on the equivalence of time and frequency domain maximum likelihood estimation maximum likelihood estimation has a rich history it has been successfully applied to many problems including dynamical system identification different approaches have been proposed in the time and frequency domains in this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data a key point in this context is how initial and final conditions are considered and how they are introduced in the likelihood function

a compute and forward scheme for gaussian bi directional relaying with inter symbol interference we provide inner and outer bounds on the capacity region for the gaussian bi directional relaying over inter symbol interference channels the outer bound is obtained by the conventional cut set argument for the inner bound we propose a compute and forward coding scheme based on lattice partition chains and study its achievable rate the coding scheme is a time domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords the proposed compute and forward coding scheme substantially outperforms decode and forward schemes while it is well known that for the point to point communication case both independent coding along sub channels and time domain coding can approach the capacity limit as a byproduct of the proposed scheme we show that for the bi directional relay case independent coding along sub channels is not optimal in general and joint coding across sub channels can improve the capacity for some channel realizations

extensions of the i mmse relationship to gaussian channels with feedback and memory unveiling a fundamental link between information theory and estimation theory the i mmse relationship by guo et al together with its numerous extensions has great theoretical significance and various practical applications on the other hand its influences to date have been restricted to channels without feedback or memory due to the absence of its extensions to such channels in this paper we propose the extensions of the i mmse relationship to discrete time and continuous time gaussian channels with feedback and or memory our approach is based on a very simple observation which can be applied to other scenarios such as a simple and direct proof of the classical de bruijn s identity

a lower bound on the cutoff rate for gaussian channels with peak limited inputs a lower bound on the cutoff rate r sub o of a dispersive gaussian channel with peak rather than average power limited input is evaluated and compared to the lower bound on capacity under the same input constraints it is assumed that the input symbols are independent and uniformly distributed both bounds exhibit the same behavior as a function of an appropriately defined signal to noise ratio snr with a discrepancy of 1 68 db to the disadvantage of r sub o at high snrs the lower bound on r sub o is evaluated for peak and slope limited signals that model magnetic recording systems and is compared to the lower bound on capacity

channel capacity under sub nyquist nonuniform sampling this paper investigates the effect of sub nyquist sampling upon the capacity of an analog channel the channel is assumed to be a linear time invariant gaussian channel where perfect channel knowledge is available at both the transmitter and the receiver we consider a general class of right invertible time preserving sampling methods which includes irregular nonuniform sampling and characterize in closed form the channel capacity achievable by this class of sampling methods under a sampling rate and power constraint our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal to noise ratio among all spectral sets of measure equal to the sampling rate this can be attained through filterbank sampling with uniform sampling grid employed at each branch with possibly different rates or through a single branch of modulation and filtering followed by uniform sampling these results reveal that for a large class of channels employing irregular nonuniform sampling sets while are typically complicated to realize in practice does not provide capacity gain over uniform sampling sets with appropriate preprocessing our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain in this scenario which is in contrast to the benefits obtained from random mixing in spectrum blind compressive sampling schemes

asymptotically equivalent sequences of matrices and capacity of a discrete time gaussian mimo channel with memory using some recent results on asymptotically equivalent sequences of matrices we present in this paper a new derivation of the capacity formula given by brandenburg and wyner for a discrete time gaussian multiple input multiple output channel with memory in this paper we tackle not only the case considered by them where the number of channel inputs and the number of channel outputs are the same but also when both numbers are different

behavior of micropolar cubic crystal due to various sources the response of a micropolar cubic crystal due to various sources acting at the free surface has been studied the eigenvalue approach using integral transforms has been employed and the transforms have been inverted by using a numerical technique the displacement stress and microrotation components in the physical domain are obtained numerically the results of displacement and stresses have been compared for micropolar cubic crystal and micropolar isotropic solid the numerical results are illustrated graphically for a particular model

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

scattering for wave maps exterior to a ball abstract we consider 1 equivariant wave maps from r t r x 3 b s 3 where b is a ball centered at 0 and b gets mapped to a fixed point on s 3 we show that 1 equivariant maps of degree zero scatter to zero irrespective of their energy for positive degrees we prove asymptotic stability of the unique harmonic maps in the energy class determined by the degree

evaluation of inverse fourier transforms through romberg integration this study deals with evaluation of inverse integral transforms through numerical integration arguments are presented to explain that such a numerical evaluation is mathematically incorrect in recent years a sudden increase has been noticed in the number of research publications in which romberg integration is said to have used in evaluating the inverse fourier transforms in this regard even the references cited in these papers do not support such an evaluation but suggest contrary an immediate concern is to caution the researchers studying the source problems in the field of solid mechanics over the use and approval of an erroneous numerical technique

multiuser transmit optimization for multicarrier broadcast channels asymptotic fdma capacity region and algorithms we derive optimal and suboptimal multiuser transmit optimization methods for a multicarrier broadcast channel with intersymbol interference under the frequency division multiple access fdma restriction the general fdma based multicarrier broadcast problem is formulated as a maximum weighted rate sum problem given each user s subchannel assignment the optimal transmit strategy is achieved by multilevel waterfilling unfortunately the problem of finding the optimal subchannel assignments is combinatorial however by relaxing the fdma restriction we obtain a convex reformulation that allows for efficient computation of the optimal solution and therefore a characterization of the fdma capacity region for a broadcast channel if all users share the same transmission medium we prove that the optimal frequency partitioning among the users has an ordered structure that can be exploited to significantly reduce the computational complexity to make multiuser transmit optimization schemes practical for applications with relatively fast time varying user data rate requirements or priorities further reduction in computational complexity is necessary this is achieved by restricting the energy distribution to be constant across the used subchannels simulations indicate the low complexity constant energy methods presented are very robust and suffer from negligible performance loss

a computationally efficient multilevel coding scheme for isi channels this paper proposes a multilevel coding scheme with linear mapping for intersymbol interference isi channels and derives a low complexity receiver structure that can achieve the isi channel capacity the transmitter superimposes many layers of independent binary antipodal streams to generate a quadrature amplitude modulation qam or gaussian like channel input the receiver performs multistage decoding with decision feedback and interference cancellation within each stage is a linear minimum mean square error mmse equalizer followed by an error correcting decoder the complexity scales linearly with the channel length and the number of layers and the process is shown to be asymptotically information lossless if a fixed input power is properly distributed over a sufficiently large number of layers this framework is then extended to achieve the capacity of the isi channel using a transmitter side spectral shaping filter that converts a gaussian input sequence with a white spectrum to one with a water filling spectrum

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

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

capacity of channels with frequency selective and time selective fading this paper finds the capacity of single user discrete time channels subject to both frequency selective and time selective fading where the channel output is observed in additive gaussian noise a coherent model is assumed where the fading coefficients are known at the receiver capacity depends on the first order distributions of the fading processes in frequency and in time which are assumed to be independent of each other and a simple formula is given when one of the processes is independent identically distributed i i d and the other one is sufficiently mixing when the frequency selective fading coefficients are known also to the transmitter we show that the optimum normalized power spectral density is the waterfilling power allocation for a reduced signal to noise ratio snr where the gap to the actual snr depends on the fading distributions asymptotic expressions for high low snr and easily computable bounds on capacity are also provided

on the design of space time and space frequency codes for mimo frequency selective fading channels the authors introduced an algebraic design framework for space time coding in flat fading channels we extend this framework to design algebraic codes for multiple input multiple output mimo frequency selective fading channels the proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel we consider two design approaches the first uses space time coding and maximum likelihood decoding to exploit the multi path nature of the channel at the expense of increased receiver complexity within this time domain framework we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios the second approach utilizes the orthogonal frequency division multiplexing technique to transform the mimo multipath channel into a mimo flat block fading channel the algebraic framework is then used to construct space frequency codes sfc that optimally exploit the diversity available in the resulting flat block fading channel finally the two approaches are compared in terms of decoder complexity maximum achievable diversity advantage and simulated frame error rate performance in certain representative scenarios

gaussian multiaccess channels with isi capacity region and multiuser water filling the capacity region of a two user gaussian multiaccess channel with intersymbol interference isi in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive gaussian noise process is discussed a geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented this method can be viewed as a nontrivial generalization of the single user water filling argument it is shown that as in the traditional memoryless multiaccess channel frequency division multiaccess fdma with optimally selected frequency bands for each user achieves the total capacity of the multiuser gaussian multiaccess channel with isi however the capacity region of the two user channel with memory is in general not a pentagon unless the channel transfer functions for both users are identical

bezout space time precoders and equalizers for mimo channels the transmitter receiver diversities in p input q output multiple input multiple output mimo channels will play a key role in future high rate wireless communication the major challenge in mimo signal recovery is the mitigation of the inevitable intersymbol interference isi and interchannel interference ici in multipath mimo channels the bezout system theory provides a simple solution for isi ici cancellation and thus can serve as a powerful mathematical foundation for mimo systems if p q and the mimo system h d is left coprime the system is perfectly recoverable via a bezout precoder assuming the channel information is available at the transmitter for a robust channel design a quantitative analysis of signal to noise ratio snr of the optimal bezout equalizer precoder can be derived from the bezout null space compared with the alamouti see ieee j select areas commun vol 16 p 1451 58 oct 1998 space time coding the bezout precoder is shown to be more appealing in slowly time varying channels where the feedback of the channel information induces minor overhead the bezout system can work well jointly with the space time block coding stbc the stbc can be adopted to artificially construct a larger q spl times p q p virtual transfer function without the channel information a necessary and sufficient condition is provided for perfect recoverability pr for the stbc induced virtual mimo systems based on the virtual transfer function both channel independent and channel dependent precoding strategies are feasible via a singular value decomposition svd analysis the bezout precoder can be shown to outperform the orthogonal frequency division multiplexing ofdm precoder in bit error rate ber transmission rate and receiver implementation the interplay of the two design parameters n and spl rho is analyzed to provide a simple guideline for an optimal configuration the combined stbc and bezout equalization techniques offer a broader spectrum of transceiver system configuration to achieve optimal design tradeoff among ber transmission rate and implementation complexity

using hermite bases in studying capacity achieving distributions over awgn channels this paper studies classes of generic deterministic discrete time memoryless and nonlinear additive white gaussian noise awgn channels subject to multiple types of constraints such as the even moment and compact support constraints or a mixture the optimal input is proved to be discrete with finite number of mass points in the vast majority of the cases only under the even moment constraint and for special cases that emulate the average power constrained linear channel capacity is found to be achieved by an absolutely continuous input the results are extended to channels where the distortion is generally piecewise nonlinear where the discrete nature of the optimal input is conserved these results are reached through the development of methodology and tools that are based on standard decompositions in a hilbert space with the hermite polynomials as a basis and it is showcased how these bases are natural candidates for general information theoretic studies of the capacity of channels affected by awgn intermediately novel results regarding the output rate of decay of gaussian channels are derived namely the output probability distribution of any channel subjected to additive gaussian noise decays necessarily slower than the gaussian itself finally numerical computations are provided for some sample cases optimal inputs are determined and capacity curves are drawn these results put into question the accuracy of adopting the widely used expression 1 1 snr for computing capacities of gaussian deterministic channels

on the symmetric information rate of two dimensional finite state isi channels we derive a pair of bounds upper and lower on the symmetric information rate of a two dimensional finite state intersymbol interference isi channel model for channels with small impulse response support they can be estimated via a modified forward recursion of the bahl cocke jelinek raviv bcjr algorithm the convergence of the bounds is also analyzed to relax the constraint on the size of the impulse response a new upper bound is proposed which allows the tradeoff of the computational complexity and the tightness of the bound these bounds are further extended to d dimensional d 2 isi channels

markov processes asymptotically achieve the capacity of finite state intersymbol interference channels recent progress in capacity evaluation has made it possible to compute a sequence of lower bounds on the capacity of a finite state intersymbol interference isi channel by finding a sequence of optimized markov input processes with increasing order for which the state of the process is the previous input symbols in this correspondence we prove that as the order goes to infinity the sequence of optimized markov sources asymptotically achieves the capacity of the channel the conclusion is extended to two dimensional finite state isi channels the binary symmetric channel bsc with constrained inputs and general indecomposable finite state channels with a mild constraint

bounds on the symmetric binary cutoff rate for dispersive gaussian channels bounds on the symmetric binary cutoff rate for a pulse amplitude modulated pam signaling over dispersive gaussian channels are evaluated and discussed these easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary two level pam schemes operating through a prefiltered additive white gaussian channel the memory of which is long enough to make the exact evaluation of the cutoff rate formidable the core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix commonly applied in large deviation problems these bounds are calculated for some examples and their respective tightness is considered further potential applications of the proposed bounding technique are pointed out

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

optimization of signal sets for partial response channels ii asymptotic coding gain for pt i see ibid vol 37 no 5 p 1327 141 1991 for a linear time invariant discrete time channel with a given transfer function h f and information rate r bits t where t is the symbol interval an optimal signal set of length k is defined to be a set of 2 sup rk inputs of length k that maximizes the minimum l sub 2 distance between pairs of outputs the author studies the minimum distance between outputs or equivalently the coding gain of optimal signal sets as k to infinity he shows how to estimate the coding gain relative to single step detection of an optimal signal set length k when k is large

the intersymbol interference channel lower bounds on capacity and channel precoding loss the discrete time additive gaussian intersymbol interference isi channel with i i d not necessarily gaussian input signals is considered several new and old lower bounds on the capacity are derived in a unified manner by assuming different front end receiver filters in particular the sampled whitened matched filter swmf and the minimum mean squared error decision feedback equalizer mmse dfe filter the features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals it is also shown that the effect of an ideal post cursor or tail cancellation in an information preserving context depends primarily on the front end filter while as is well known ideal post cursor cancellation at the output of the swmf decreases the information the opposite trend is seen when an mmse dfe front filter is considered this observation reflects the basic theoretical obstacles in precoding i e ideal post cursor cancellation in the presence of a pre cursor it is used to assess the inherent loss in terms of information rates as compared to the rates achievable with the hypothetical ideal post cursor cancellation associated with any post cursor cancellation technique such as precoding dfe or other variants when operating in synergy with the mmse dfe front end filter the effect of the front end filter on an ideally interleaved precoded coded modulation system is also addressed

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

dual capacity upper bounds for binary input single tap isi channels the capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases in this paper we consider single tap binary input gaussian channels with inter symbol interference isi the dual capacity method is used to obtain upper bounds using markov test distributions the bound expressed as a single letter optimization problem is solved numerically for higher memory the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem bounds were obtained for the important case of the dicode channel and these are better than the previously known upper bounds and are close to achievable rates over a wide range of snrs

capacity scaling and spectral efficiency in wide band correlated mimo channels the dramatic linear increase in ergodic capacity with the number of antennas promised by multiple input multiple output mimo wireless communication systems is based on idealized channel models representing a rich scattering environment is such scaling sustainable in realistic scattering scenarios existing physical models although realistic are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters such as the angles of arrival and delays in this paper we leverage a recently introduced virtual representation of physical models that is essentially a fourier series representation of wide band mimo channels in terms of fixed virtual angles and delays motivated by physical considerations we propose a d connected model for correlated channels defined by a virtual spatial channel matrix consisting of d nonvanishing diagonals with independent and identically distributed i i d gaussian entries the parameter d provides a meaningful and tractable measure of the richness of scattering we derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth in the large antenna regime we show that linear capacity scaling is possible if d scales linearly with the number of antennas this in turn is possible if the number of resolvable paths grows quadratically with the number of antennas the capacity saturates for linear growth in the number of paths fixed d the ergodic capacity does not depend on frequency selectivity of the channel in the wide band case increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior for large bandwidth the capacity scales linearly with the signal to noise ratio snr as well we also provide an explicit characterization of the wide band slope recently proposed by verdu numerical results are presented to illustrate the key theoretical results

optimal linear precoding strategies for wideband non cooperative systems based on game theory part ii algorithms in this two part paper we address the problem of finding the optimal precoding multiplexing scheme for a set of noncooperative links sharing the same physical resources e g time and bandwidth we consider two alternative optimization problems p l the maximization of mutual information on each link given constraints on the transmit power and spectral mask and p 2 the maximization of the transmission rate on each link using finite order constellations under the same constraints as in p l plus a constraint on the maximum average error probability on each link aiming at finding decentralized strategies we adopted as optimality criterion the achievement of a nash equilibrium and thus we formulated both problems p l and p 2 as strategic noncooperative matrix valued games in part i of this two part paper after deriving the optimal structure of the linear transceivers for both games we provided a unified set of sufficient conditions that guarantee the uniqueness of the nash equilibrium in this part ii of the paper we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games specifically the new proposed algorithms are the following 1 the sequential and simultaneous iterative waterfilling based algorithms incorporating spectral mask constraints and 2 the sequential and simultaneous gradient projection based algorithms establishing an interesting link with variational inequality problems our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which although derived under stronger constraints incorporating for example spectral mask constraints have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm

optimum power allocation for parallel gaussian channels with arbitrary input distributions the mutual information of independent parallel gaussian noise channels is maximized under an average power constraint by independent gaussian inputs whose power is allocated according to the waterfilling policy in practice discrete signaling constellations with limited peak to average ratios m psk m qam etc are used in lieu of the ideal gaussian signals this paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions such policy admits a graphical interpretation referred to as mercury waterfilling which generalizes the waterfilling solution and allows retaining some of its intuition the relationship between mutual information of gaussian channels and nonlinear minimum mean square error mmse proves key to solving the power allocation problem

on properties of the support of capacity achieving distributions for additive noise channel models with input cost constraints we study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion we derive a simple relation between three parameters the input output function the input cost function and the noise probability density function one which dictates the type of the optimal input in layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cutoff growth rate equal to the logarithm of the inverse of the noise probability density function evaluated at the input output function furthermore we prove a converse statement that says whenever the cost grows slower than the cutoff rate the optimal input has necessarily an unbounded support in addition we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties we argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cutoff rate our results are valid for any cost function that is super logarithmic they summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models such as gaussian mixtures generalized gaussians and heavy tailed noise models that we state along with numerical computations

weak solutions and development of singularities of the su 2 σ model pour toutes donnees initiales d energie finie le modele sigma o k a des solutions faibles globales en chaque dimension d espace temps

on the elementwise convergence of continuous functions of hermitian banded toeplitz matrices toeplitz matrices and functions of toeplitz matrices such as the inverse of a toeplitz matrix powers of a toeplitz matrix or the exponential of a toeplitz matrix arise in many different theoretical and applied fields they can be found in the mathematical modeling of problems where some kind of shift invariance occurs in terms of space or time r m gray s excellent tutorial monograph on toeplitz and circulant matrices has been and remains the best elementary introduction to the szegouml distribution theory on the asymptotic behavior of continuous functions of toeplitz matrices his asymptotic results widely used in engineering due to the simplicity of its mathematical proofs do not concern individual entries of these matrices but rather they describe an average behavior however there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a toeplitz matrix using similar mathematical tools and to gain insight into the solutions of this sort of problems the present correspondence derives new theoretical results regarding the convergence of these entries

time decay for solutions of schrodinger equations with rough and time dependent potentials in this paper we establish dispersive estimates for solutions to the linear schrodinger equation in three dimensions frac 1 i partial t psi triangle psi v psi 0 qquad psi s f 0 1 where v t x is a time dependent potential that satisfies the conditions sup t v t cdot l frac 3 2 mathbb r 3 sup x in mathbb r 3 int mathbb r 3 int infty infty frac v hat tau x x y d tau dy c 0 here c0 is some small constant and v hat tau x denotes the fourier transform with respect to the first variable we show that under these conditions 0 1 admits solutions l t l2x 3 l2t l6x 3 for any f l2 3 satisfying the dispersive inequality psi t infty le c t s frac32 f 1 text for all times t s 0 2 for the case of time independent potentials v x 0 2 remains true if int mathbb r 6 frac v x v y x y 2 dxdy 4 pi 2 text and v mathcal k sup x in mathbb r 3 int mathbb r 3 frac v y x y dy 4 pi we also establish the dispersive estimate with an e loss for large energies provided v mathcal k v 2 infty

comparison of the achievable rates in ofdm and single carrier modulation with i i d inputs we compare the maximum achievable rates in single carrier sc and orthogonal frequency division multiplexing ofdm modulation schemes under the practical assumptions of independent identically distributed finite alphabet inputs and linear intersymbol interference with additive gaussian noise we show that the shamai laroia approximation serves as a bridge between the two rates while it is well known that this approximation is often a lower bound on the sc achievable rate it is revealed to also essentially upper bound the ofdm achievable rate we apply information estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used pulse amplitude modulation pam and quadratic amplitude modulation constellations to this end novel bounds on minimum mean square error estimation of pam inputs to a scalar gaussian channel are derived which may be of general interest our results show that under reasonable assumptions optimal sc schemes may offer spectral efficiency significantly superior to that of ofdm motivating further research of such systems

real discrete fourier transform the real discrete fourier transform rdft corresponds to the fourier series for sampled periodic signals with sampled periodic frequency responses just as discrete fourier transform dft corresponds to the complex fourier series for the same type of signals rdft has better performance than dft in data compression and filtering for all signals in the sense that pearl s measure for rdft is less than pearl s measure for dft by an amount w rdft also has better performance than dft in the computation of real convolution because of the reduced number of operations and the fact that forward and inverse transforms can be implemented with the same signal flowgraph thereby facilitating hardware and software design

novel analytical performance bounds for symbol by symbol decoding of digital data impaired by isi and awgn new analytical upper bounds are derived for the performance of symbol by symbol maximum likelihood ml abend fritchman type detectors for multi amplitude phase modulated digital sequences transmitted over time dispersive generally time variant linear channels introducing finite intersymbol interference isi and additive white gaussian noise awgn the proposed bounds are obtained starting from a novel form of the standard bhattacharyya bound and take explicitly into account the allowed decoding delay both deterministic and random multipath slow fading rayleigh transmission isi channels are considered simulation results obtained for some test channels of practical interest show the tightness of the derived analytical bounds