading channels or over an infinite number of rationally independent signal levels in the case of time frequency invariant channels in this paper we consider a wireless cellular system scenario where the promised optimal dofs are achieved with linear precoding in one shot i e over a single time frequency slot we focus on the uplink of a symmetric cellular system where each cell is split into three sectors with orthogonal intrasector multiple access in our model interference is local i e it is due to transmitters in neighboring cells only we consider a noniterative local cooperation scheme where base stations pass to their neighbors their decoded messages such that interference from already decoded messages can be canceled therefore for a given decoding order the interference between sectors is described by a directed locally connected graph the problem consists of maximizing the per sector dofs over all possible decoding orders and precoding schemes in particular we provide a decoding order and a one shot interference alignment scheme able to achieve optimal per sector dofs up to an additive gap due to boundary effects that vanishes as the size of the network becomes large then we extend our treatment by considering the case of intersector interference with joint processing of the three sector at each cell site in order to avoid signaling schemes relying on the strength of interference we further introduce the notion of topologically robust schemes which are able to guarantee a minimum rate or dofs irrespectively of the strength of the interfering links toward this end we design a different decoding order and alignment scheme which is topologically robust and still achieves the same optimum dofs finally we provide a new scheme for the downlink based on local base station cooperation where base stations pass to their neighbors a quantized version of their dirty paper coded signals for the proposed downlink scheme we can prove a dofs duality result showing that for an appropriate choice of the precoding order and of the alignment beamforming vectors it can achieve the same per sector dofs of the corresponding uplink schemes

a deterministic equivalent for the analysis of non gaussian correlated mimo multiple access channels using large dimensional random matrix theory rmt we conduct mutual information analysis of a multiple input multiple output mimo multiple access channel mac our channel model reflects the characteristics in small cell networks where antenna correlations line of sight components and general type of fading distributions have to be included the mutual information expression can be expressed as functionals of the stieltjes transform through the so called shannon transform ideally if the stieltjes transform is known in the context of the large dimensional rmt then the problem is solved however it is difficult to derive the stieltjes transform of the considered channel models directly especially when the transmit correlation matrices are generally nonnegative definite and the channel entries are non gaussian to overcome this we use the generalized lindeberg principle to show that the stieltjes transforms of this class of random matrices with gaussian or non gaussian independent entries coincide in the large dimensional regime this result permits to derive the deterministic equivalents e g the stieltjes transform and the ergodic mutual information for non gaussian mimo channels from the known results developed for gaussian mimo channels as an application we determine the capacity achieving input covariance matrices for the mimo macs and prove that the capacity achieving input covariance matrices are asymptotically independent of the fading distribution

shannon theoretic approach to a gaussian cellular multiple access channel with fading shannon theoretic limits on the achievable throughput for a simple infinite cellular multiple access channel mac model wyner 1994 in the presence of fading are presented in this model which is modified to account for flat fading the received signal at a given cell site s antenna is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor spl alpha spl isin 0 1 times the sum of the faded signals received from the adjacent cells accompanied by gaussian additive noise this model serves as a tractable model providing considerable insight into complex and analytically intractable real world cellular communications both linear and planar cellular arrays are considered with exactly k active users in each cell we assume a hyper receiver jointly decoding all of the users incorporating the received signals from all of the active cell sites the hyper receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system in this work we consider the intracell time division multiple access tdma and the wideband wb protocols we focus on the maximum reliably transmitted equal rate bounds to this rate are found for the intracell tdma protocol by incorporating information theoretic inequalities and the chebyshev markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices we demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a rayleigh distribution i e rayleigh fading for this special case we observe the rather surprising result that fading may increase the maximum equal rate for a certain range of spl alpha as compared to the nonfaded case in this setting the wb strategy which achieves the maximum reliable equal rate of the model is proved to be superior to the tdma scheme an upper bound to the maximum equal rate of the wb scheme is also obtained this bound is asymptotically tight when the number of users is large k spl gt 1 the asymptotic bound shows that the maximum equal rate of the wb scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor spl alpha spl isin 0 1 signal to noise ratio snr values this result is found to be independent of the statistics of the fading coefficients

adaptive pseudospectral solution of a diffuse interface model a diffuse interface type model using an energy based variational formulation with a free energy that is a function of the density and its gradients is presented all of the boundary terms are retained and related to external surface forces which can be of particular interest when considering the fluid fluid solid region the numerical solution of these types of problems can be troublesome if a thin transition layer is desired here chebyshev pseudospectral methods with mesh adaptation for the solution of diffuse interface type problems are studied a mesh adaptation algorithm based in the equidistribution principle following a continuation process is derived in order to achieve high precision for problems exhibiting thin transition layers a modified version of the arc length monitor function is proposed which yields a sufficiently smooth coordinate transformation at every step of the continuation process a fixed number of iterations is implemented so that the equidistribution equations are not solved completely at each step which saves a considerable amount of computational effort numerical results for the static phase field model exhibiting thin transition layers are presented

video coding scheme using dct pyramid vector quantization a new and effective video coding scheme for contribution quality is proposed the cmtt 2 a joint committee of ccir and ccitt has proposed a video coding scheme already approved at european level by ets working at 34 45 mbit s basically this proposal includes a dct transform for spatial correlation removal and motion compensation for temporal correlation removal the individual transform coefficients are then scalar quantized with a non uniform bit assignment starting from the cmtt 2 proposal the study presents a new video coding scheme designed using a vector quantizer solution instead of the scalar one specifically the pyramid vector quantization pvq has been chosen as the vector quantization method as it is able to reduce the dct coefficients laplacian distribution simulation results show that the proposed video coding scheme gives the same contribution quality at 22 mbit s as the one obtained with the cmtt 2 proposal at 45 mbit s

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

geometric source coding and vector quantization a geometric formulation is presented for source coding and vector quantizer design motivated by the asymptotic equipartition principle the authors consider two broad classes of source codes and vector quantizers elliptical codes and quantizers based on the gaussian density function and pyramid codes and quantizers based on the laplacian density function elliptical and weighted pyramid vector quantizers are developed by selecting codewords as points in a lattice that lie on or near a specified ellipse or pyramid the combination of geometric structure and lattice basis allows simple encoding and decoding algorithms

solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post processing a coordinate transformation approach is described that enables pseudospectral methods to be applied efficiently to unsteady differential problems with steep solutions the work is an extension of a method presented by mulholland huang and sloan for the adaptive pseudospectral solution of steady problems a coarse grid is generated by a moving mesh finite difference method that is based on equidistribution and this grid is used to construct a time dependent coordinate transformation a sequence of spatial transformations may be generated at discrete points in time or a single transformation may be generated as a continuous function of space and time the differential problem is transformed by the coordinate transformation and then solved using a method that combines pseudospectral discretisation in space with a suitable integrator in time numerical results are presented for unsteady problems in one space dimension

error resilient pyramid vector quantization for image compression pyramid vector quantization pvq uses the lattice points of a pyramidal shape in multidimensional space as the quantizer codebook it is a fixed rate quantization technique that can be used for the compression of laplacian like sources arising from transform and subband image coding where its performance approaches the optimal entropy coded scalar quantizer without the necessity of variable length codes in this paper we investigate the use of pvq for compressed image transmission over noisy channels where the fixed rate quantization reduces the susceptibility to bit error corruption we propose a new method of deriving the indices of the lattice points of the multidimensional pyramid and describe how these techniques can also improve the channel noise immunity of general symmetric lattice quantizers our new indexing scheme improves channel robustness by up to 3 db over previous indexing methods and can be performed with similar computational cost the final fixed rate coding algorithm surpasses the performance of typical joint photographic experts group jpeg implementations and exhibits much greater error resilience

3 d wave simulation in anelastic media using the kelvin voigt constitutive equation we design a numerical algorithm for wave simulation in anelastic media in the presence of free surface which can be used to model seismic waves at the earth s surface and ultrasonic waves in heterogeneous materials the stress strain relation is based on the kelvin voigt mechanical model which has the advantage of not requiring additional field variables the model requires two anelastic parameters and twice the spatial derivatives of the lossless case the high frequency components of the wave field are more attenuated than the low frequency components with the attenuation factors being approximately proportional to the square of the frequency the modeling simulates 3 d waves by using the fourier and chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions respectively we stretch the mesh in the vertical direction to increase the minimum grid spacing and reduce the computational cost instabilities of the chebyshev differential operator due to the implementation of the free surface boundary conditions are solved with a characteristic approach where the characteristic variables are evaluated at the source central frequency the results of the modeling are verified by comparisons to the analytical solutions for lamb s problem and propagation in unbounded homogeneous media examples illustrating the propagation of rayleigh and love waves are presented

sum capacity of gaussian vector broadcast channels this paper characterizes the sum capacity of a class of potentially nondegraded gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers coordination is allowed among the transmit terminals but not among the receive terminals the sum capacity is shown to be a saddle point of a gaussian mutual information game where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information the sum capacity is achieved using a precoding strategy for gaussian channels with additive side information noncausally known at the transmitter the optimal precoding structure is shown to correspond to a decision feedback equalizer that decomposes the broadcast channel into a series of single user channels with interference pre subtracted at the transmitter

a dynamical pseudo spectral domain decomposition technique a dynamical spectral domain decomposition method is presented in each subdomain a transformation of coordinate is used both the locations of the interfaces and the parameters of the mappings are dynamically adapted by minimizing theh 2 norm of the calculated solution we show on some functions that the total norm of the chebyshev series depends on the location of the interfaces moreover there exists a minimum that defines the best location of the interface this defines a dynamical generation of chebyshev collocation points this numerical method is applied on partial differential equations and it is shown that both the overall accuracy and the matching at the interfaces are improved with respect to a fixed interface calculation this algorithm is then used for the numerical solution of the time dependent full navier stokes equations the solution technique consists in a fourier chebyshev collocation method combined with a matching method the computational domain is decomposed into subdomains in the vertical direction in each subdomain a coordinate transform is used and the locations of the interfaces are dynamically determined the elliptic problems coming from the viscous terms are solved by means of the chebyshev acceleration method density is matched with an upwind procedure whereas the velocities the temperature and the concentration are handled with the influence matrix method numerical examples are carried out on the compressible kelvin helmholtz and rayleigh taylor flows

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

impact of antenna correlation on the capacity of multiantenna channels this paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels the analysis is not restricted to the popular separable correlation model but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature for arbitrary signal to noise ratios snr the characterization is conducted in the regime of large numbers of antennas for the low and high snr regions in turn we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power bandwidth and rate

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