capacity scaling in mimo wireless systems under correlated fading previous studies have shown that single user systems employing n element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n assuming independent rayleigh fading between antenna pairs we explore the capacity of dual antenna array systems under correlated fading via theoretical analysis and ray tracing simulations we derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases the latter is derived under some assumptions about the scaling of the fading correlation structure in both cases the theoretic capacity growth is linear in n but the growth rate is 10 20 smaller in the presence of correlated fading we analyze our assumption of separable transmit receive correlations via simulations based on a ray tracing propagation model results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n 16 we present results for both the cases when the transmitter does and does not know the channel realization

optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information we study the optimal transmission strategy of a multiple input single output miso wireless communication link the receiver has perfect channel state information csi while the transmitter has different types of csi i e either perfect csi or no csi or long term knowledge of the channel covariance matrix for the case in which the transmitter knows the channel covariance matrix it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix however the optimal eigenvalues are difficult to compute we derive a characterization of the optimum power allocation furthermore we apply this result to provide an efficient algorithm which computes the optimum power allocation in addition to this we analyze the impact of correlation on the ergodic capacity of the miso system with different csi schemes at first we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated next we show that the ergodic capacity with perfect csi and without csi at the transmitter is schur concave i e the more correlated the transmit antennas are the less capacity is achievable in addition we show that the ergodic capacity with covariance knowledge at the transmitter is schur convex with respect to the correlation properties these results completely characterize the impact of correlation on the ergodic capacity in miso systems furthermore the capacity loss or gain due to correlation is quantified for no csi and perfect csi at the transmitter the capacity loss due to correlation is bounded by some small constant whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix finally we illustrate all theoretical results by numerical simulations

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

efficient geostatistical inverse methods for structured and unstructured grids 1 the geostatistical inverse approach of kitanidis 1995 requires the covariance matrix of a discretized spatial random variable and matrix multiplications of the covariance matrix the explicit computation of the full covariance matrix is prohibitive for large scale problems discrete spectral methods which help to reduce computational costs dramatically are restricted to regular grids to make the geostatistical inverse approach applicable to unstructured grids which may be of great interest for practical applications we use the functional parameterization of the spatial random field by the karhunen loeve kl expansion in which the spatial variable is parameterized by weighted base functions that are derived from the covariance function in the inverse approach the estimation of the spatial variable becomes estimating the weights of base functions the prior covariance matrix of the weights is the identity matrix the base functions are continuous in space and can be discretized in any fashion for the derivation of the base functions we embed the domain into a larger unit cell of a periodic domain then the base functions are sinusoidal and can be derived by spectral methods which are independent of the discretization used for forward and inverse modeling for illustration we present case studies using synthetic data to estimate hydraulic conductivities on regular and unstructured grids the results show that we can efficiently obtain a good estimate using the inverse method in conjunction with the kl expansion we also demonstrate how to estimate structural parameters and to generate conditional realizations in the framework of our method

the secrecy capacity of the mimo wiretap channel we consider the mimo wiretap channel that is a mimo broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver while the other user is an eavesdropper perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate while insuring that the eavesdropper gets zero bits of information in this paper we compute the perfect secrecy capacity of the multiple antenna mimo broadcast channel where the number of antennas is arbitrary for both the transmitter and the two receivers our technique involves a careful study of a sato like upper bound via the solution of a certain algebraic riccati equation

characterizing the statistical properties of mutual information in mimo channels we consider gaussian multiple input multiple output mimo frequency selective spatially correlated fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver for gaussian codebooks using results from multivariate statistics we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal to noise ratio snr we show that our bound is tighter than previously reported analytical lower bounds and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity based on a closed form approximation of the variance of mutual information in correlated flat fading mimo channels we provide insights into the multiplexing diversity tradeoff for gaussian code books furthermore for a given total number of antennas we consider the problem of finding the optimal ergodic capacity maximizing number of transmit and receive antennas and we reveal the snr dependent nature of the maximization strategy finally we present numerical results and comparisons between our capacity bounds and previously reported bounds

secure transmission with multiple antennas part ii the mimome wiretap channel the capacity of the gaussian wiretap channel model is analyzed when there are multiple antennas at the sender intended receiver and eavesdropper the associated channel matrices are fixed and known to all the terminals a computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem the converse is based on a sato type argument used in other broadcast settings and the coding theorem is based on gaussian wiretap codebooks at high signal to noise ratio snr the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition and independently coding across the resulting parallel channels the associated capacity is expressed in terms of the corresponding generalized singular values it is shown that a semi blind masked multi input multi output mimo transmission strategy that sends information along directions in which there is gain to the intended receiver and synthetic noise along directions in which there is not can be arbitrarily far from capacity in this regime necessary and sufficient conditions for the secrecy capacity to be zero are provided which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed the resulting scaling laws establish that to prevent secure communication the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly and that the optimum division of antennas between sender and intended receiver is in the ratio of 2 1

a stochastic projection method for fluid flow i basic formulation we describe the construction and implementation of a stochastic navier stokes solver the solver combines a spectral stochastic uncertainty representation scheme with a finite difference projection method for flow simulation the uncertainty quantification scheme is adapted from the spectral stochastic finite element method ssfem which is based on regarding uncertainty as generating a new dimension and the solution as being dependent on this dimension in the ssfem formalism the stochastic dependence is represented in terms of the polynomial chaos system and the coefficients in the corresponding spectral representation are obtained using a galerkin approach it is shown that incorporation of the spectral uncertainty representation scheme into the projection method results in a coupled system of advection diffusion equations for the various uncertainty fields and in a decoupled system of pressure projection steps this leads to a very efficient stochastic solver whose advantages are illustrated using steady and transient simulations of transport and mixing in a microchannel

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

on the ergodic secret key agreement over spatially correlated multiple antenna channels with public discussion we consider secret key agreement with public discussion over multiple input multiple output mimo rayleigh fast fading channels under correlated environment we assume that transmit legitimate receiver and eavesdropper antennas are correlated the legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge while the transmitter has only knowledge of the correlation matrices first we derive the expression of the secret key capacity under the considered setup we prove that the optimal transmit strategy achieving the secret key capacity consists in transmitting independent gaussian signals along the eingenvectors of the transmit correlation matrix the powers allocated to each channel mode are determined as the solution to a numerical optimization problem a necessary and sufficient condition for beamforming i e transmitting along the strongest channel mode to be capacity achieving is derived moreover we analyze the impact of correlation matrices on the system performance finally we study the system s performance in the two extreme power regimes in the high power regime we provide closed form expressions of the gain loss due to correlation in the low signal to noise ratio snr regime we investigate the energy efficiency of the system by determining the minimum energy required for sharing a secret key bit and the wideband slope while highlighting the impact of correlation matrices

secure communication in the low snr regime secrecy capacity of a multiple antenna wiretap channel is studied in the low signal to noise ratio snr regime expressions for the first and second derivatives of the secrecy capacity with respect to snr at snr 0 are derived transmission strategies required to achieve these derivatives are identified in particular it is shown that it is optimal in the low snr regime to transmit in the maximal eigenvalue eigenspace of hm hm nm ne he he where hm and he denote the channel matrices associated with the legitimate receiver and eavesdropper respectively and nm and ne are the noise variances at the receiver and eavesdropper respectively energy efficiency is analyzed by finding the minimum bit energy required for secure and reliable communications and the wideband slope increased bit energy requirements under secrecy constraints are quantified finally the impact of fading is investigated and the benefits of fading in terms of energy efficiency are shown

l p boundedness of wave operators for two dimensional schrodinger operators let be the two dimensional schrodinger operator with the real valued potential v which satisfies the decay condition at infinity for we show that the wave operators are bounded in for any 1 p under the condition that h has no zero bound states or zero resonance extending the corresponding results for higher dimensions as w intertwine h 0 and the absolutely continuous part h p ac of h f h p ac w f h 0 w for any borel function f on 1 this reduces the various l p mapping properties of f h p ac to those of f h 0 the convolution operator by the fourier transform of the function f 2

rkc an explicit solver for parabolic pdes the fortran program rkc is intended for the time integration of parabolic partial differential equations discretized by the method of lines it is based on a family of runge kutta chebyshev formulas with a stability bound that is quadratic in the number of stages remarkable properties of the family make it possible for the program to select at each step the most efficient stable formula as well as the most efficient step size moreover they make it possible to evaluate the explicit formulas in just a few vectors of storage these characteristics of the program make it especially attractive for problems in several spatial variables rkc is compared to the bdf solver vodpk on two test problems in three spatial variables

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems we consider a bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field endowed with a hierarchical gaussian process prior computational challenges in this construction arise from the need for repeated evaluations of the forward model e g in the context of markov chain monte carlo and are compounded by high dimensionality of the posterior we address these challenges by introducing truncated karhunen loeve expansions based on the prior distribution to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior we seek a solution of this problem using galerkin projection on a polynomial chaos basis and use the solution to construct a reduced dimensionality surrogate posterior density that is inexpensive to evaluate we demonstrate the formulation on a transient diffusion equation with prescribed source terms inferring the spatially varying diffusivity of the medium from limited and noisy data