a joint source and relay power allocation scheme for a class of mimo relay systems a joint power allocation pa scheme for a class of mimo relay systems is presented in this paper based on the maximization of the capacity or minimization of the mean square error mse two joint pa optimization problems are first formulated since the cost functions thus obtained are in general not convex a tight lower bound of the capacity and a similar upper bound of the mse are derived and employed to modify the two cost functions so as to obtain a convex optimization problem it is confirmed through computer simulations that the proposed pa scheme outperforms the existing method in terms of both the capacity and the mse of mimo relay systems

pre equalization in the downlink of a multicarrier wireless network under utility and sum rate optimization this paper studies the problem of downlink pre equalization in a multicarrier wireless network under utility and sum rate maximization the network utility depends on two main factors an efficiency mapping which is a function of the signal to interference noise ratio sinr and the power of the pre equalization variables meanwhile the sum rate index is constructed by the summation of a logarithmic function of the sinrs of the active users the network utility and sum rate maximization problems are formulated here by assuming that the data estimation at the mobile units mus is carried out by a simple matched filter the optimal solutions are derived in this work for the pre equalization factors by following a strategy that is distributed with respect to the channel state information csi and data rates but centralized with respect to the spreading sequences of all active users the construction of these optimal solutions requires in each case a two step procedure first the optimal sinr is computed for the maximum utility and sum rate solutions based on the efficiency mapping and on the bound of the transmission power respectively then exploiting the induced diversity by the multiple subcarriers the pre equalization algorithms cancel the multiple access interference mai and channel distortions minimize the transmission power and achieve the optimal sinr after signal detection a comprehensive numerical evaluation is presented at the end of the paper to validate the analytical derivations applications of the proposed pre equalization schemes could be associated among others to cellular communication systems and wireless networks of actuators

moment analysis for localization in random schrodinger operators we study localization effects of disorder on the spectral and dynamical properties of schrodinger operators with random potentials the new results include exponentially decaying bounds on the transition amplitude and related projection kernels including in the mean these are derived through the analysis of fractional moments of the resolvent which are finite due to the resonance diffusing effects of the disorder the main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the lifshitz krein spectral shift associated with the local potential terms the difficulty is avoided here through the use of a weak l 1 estimate concerning the boundary value distribution of resolvents of maximally dissipative operators combined with standard tools of relative compactness theory

predistorter for mimo system with nonlinear power amplifiers a multiple input multiple output mimo system with nonlinear power amplifiers pas is considered the nonlinear pas distort the transmitted signal causing performance degradation the common approach for the mitigation of nonlinear distortions is the linearization of each one of the pas in the mimo system separately we propose to apply a more generic approach in the form of a global linearization of the entire nonlinear mimo channel the aim of the global linearization is to reduce the nonlinear distortions seen at the receiver an iterative technique is proposed for the implementation of such a linearization the proposed technique improves the system performance including 1 power efficiency of the pas 2 quality of the received signal measured in terms of symbol error rate and 3 spectral purity of the transmitted signals

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

finite length mmse tomlinson harashima precoding for frequency selective vector channels we design tomlinson harashima precoding for decentralized receivers and frequency selective channels based on the minimum mean square error criterion where the feedforward filter is restricted to have finite length contrary to most other publications on tomlinson harashima precoding which rely on solutions for decision feedback equalization to find the corresponding precoding filters in a heuristic manner we deduce the optimization for tomlinson harashima precoding from the optimization for the linear minimum mean square error transmit filter thereby we include the precoding order explicitly in the problem formulation and thus obtain the precoding filter solutions together with the algorithms to compute the latency time i e the time difference between application of the precoder at the transmitter and detection at the receiver and the precoding order from a single optimization since the algorithm for thp filter computation resulting from the optimization has a high computational complexity we present an alternative algorithm to compute the tomlinson harashima precoding filters based on a cholesky factorization with symmetric permutation resulting in an order of complexity that is the same as for the computation of the linear transmit filters the simulations reveal that the latency time optimization can be omitted without performance degradation for most practical channel models i e the latency time can be chosen to be the order of the feedforward filter

wireless mimo switching weighted sum mean square error and sum rate optimization this paper addresses joint transceiver and relay design for a wireless multiple input multiple output mimo switching scheme that enables data exchange among multiple users here a multiantenna relay linearly precodes the received uplink signals from multiple users and forwards the signal in the downlink where the purpose of precoding is to let each user receive its desired signal with interference from other users suppressed the problem of optimizing the precoder based on various design criteria is typically nonconvex and difficult to solve the main contribution of this paper is a unified approach to solve the weighted sum mean square error mse minimization and weighted sum rate maximization problems in mimo switching specifically an iterative algorithm is proposed for jointly optimizing the relay s precoder and the users receive filters to minimize the weighted sum mse it is also shown that the weighted sum rate maximization problem can be reformulated as an iterated weighted sum mse minimization problem and can therefore be solved similarly to the case of weighted sum mse minimization with properly chosen initial values the proposed iterative algorithms are asymptotically optimal in both high and low signal to noise ratio regimes for mimo switching either with or without self interference cancellation a k a physical layer network coding numerical results show that the optimized mimo switching scheme based on the proposed algorithms significantly outperforms existing approaches in the literature

fourier based transmit beampattern design using mimo radar in multiple input multiple output mimo radar settings it is often desirable to transmit power only to a given location or set of locations defined by a beampattern transmit waveform design is a topic that has received much attention recently involving synthesis of both the signal covariance matrix r as well as the actual waveforms current methods involve a two step process of designing r via iterative solutions and then using r to generate waveforms that fulfill practical constraints such as having a constant envelope or drawing from a finite alphabet in this paper a closed form method to design r for a uniform linear array is proposed that utilizes the discrete fourier transform dft coefficients and toeplitz matrices the resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniform elemental power constraint and provides performance similar to that of iterative methods which require a much greater computation time next a transmit architecture is presented that exploits the orthogonality of frequencies at discrete dft values to transmit a sum of orthogonal signals from each antenna the resulting waveforms provide a lower mean square error than current methods at a much lower computational cost and a simulated detection scenario demonstrates the performance advantages achieved

a note on fractional moments for the one dimensional continuum anderson model we give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one dimensional continuum anderson model via the fractional moments method this follows via exponential decay of fractional moments of the green function which is shown to hold at arbitrary energy and for any single site distribution with bounded compactly supported density

limited feedback low encoding complexity precoder design for downlink of fdd multi user massive mimo systems we investigate a limited feedback precoder based on symbol pairwise error probability pep for a block faded k times n t downlink multiple input multiple output mimo channel in the considered system k lfloor n t alpha rfloor single antenna users feedback quantized channel state information to the n t antenna transmitter using b bits per transmit antenna per user we analytically show that for alpha b geq 1 and n t rightarrow infty both symbol pep and achievable rate of each of the k downlink users almost surely converge to the symbol pep and achievable rate of k parallel additive white gaussian noise awgn channels respectively we show that the encoding complexity of the precoder is o n t k we also show that if channel coefficients estimated by the user are corrupted by awgn noise the symbol pep and achievable rate of each user almost surely converge to the symbol pep and achievable rate in a scaled awgn channel with b 1 and n t rightarrow infty for correlated channels we derive a condition which enables the proposed precoder almost surely to cancel multi user interference for large n t values finally we numerically compare the bit error rate encoding complexity and per user achievable rate of the proposed scheme with the existing designs

symbolic extensions and smooth dynamical systems let f x x be a homeomorphism of the compact metric space x a symbolic extension of f x is a subshift on a finite alphabet g y which has f as a topological factor we show that a generic c1 non hyperbolic i e non anosov area preserving diffeomorphism of a compact surface has no symbolic extensions for r 1 we exhibit a residual subset mathcal r of an open set mathcal u of cr diffeomorphisms of a compact surface such that if f in mathcal r then any possible symbolic extension has topological entropy strictly larger than that of f these results complement the known fact that any c diffeomorphism has symbolic extensions with the same entropy we also show that cr generically on surfaces homoclinic closures which contain tangencies of stable and unstable manifolds have hausdorff dimension two

on convex vector precoding for multiuser mimo broadcast channels we propose different convex alphabet relaxation schemes for vector precoding in mimo broadcast channels using binary quaternary and octonary modulation expressions are presented for the probability of the different precoding schemes to achieve interference free communication over singular channels the energy of transmission is evaluated in the many user limit using the replica method from statistical physics an alternative channel inversion technique is proposed which makes purely real binary alphabets perform as well as their complex extensions resulting in reduced complexity in the optimization process the relevance of the asymptotic analysis is confirmed by finite size simulations

a weighted combining algorithm for spatial multiplexing mimo df relaying systems jointly detecting the signals from the source and relay in a spatial multiplexing sm multiple input multiple output mimo relaying system improves the transmit reliability significantly however the existing joint detection schemes for sm mimo relaying systems which achieve full diversity such as the near maximum likelihood ml decoder suffer from high complexity in this paper we propose a weighted combining wc algorithm which is applied before the detector in the sm mimo decode and forward relaying system the proposed algorithm merges the received signal vectors from the source and relay into a combined signal without expanding their dimension and formulates an equivalent mimo channel matrix for the combined signal resulting in a lower complexity for the subsequent detection we analyze the performance of the proposed wc algorithm with ml detection in terms of the diversity order and computational complexity an approximate upper bound on the symbol error probability sep for the proposed algorithm is also derived simulation results show that in symmetric networks the proposed wc algorithm achieves substantially lower complexity while maintaining an sep performance similar to that of the benchmark nml decoder the consistency of the derived upper bound on the sep is also verified by simulations

generalized design of low complexity block diagonalization type precoding algorithms for multiuser mimo systems block diagonalization bd based precoding techniques are well known linear transmit strategies for multiuser mimo mu mimo systems by employing bd type precoding algorithms at the transmit side the mu mimo broadcast channel is decomposed into multiple independent parallel single user mimo su mimo channels and achieves the maximum diversity order at high data rates the main computational complexity of bd type precoding algorithms comes from two singular value decomposition svd operations which depend on the number of users and the dimensions of each user s channel matrix in this work low complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of bd type precoding algorithms we devise a strategy based on a common channel inversion technique qr decompositions and lattice reductions to decouple the mu mimo channel into equivalent su mimo channels analytical and simulation results show that the proposed precoding algorithms can achieve a comparable sum rate performance as bd type precoding algorithms substantial bit error rate ber performance gains and a simplified receiver structure while requiring a much lower complexity

a new beamforming design for mimo af relaying systems with direct link in this paper we propose a new beamforming technique that maximizes the end to end signal to noise ratio snr for amplify and forward multiple input multiple output cooperative relaying systems with direct link between thesource and the destination instead of conventional schemes resorting to an iterative method such as a gradient ascentalgorithm our scheme provides a simple closed form solution for source relay joint beamformer designs to this end wefirst derive a new expression of the end to end snr for the cooperative relaying systems and its lower bound which isgiven as the harmonic mean of two individual snrs then a new beamforming scheme which adaptively optimizes one of the two snrs depending on the channel condition is proposed in addition we perform a diversity order analysis of the proposed scheme and show that our scheme achieves a full diversity order of relaying systems with direct link it is confirmed by simulation results that the proposed technique obtains almost identical performance to the gradient ascent algorithm with much reduced complexity and our analytical work accurately predicts the numerical results

local fluctuation of the spectrum of a multidimensional anderson tight binding model we consider the anderson tight binding modelh v acting inl 2 z d and its restrictionh to finite hypercubes z d herev v x x z d is a random potential consisting of independent identically distributed random variables let e j j be the eigenvalues ofh and let j e e j e j 1 be its rescaled eigenvalues then assuming that the exponential decay of the fractional moment of the green function holds for complex energies neare and that the density of statesn e exists ate we shall prove that the random sequence j e j considered as a point process onr 1 converges weakly to the stationary poisson point process with intensity measuren e dx as gets large thus extending the result of molchanov proved for a one dimensional continuum random schrodinger operator on the other hand the exponential decay of the fractional moment of the green function was established recently by aizenman molchanov and graf as a technical lemma for proving anderson localization at large disorder or at extreme energy thus our result in this paper can be summarized as follows near the energye where anderson localization is expected there is no correlation between eigenvalues ofh if is large

robust precoding with bayesian error modeling for limited feedback mu miso systems we consider the robust precoder design for multiuser multiple input single output mu miso systems where the channel state information csi is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas we propose to compress the feedback data by projecting the channel estimates onto a vector basis known at the receivers and the transmitter and quantizing the resulting coefficients the channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean square error mse between the true and the rank reduced csi expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design these expressions take into account the following sources of error channel estimation truncation for rank reduction quantization and feedback channel delay as an example for the robust problem formulation vector precoding vp is designed based on the expectation of the mse conditioned on the fed back csi our results show that robust precoding based on fed back csi clearly outperforms conventional precoding designs which do not take into account the errors in the csi

dynamical localization for discrete anderson dirac operators we establish dynamical localization for random dirac operators on the d dimensional lattice with d in left 1 2 3 right in the three usual regimes large disorder band edge and 1d these operators are discrete versions of the continuous dirac operators and consist in the sum of a discrete free dirac operator with a random potential the potential is a diagonal matrix formed by different scalar potentials which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support we prove the exponential decay of fractional moments of the green function for such models in each of the above regimes i e j throughout the spectrum at larger disorder jj for energies near the band edges at arbitrary disorder and jjj in dimension one for all energies in the spectrum and arbitrary disorder dynamical localization in theses regimes follows from the fractional moments method the result in the one dimensional regime contrast with one that was previously obtained for 1d dirac model with bernoulli potential

improved linear transmit processing for single user and multi user mimo communications systems in this paper we propose a novel linear transmit precoding strategy for multiple input multiple output mimo systems employing improper signal constellations in particular improved zero forcing zf and minimum mean square error mmse precoders are derived based on modified cost functions and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders the superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results the novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi user channels in both cases the improved precoding schemes yield significant performance gain compared to the conventional counterparts

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

localization for one dimensional continuum bernoulli anderson models we use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional continuum anderson type models with singular distributions in particular the case of a bernoulli dis tribution is covered the operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi scale analysis we show that non reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs

new approach for error compensation in coded v blast ofdm systems in this paper we investigate coded layered space time architectures for frequency selective fading multiple input multiple output orthogonal frequency division multiplexing ofdm channels by computing outage capacity formulas we will show that the capacity of the vertical bell labs layered space time v blast architecture can closely approach the shannon capacity in the frequency selective ofdm environment motivated by the capacity analysis we propose pragmatic approaches which preserve the optimality of the layered space time concept we present methods to prevent the error propagation from catastrophically affecting the signal detection in subsequent layers first we start with a comprehensive signal modeling which includes error propagation we derive an improved signal detector and describe the optimal soft bit log likelihood ratio value computation method by taking decision errors into account for soft input channel decoding then to further enhance the v blast performance we show that cancellation using decoded decisions from previous layers makes the decision errors almost completely disappear so that the layered space time architecture can approach the attainable channel capacity finally simulations confirm that the proposed schemes show a significant performance improvement over the conventional methods

lower transport bounds for one dimensional continuum schrodinger operators we prove quantum dynamical lower bounds for one dimensional continuum schrodinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states this general result is applied to a number of models including the bernoulli anderson model with a constant single site potential

coalitional games in miso interference channels epsilon core and coalition structure stable set the multiple input single output interference channel is considered each transmitter is assumed to know the channels between itself and all receivers perfectly and the receivers are assumed to treat interference as additive noise in this setting noncooperative transmission does not take into account the interference generated at other receivers which generally leads to inefficient performance of the links to improve this situation we study cooperation between the links using coalitional games the players links in a coalition either perform zero forcing transmission or wiener filter precoding to each other the epsilon core is a solution concept for coalitional games that takes into account the overhead required in coalition deviation we provide necessary and sufficient conditions for the strong and weak epsilon core of our coalitional game not to be empty with zero forcing transmission since the epsilon core only considers the possibility of joint cooperation of all links we study coalitional games in partition form in which several distinct coalitions can form we propose a polynomial time distributed coalition formation algorithm based on coalition merging and prove that its solution lies in the coalition structure stable set of our coalition formation game simulation results reveal the cooperation gains for different coalition formation complexities and deviation overhead models

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

sampling uniformly from the set of positive definite matrices with trace constraint we derive a parameterization of positive definite matrices using the cholesky decomposition in combination with hyperspherical coordinates based on the parameterization we develop a simple and efficient method to randomly generate positive definite matrices with constant or bounded trace according to a uniform distribution further we present an efficient implementation using the inversion method and either rejection sampling or transforming a beta distribution the matrix parameterization might be of independent interest whereas the random sampling algorithm finds applications in monte carlo simulations testing of algorithms and performance studies with the help of an abstract example we describe how the sampling method can be used to approximate the optimum in a difficult e g nonconvex optimization problem for which no solution or efficient global optimization algorithm is known in this paper we consider real as well as complex matrices

regularized channel diagonalization for multiuser mimo downlink using a modified mmse criterion we propose a regularized channel diagonalization method for a joint transmit receive linear optimization in the downlink of a multiuser multiple input multiple output mimo communication system this method is based on the use of a modified minimum mean square error mmse criterion which employs a weighted information symbol vector for the target and signal scaling the weights for the target are the equivalent channel gain resulting from a zero forcing zf based mimo channel diagonalization a joint iterative algorithm for minimizing the mean square error mse under a total transmit power constraint is derived and its convergence is proved the signal to interference plus noise ratio sinr is analyzed and the sum rates evaluated in a computer simulation the results demonstrate that the proposed method outperforms the existing zf and mmse based methods

performance analysis of mmse based amplify and forward spatial multiplexing mimo relaying systems in this paper we propose a general framework to quantify the average error probability of the minimum mean squared error based precoding schemes in amplify and forward relay networks where all nodes are equipped with multiple antennas especially we investigate spatial multiplexing schemes which transmit multiple data streams simultaneously due to difficulty in finding an exact expression of the average error rate we exploit the high signal to noise ratio snr based approach which allows a simple and accurate characterization of the performance then we derive new closed form expressions for bit error rate performance of both the optimal source relay joint precoding schemes and the optimal relay only precoding schemes in terms of a coding gain as well as a diversity gain taking a different pathloss in each hop into consideration we evaluate the performance in a generalized environment through our analysis we discuss several interesting observations and provide a helpful guideline for designing mmse based relaying systems monte carlo simulations show that our analytical work accurately predicts numerical results

the entropy theory of symbolic extensions fix a topological system x t with its space k x t of t invariant borel probabilities if y s is a symbolic system subshift and y s x t is a topological extension factor map then the function h ext on k x t which assigns to each the maximal entropy of a measure on y mapping to is called the extension entropy function of the infimum of such functions over all symbolic extensions is called the symbolic extension entropy function and is denoted by h sex in this paper we completely characterize these functions in terms of functional analytic properties of an entropy structure on x t the entropy structure is a sequence of entropy functions h k defined with respect to a refining sequence of partitions of x or of x z for some auxiliary system z r with simple dynamics whose boundaries have measure zero for all the invariant borel probabilities we develop the functional analysis and computational techniques to produce many dynamical examples for instance we resolve in the negative the question of whether the infimum of the topological entropies of symbolic extensions of x t must always be attained and we show that the maximum value of h sex need not be achieved at an ergodic measure we exhibit several characterizations of the asymptotically h expansive systems of misiurewicz which emerge as a fundamental natural class in the context of the entropy structure the results of this paper are required for the downarowicz newhouse results dn on smooth dynamical systems

precoder design for multiuser miso systems exploiting statistical and outdated csit we propose a multiuser downlink transmission scheme exploiting both statistical and outdated channel state information csi at the transmitter based on the outdated csi aided transmission scheme introduced in denoted as mat the proposed scheme reduces the original k user mat system to a two user virtual mat system through statistical precoding in the first two transmission slots thus the proposed scheme denoted as v mat reduces efficiently the implementation complexity while increasing the achievable rate at finite signal to noise ratios snrs for the v mat scheme we derive an analytical high snr rate approximation for correlated rayleigh fading furthermore for independent and identically distributed rayleigh fading we derive an exact rate expression at high snrs as well as a tight lower bound which applies for arbitrary snrs then precoder design is investigated where an efficient near optimal solution is proposed for arbitrary number of transmit antennas and a closed form optimal solution is derived for the two antenna case it is demonstrated that the proposed v mat scheme yields higher achievable rate than the original mat scheme at practical snrs moreover by combining the v mat scheme and the generalized mat scheme of where precoding is implemented in the third transmission slot the achievable rate can be further increased

finite volume fractional moment criteria for anderson localization a technically convenient signature of localization exhibited by discrete operators with random potentials is exponential decay of the fractional moments of the green function within the appropriate energy ranges known implications include spectral localization absence of level repulsion strong form of dynamical localization and a related condition which plays a significant role in the quantization of the hall conductance in two dimensional fermi gases we present a family of finite volume criteria which under some mild restrictions on the distribution of the potential cover the regime where the fractional moment decay condition holds the constructive criteria permit to establish this condition at spectral band edges provided there are sufficient lifshitz tail estimates on the density of states they are also used here to conclude that the fractional moment condition and thus the other manifestations of localization are valid throughout the regime covered by the multiscale analysis in the converse direction the analysis rules out fast power law decay of the green functions at mobility edges

optimized one way relaying strategy with outdated csi quantization for spatial multiplexing this correspondence considers a mimo relay downlink system using precoding and limited feedback since the conventional precoding matrices are directly obtained by treating the quantized channel state information csi feedback as real csi we propose an optimized relay precoding strategy by taking both effects of channel quantization error and feedback delay into account conditioned on the outdated csi quantization available at the relay station the relay precoding is optimized via minimizing an expected mean square error mse criterion over csi mismatches by using karush kuhn tucker kkt conditions a closed form solution to the relay design is achieved with comparable computational complexity relative to the conventional approach numerical results verify the effectiveness of the proposed scheme

transmitter optimization for per antenna power constrained multi antenna downlinks an slnr maximization methodology in this paper we consider signal to leakage plus noise ratio slnr maximized precoding for multi antenna downlinks under per antenna power constraints papcs in contrast to the conventional sum power constraint the per antenna power constrained slnr precoder design problem no longer admits a simple closed form solution and achieving its optimal solution turns out to be much more challenging to conquer the difficulty we first propose to perform the charnes cooper transformation on the problem of interest which yields a solvable simpler second order cone program socp moving beyond this approach we are then able to obtain a semi closed form solution to the optimal slnr precoder the power allocation among users is also optimized for further performance enhancement for which we devise two numerical methods based on gradient projection and a low complexity approximation finally focusing on the imperfect channel state information csi scenario we develop a robust slnr based precoder to combat the performance degradation caused by random csi errors the superiority of all proposed precoder designs in this work is confirmed by numerical simulations

robust joint design of linear relay precoder and destination equalizer for dual hop amplify and forward mimo relay systems this paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual hop amplify and forward af multiple input multiple output mimo relay system with gaussian random channel uncertainties in both hops by taking the channel uncertainties into account two robust design algorithms are proposed to minimize the mean square error mse of the output signal at the destination one is an iterative algorithm with its convergence proved analytically the other is an approximated closed form solution with much lower complexity than the iterative algorithm although the closed form solution involves a minor relaxation for the general case when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix no relaxation is needed and the proposed closed form solution is the optimal solution simulation results show that the proposed algorithms reduce the sensitivity of the af mimo relay systems to channel estimation errors and perform better than the algorithm using estimated channels only furthermore the closed form solution provides a comparable performance to that of the iterative algorithm

precoding designs based on minimum distance for two way relaying mimo systems with physical network coding in this paper we propose new precoding methods for two way multiple input multiple output physical network coding pnc systems which employ the modulo operation in our work the transmit and receive filters are determined to maximize the minimum distance of the received constellations assuming global channel state information the precoding operations are separately optimized for the multiple access ma and the broadcast stages and the optimal precoding is obtained by applying a semidefinite relaxation method especially we prove that for the system with linear detection the modulo operation for the pnc achieves optimality with the derived precoding for the ma stage in terms of the minimum distance also we present a closed form solution for the optimal filter designs for two special cases for computing solutions we transform our max min problem into a simple maximization problem by imposing additional constraints also we propose a suboptimal non iterative precoding scheme whose performance is within 1 db at a bit error rate ber of 10 4 compared to the optimum iterative method with much reduced complexity finally the simulation results show that the proposed systems achieve 2 3 db gains at a ber of 10 4 compared to the optimal amplify and forward systems

quantum harmonic oscillator systems with disorder we study many body properties of quantum harmonic oscillator lattices with disorder a sufficient condition for dynamical localization expressed as a zero velocity lieb robinson bound is formulated in terms of the decay of the eigenfunction correlators for an effective one particle hamiltonian we show how state of the art techniques for proving anderson localization can be used to prove that these properties hold in a number of standard models we also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one particle eigenfunction correlators in particular we show that static correlations decay exponentially fast if the corresponding effective one particle hamiltonian exhibits localization at low energies regardless of whether there is a gap in the spectrum above the ground state or not our results apply to finite as well as to infinite oscillator systems the eigenfunction correlators that appear are more general than those previously studied in the literature in particular we must allow for functions of the hamiltonian that have a singularity at the bottom of the spectrum we prove exponential bounds for such correlators for some of the standard models

anderson localization and the space time characteristic of continuum states a proof of anderson localization is obtained by ruling out any continuous spectrum on the basis of the space time characteristic of its states

subchannel allocation in multiuser multiple input multiple output systems assuming perfect channel state information at the transmitter of a gaussian broadcast channel strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel for the general sum capacity maximizing solution which has recently been found a method is proposed that transforms each of the resulting vector channels into a set of scalar channels this makes possible to achieve capacity by simply using scalar coding and detection techniques the high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero forcing allocation strategy that directly results in a set of virtually decoupled scalar channels simulation results show that this technique tightly approaches the performance of the optimum solution i e complexity reduction comes at almost no cost in terms of sum capacity as the optimum solution the zero forcing allocation strategy applies to any number of transmit antennas receive antennas and users

robust mmse precoding in mimo channels with pre fixed receivers in this paper we design robust precoders under the minimum mean square error mmse criterion for different types of channel state information csi in multiple input multiple output mimo channels we consider low complexity pre fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter in particular three types of csi are taken into account i perfect csi ii statistical csi in the form of mean feedback and iii deterministic imperfect csi assuming that the actual channel is within the neighborhood of a nominal channel which leads to the worst case robust design that is the focus of this paper interestingly it is found that under some mild conditions the optimal transmit directions i e the left singular vectors of the precoder are equal to the right singular vectors of the channel the channel mean and the nominal channel for perfect csi statistical csi and the worst case design respectively consequently the matrix valued problems can be simplified to scalar power allocation problems that either admit closed form solutions or can be efficiently solved by the proposed algorithm

inverse tunnelingestimates and applications to the study of spectral statistics ofrandom operators on the real line we present a proof of a minami type estimate for one dimensional random schrodinger operators valid at all energies in the localization regime provided a wegner estimate is known to hold the minami type estimate is then applied to two models to obtain results on their spectral statistics the heuristics underlying our proof of minami type estimates is that close by eigenvalues of a one dimensional schrodinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena in the second case one can undo the tunneling and thus construct quasi modes that live far away from each other in space resume nous demontrons une inegalite de type minami pour des operateurs de schrodinger aleatoires uni dimensionnel dans toute la region localisee si une estimee de wegner est connue cette estimee de type de minami est alors appliquee pour obtenir les statistiques spectrales pour deux modeles l heuristique qui guide ce travail est que des valeurs propres proches pour un operateur de schrodinger sur un intervalle sont soient localisees loin l une de l autre soit sont la consequence d un phenomene d effet tunnel dans le second cas on peut en defaisant cet effet tunnel construire des quasi modes qui sont localises loin l un de l autre 0 introduction consider the following two random operators on the real line the anderson model 0 1 h d2 dx2 w

symbolic extensions and uniform generators for topological regular flows abstract building on the theory of symbolic extensions and uniform generators for discrete transformations we develop a similar theory for topological regular flows in this context a symbolic extension is given by a suspension flow over a subshift

bounds for multihop relayed communications in nakagami m fading we present closed form lower bounds for the performance of multihop transmissions with nonregenerative relays over not necessarily identically distributed nakagami m fading channels the end to end signal to noise ratio is formulated and upper bounded by using an inequality between harmonic and geometric means of positive random variables rvs novel closed form expressions are derived for the moment generating function the probability density function and the cumulative distribution function of the product of rational powers of statistically independent gamma rvs these statistical results are then applied to studying the outage probability and the average bit error probability for phase and frequency modulated signaling numerical examples compare analytical and simulation results verifying the tightness of the proposed bounds

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

harmonic mean and end to end performance of transmission systems with relays closed form expressions for the statistics of the harmonic mean of two independent and identically distributed gamma variates are presented the probability density function of the harmonic mean of two f variates is also derived these statistical results are then applied to study the performance of wireless communication systems with nonregenerative relays over flat nakagami fading channels more specifically outage probability formulas for noise limited systems as well as systems affected by interference are obtained furthermore general expressions for average bit error rates are also derived finally comparisons between regenerative and nonregenerative systems are presented numerical results show that the former systems clearly outperform the latter ones for low average signal to noise ratios snrs they also show that the two systems have similar performance at high average snrs