cyclic hopf orders defined by isogenies of formal groups using degree 2 polynomial formal groups we construct hopf algebras over valuation rings of local number fields k that are orders in kg g cyclic of order p n the construction does not yield all greither orders when n 2 but does yield new classes of hopf orders for all n 3 and shows that a general hopf order in kg g cyclic of order p n involves at least n n 1 2 parameters

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

on a class of frozen regularized gauss newton methods for nonlinear inverse problems in this paper we consider a class of regularized gauss newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration such methods have the frozen feature that they require only the computation of the frechet derivative at the initial approximation thus the computational work is considerably reduced under certain mild conditions we give the convergence analysis and derive various estimates including the order optimality on these methods

outage analysis in mobile radio systems with generically correlated log normal interferers a novel methodology is proposed for computing the outage probability in mobile radio systems in the presence of log normal shadowing a relevant feature is that the proposed analysis assumes a general correlation for any pair of links various approaches are considered to compute the statistics of user signal to interference ratio sir namely schwartz and yeh s method wilkinson s method and fenton s method by a simple reformulation of the problem these methods can be used to calculate in a straightforward way the parameters of the sir the accuracy of the methods is checked in a number of situations of interest moreover when the same correlation is assigned to any pair of links the novel analysis is more accurate than previously proposed approaches

the performance of space time block codes from coordinate interleaved orthogonal designs over nakagami m fading channels space time block codes stbcs from coordinate interleaved orthogonal designs ciods offer several advantages including full diversity and single symbol decodability in an effort to assess their performance in quasi static frequency nonselective i i d nakagami m fading channels we analyze the error rate outage capacity and information outage probability first based on an accurate closed form formula for the average symbol pairwise error rate sper we derive tight union upper and lower bounds on the symbol error rate ser second we apply gaussian and gamma approximations to provide closed form expressions for the outage capacity third using high signal to noise ratio snr and moment matching approximation techniques we also derive accurate closed form approximations for the information outage probability iop finally we show that stbcs from ciods provide full diversity by deriving ser based and iop based asymptotic and instantaneous diversity orders monte carlo simulations show that the analytical results agree with simulation experiments

newton s method for a class of optimal shape design problems a class of optimal shape design problems is considered where a part of the boundary of the domain represents the free parameter the variable domain is parametrized by a class of functions in such a way that the optimal design problem results in an optimal control problem on a fixed domain the functions for the parametrization of the domain are used as controls and the corresponding states are then given by the solution of an elliptic boundary value problem on a fixed domain discretizing this control problem normally leads to a large scale optimization problem where the corresponding solution methods are characterized by the requirement of solving many boundary value problems in spite of this interesting numerical challenge until now little work has been done to derive more efficient algorithms by taking advantage of the specific structure of this kind of problem in this report newton s method in function space is derived resulting in an efficient algorithm for the discretized optimization problems by using the specific structure of these optimal shape design problems an efficient implementation of the numerical algorithm is introduced the properties of this algorithm are compared with those of the gradient method using illustrative numerical examples

complete characterization of the equivalent mimo channel for quasi orthogonal space time codes recently a quasi orthogonal space time block code qstbc capable of achieving a significant fraction of the outage mutual information of a multiple input multiple output mimo wireless communication system for the case of nt 4 transmit and nr 1 receive antennas was proposed we generalize these results to nt 2n transmit and an arbitrary number of receive antennas furthermore we completely characterize the structure of the equivalent channel for the general case and show that for all nt 2n and nr the eigenvectors of the equivalent channel are fixed and independent from the channel realization furthermore the eigenvalues of the equivalent channel are independent identically distributed random variables each following a noncentral chi square distribution with 4nr degrees of freedom based on these important insights into the structure of the qstbc we derive tight lower and upper bounds for the outage probability achieved with qstbc finally by utilizing the special structure of the qstbc we propose a new transmit strategy which decouples the signals transmitted from different antennas in order to detect the symbols separately with a linear ml detector rather than joint detection an up to now only known advantage of orthogonal space time block codes ostbc

a simplified generalized gauss newton method for nonlinear ill posed problems iterative regularization methods for nonlinear ill posed equations of the form f x y where f d f x y is an operator between hilbert spaces x and y usually involve calculation of the frechet derivatives of f at each iterate and at the unknown solution x in this paper we suggest a modified form of the generalized gauss newton method which requires the frechet derivative of f only at an initial approximation x0 of the solution x the error analysis for this method is done under a general source condition which also involves the frechet derivative only at x0 the conditions under which the results of this paper hold are weaker than those considered by kaltenbacher 1998 for an analogous situation for a special case of the source condition

second order methods for optimal control of time dependent fluid flow second order methods for open loop optimal control problems governed by the two dimensional instationary navier stokes equations are investigated optimality systems based on a lagrangian formulation and adjoint equations are derived the newton and quasi newton methods as well as various variants of sqp methods are developed for applications to optimal flow control and their complexity in terms of system solves is discussed local convergence and rate of convergence are proved a numerical example illustrates the feasibility of solving optimal control problems for two dimensional instationary navier stokes equations by second order numerical methods in a standard workstation environment

secure diversity multiplexing tradeoff of zero forcing transmit scheme at finite snr in this paper we address the finite signal to noise ratio snr diversity multiplexing tradeoff dmt of the multiple input multiple output mimo wiretap channel where a zero forcing zf transmit scheme that intends to send the secret information in the orthogonal space of the eavesdropper channel is used first we introduce the secrecy multiplexing gain at finite snr that generalizes the definition at high snr then we provide upper and lower bounds on the outage probability under secrecy constraint from which secrecy diversity gain estimates of zf are derived through asymptotic analysis we show that the upper bound underestimates the secrecy diversity gain whereas the lower bound is tight at high snr and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the mimo wiretap channel

estimating the distribution of a sum of independent lognormal random variables four methods that can be used to approximate the distribution function df of a sum of independent lognormal random variables rvs are compared the aim is to determine the best method to compute the df considering both accuracy and computational effort the investigation focuses on values of the db spread valid for practical problems in wireless transmission where is between 6 db and 12 db contrary to some previous reports our results show that the simpler wilkinson s approach gives a more accurate estimate in some cases of interest than schwartz and yeh s 1982 approach

weak convergence and rate of convergence of mimo capacity random variable recent works on the distribution function of the capacity of independent and identically distributed i i d and semicorrelated narrowband channels show that the outage capacity computed using a gaussian approximation is close to the true outage capacity even for few antennas motivated by physical scattering considerations we study a multi antenna channel model with independent entries that are not necessarily identically distributed and show the weak convergence of capacity to a gaussian random variable the channel model considered in this paper subsumes well studied cases like the i i d and separable correlation models and thus we generalize previous results on weak convergence of multi antenna capacity using recent results from random matrix theory we also study the rate of convergence of ergodic capacity of i i d channels to its limit value employing a well known conjecture from random matrix theory we establish tight results for the rate of convergence and show a dependence of this rate on signal to noise ratio

information capacity of a random signature multiple input multiple output channel a closed form expression for information capacity of the random signature multiple input multiple output channel is given a direct calculation of the capacity is provided additional to the proof involving the capacity of minimum mean square error systems provided by verdu and shamai see ieee trans inform theory vol 45 p 622 40 1999

hopf orders via breuil modules abstract let r be a discrete valuation ring with quotient field k and residue field k of characteristic p 2 each finite flat abelian r hopf algebra of rank p n has a corresponding breuil module we determine the breuil modules for the hopf algebras which are generically isomorphic to kg where g is an elementary abelian p group and give an explicit classification for p 3 n 2

an approximate capacity distribution for mimo systems in this letter we derive the exact variance of the capacity of a multiple input multiple output mimo system this enables an investigation of the accuracy of a gaussian approximation to the capacity foreshadowed by various central limit theorems we confirm recent results which state that the capacity variance appears to converge to a limit independent of absolute antenna numbers but dependent on the ratio of the numbers of receive to transmit antennas the gaussian approximation itself is surprisingly good even in the worst cases giving satisfactory results

accurate computation of the mgf of the lognormal distribution and its application to sum of lognormals sums of lognormal random variables rvs are of wide interest in wireless communications and other areas of science and engineering since the distribution of lognormal sums is not log normal and does not have a closed form analytical expression many approximations and bounds have been developed this paper develops two computational methods for the moment generating function mgf or the characteristic function chf of a single lognormal rv the first method uses classical complex integration techniques based on steepest descent integration the saddle point of the integrand is explicitly expressed by the lambert function the steepest descent optimal contour and two closely related closed form contours are derived a simple integration rule e g the midpoint rule along any of these contours computes the mgf chf with high accuracy the second approach uses a variation on the trapezoidal rule due to ooura and mori importantly the cumulative distribution function of lognormal sums is derived as an alternating series and convergence acceleration via the epsilon algorithm is used to reduce in some cases the computational load by a factor of 106 overall accuracy levels of 13 to 15 significant digits are readily achievable

instantaneous mutual information and eigen channels in mimo mobile rayleigh fading in this paper we study two important metrics in multiple input multiple output mimo time varying rayleigh flat fading channels one is the eigen channel and the other is the instantaneous mutual information imi their second order statistics such as the correlation coefficient level crossing rate lcr and average fade outage duration are investigated assuming a general nonisotropic scattering environment exact closed form expressions are derived and monte carlo simulations are provided to verify the accuracy of the analytical results for the eigen channels we found they tend to be spatio temporally uncorrelated in large mimo systems for the imi the results show that its correlation coefficient can be well approximated by the squared amplitude of the correlation coefficient of the channel under certain conditions moreover we also found the lcr of imi is much more sensitive to the scattering environment than that of each eigen channel

outage mutual information of space time mimo channels we derive analytical expressions for the probability density function pdf of the random mutual information between transmitted and received vector signals of a random space time independent and identically distributed i i d multiple input multiple output mimo channel assuming that the transmitted signals from the multiple antennas are gaussian i i d we show that this pdf can be well approximated by a gaussian distribution and such a gaussian approximation is based on expressions for the given pdfs mean and variance that we derive we prove that at high signal to noise ratio snr every factor of 2 increase in snr leads to an increase in outage rate in the amount of min m n bits where m and n denote the number of transmit and receive antennas respectively a simple expression for the moment generating function mgf of the mutual information pdf is also provided based on which we establish normality of the pdf when both m and n are large and the snr is large

on the information rate of mimo systems with finite rate channel state feedback using beamforming and power on off strategy it is well known that multiple input multiple output mimo systems have high spectral efficiency especially when channel state information at the transmitter csit is available in many practical systems it is reasonable to assume that the csit is obtained by a limited i e finite rate feedback and is therefore imperfect we consider the design problem of how to use the limited feedback resource to maximize the achievable information rate in particular we develop a low complexity power on off strategy with beamforming or grassmann precoding and analytically characterize its performance given the eigenvalue decomposition of the covariance matrix of the transmitted signal refer to the eigenvectors as beams and to the corresponding eigenvalues as the beam s power a power on off strategy means that a beam is either turned on with a constant power or turned off we will first assume that the beams match the channel perfectly and show that the ratio between the optimal number of beams turned on and the number of antennas converges to a constant when the numbers of transmit and receive antennas approach infinity proportionally this motivates our power on off strategy where the number of beams turned on is independent of channel realizations but is a function of the signal to noise ratio snr when the feedback rate is finite beamforming cannot be perfect and we characterize the effect of imperfect beamforming by quantization bounds on the grassmann manifold by combining the results for power on off and beamforming a good approximation to the achievable information rate is derived simulations show that the proposed strategy is near optimal and the performance approximation is accurate for all experimented snrs

the valuative condition and r hopf algebra orders in kc p 3 let k be a finite extension of qp endowed with the p adic valuation and let r be its ring of integers in this paper we give a complete classification of r hopf algebra orders in the group ring kcp3 for an arbitrary hopf order h we show that either the group scheme sph or the group scheme sph with h the linear dual can be viewed as the middle term of the baer product of a distinguished extension with a generically trivial extension using this characterization we then compute algebra generators for either h or h

mimo channel modeling and the principle of maximum entropy we devise theoretical grounds for constructing channel models for multiple input multiple output mimo systems based on information theoretic tools the paper provides a general method to derive a channel model which is consistent with one s state of knowledge the framework we give here has already been fruitfully explored with success in the context of bayesian spectrum analysis and parameter estimation for each channel model we conduct an asymptotic analysis in the number of antennas of the achievable transmission rate using tools from random matrix theory a central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations the results are useful both in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks

dual diversity over correlated log normal fading channels a great deal of attention has been devoted in the literature to studying the bit error rate ber performance of diversity combining systems in the presence of rayleigh rice and nagakami m fading by comparison the literature is relatively sparse in comparable analyses over log normal channels which typically characterize shadowing from indoor obstacles and moving human bodies one reason for this disparity stems from the difficulty in evaluating the exact average ber when log normal variates are involved using for example the moment generating function mgf approach due to the inability of expressing the mgf itself in a simple closed form since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function cdf associated with a log normal distribution in closed form we rather focus here on other performance measures namely average combined output signal to noise ratio amount of fading and outage probability the first two performance measures depend only on the moments whereas the outage probability depends solely on the cdf closed form expressions in terms of known functions single integral representations or upper and lower bounds are obtained for these measures corresponding to maximal ratio combining selection combining and switch and stay combining schemes allowing for the possibility of correlation between the two branches numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented

bounds on the distribution of a sum of correlated lognormal random variables and their application the cumulative distribution function cdf of a sum of correlated or even independent lognormal random variables rvs which is of wide interest in wireless communications remains unsolved despite long standing efforts several cdf approximations are thus widely used this letter derives bounds for the cdf of a sum of 2 or 3 arbitrarily correlated lognormal rvs and of a sum of any number of equally correlated lognormal rvs the bounds are single fold integrals of readily computable functions and extend previously known bounds for independent lognormal summands an improved set of bounds are also derived which are expressed as 2 fold integrals for correlated lognormal fading channels new expressions are derived for the moments of the output snr and amount of fading for maximal ratio combining mrc selection combining sc and equal gain combining egc and outage probability expressions for sc

integral hopf galois structures on degree p2 extensions of p adic fields abstract let l k be a totally ramified normal extension of p adic fields of degree p2 we investigate the behavior of the valuation ring o l in the various hopf galois structures on l k specifically we determine when o l is hopf galois with respect to a hopf order in the corresponding hopf algebra when this occurs o l is necessarily a free module over this hopf order we also determine which hopf orders can arise in this way for cyclic extensions l k of degree p2 l n childs has shown under certain restrictions on the ramification numbers that if o l is hopf galois with respect to a hopf order in one of the hopf galois structures on l k then the same is true in all p hopf galois structures on l k we show that this no longer holds if the ramification conditions are relaxed or if elementary abelian extensions of degree of p2 are considered we illustrate our results with a special family of kummer extensions and with certain extensions arising from lubin tate formal groups

on the capacity of log normal fading channels in this letter we provide an analytical expression for the moments of the capacity for the log normal fading channel since the developed expression involves infinite series we show that the error that results from the truncation of these series is insignificant we also analyze in more details the ergodic capacity by giving a simpler expression for the remainder of the truncated series relying on the fact that the sum of log normal random variables rv is well approximated by another lognormal rv we further utilize the obtained results to approximate the capacity of diversity combining techniques in correlated lognormal fading channels the results that we provide in this letter are an important tool for measuring the performance of communication links in a log normal environment

approximating the linear combination of log normal rvs via pearson type iv distribution for uwb performance analysis approximating the sum of log normal random variables rvs is a long standing open issue and many studies in the old and recent literature resort to assume that the power sum can be well modeled via another log normal rv such a log normal approximation can be effectively used for accurate outage probability pout analysis and modeling of signal to noise interference ratio snir behaviors in the context of radio resource management in wireless systems nevertheless it is recognized that i an adequate accuracy can only be obtained for a sub range of values taken by the distribution ii the achievable accuracy depends on the parameters of the set of rvs iii log normal approximation may not provide a satisfactory accuracy for estimating bit error probabilities moreover all contributions in the open technical literature are referred to model the power sum distribution i e the weighted linear combination of log normal rvs with weights that may take only positive values while this setup is consistent with typical scenarios where summands add incoherently it has recently been shown that in some high frequency selective multipath channels with log normal distributed shadow and fast fading e g in impulse radio ultra wide band ir uwb systems the signal to noise ratio snr is more accurately modeled by the weighted linear combination of log normal rvs with weights that may assume both positive and negative values motivated by the above considerations and moving from recent results which show that approximating the power sum of log normal rvs can boil down to a model selection problem within the pearson system of distributions the specific contribution of this paper can be summarized as follows i we show that the pearson type iv distribution can not only be used to accurately approximate the probability density function pdf of the power sum of log normal rvs with positive weights but it can also accurately model the scenario with both positive and negative weights as well as the scenario with generically correlated rvs ii for the scenario with independent rvs we propose a numerical technique which is based on the moment generating function mgf matching principle and uses a least squares criterion to accurately estimate the four parameters of the pearson type iv distribution iii a byproduct of this analysis

stationary random fields in space and time with rational spectral densities this paper introduces three spatio temporal stationary random fields with simple correlation functions and rational spectral densities the correlation functions have similar forms but are defined on different space time domains or related to different spatial norms positive and negative correlations are allowed and the domain of certain model parameters may rely on the spatial dimensional parameter so that the model may be available in a limited space or in all dimensions the distinctions are discussed among the three basic correlation models moreover families of spatio temporal stationary random fields are derived by randomizing the spatial and temporal coordinates of the base random fields the resulting correlation functions are semiparametric and include separable spatio temporal models as special cases

duality for hopf orders in this paper we use duality to construct new classes of hopf orders in the group algebra kc p3 where k is a finite extension of q p and c p3 denotes the cyclic group of order p 3 included in this collection is a subcollection of hopf orders which are realizable as galois groups

on an efficient k step iterative method for nonlinear equations this paper is devoted to the construction and analysis of an efficient k step iterative method for nonlinear equations the main advantage of this method is that it does not need to evaluate any high order frechet derivative moreover all the k step have the same matrix in particular only one lu decomposition is required in each iteration we study the convergence order the efficiency and the dynamics in order to motivate the proposed family we prove using some recurrence relations a semilocal convergence result in banach spaces finally a numerical application related to nonlinear conservative systems is presented

closed form statistics for the sum of squared nakagami m variates and its applications we present closed form expressions for the probability density function pdf and the cumulative distribution function cdf of the sum of non identical squared nakagami m random variables rvs with integer order fading parameters as it is shown they can be written as a weighted sum of erlang pdfs and cdfs respectively while the analysis includes both independent and correlated sums of rvs the proposed formulation significantly improves previously published results which are either in the form of infinite sums or higher order derivatives of the fading parameter m the obtained formulas can be applied to the performance analysis of diversity combining receivers operating over nakagami m fading channels

maximum efficiency for a family of newton like methods with frozen derivatives and some applications a generalized k step iterative application of newton s method with frozen derivative is studied and used to solve a system of nonlinear equations the maximum computational efficiency is computed a sequence that approximates the order of convergence is generated for the examples and it numerically confirms the calculation of the order of the method and computational efficiency this type of method appears in many applications where the authors have heuristically chosen a given number of steps with frozen derivatives an example is shown in which the total variation tv minimization model is approximated using the schemes described in this paper

predetermining the number of periodic steps in multi step newton like methods for solving equations and systems of equations abstract the goal of this paper is to predetermine the steps m after which the first derivative is re evaluated for multi step newton type method used to approximate solutions of equations

free space optical communication a diversity multiplexing tradeoff perspective due to the rapid growth of free space optical fso communication over the last few years there is an exigency to develop diversity multiplexing tradeoff dmt metric in order to compare and design new multiple input multiple output mimo fso schemes this paper introduces the dmt for mimo fso systems that utilize the intensity modulation and direct detection technique for which the channel gains are real and positive contrary to mimo radio frequency mimo rf systems where the channel gains are complex log normal gamma gamma and negative exponential channel models are used in this paper to cover weak to saturated turbulence environments it is shown that at zero multiplexing gain r the log normal channel offers maximum but finite diversity order that depends on the block length within which the channel matrix is constant on the other hand negative exponential channel offers minimum diversity order however for r geq 1 dmt curves under all channel models are of the same nature and for a given r the diversity is half as that observed in the mimo rf channels to gain additional insights into the dmt of an mimo fso system we also develop upper and lower bound expressions of dmt and determine the minimum block length at which these bounds are identical

approximation for a sum of on off log normal processes with wireless applications in this paper a log normal approximation is proposed for the sum of log normal processes weighted by binary processes the analytical approach moves from the method earlier proposed by wilkinson for approximating first order statistics of the sum of log normal components and extends to incorporate second order statistics and the presence of both time correlated random binary weights and cross correlated log normal components in moments matching since the sum of weighted log normal processes models the signal to interference plus noise ratio of wireless systems the method can be applied to evaluate in an effective and accurate way the outage occurrence rate and outage duration for different wireless systems of practical interest in a frequency reuse based cellular system the method is applied to various propagation scenarios characterized by different shadowing correlation decay distances and correlations among shadowing components a further case of relevant interest is related to power controlled wideband wireless systems where the random weights are binary random variables denoting the activity status of each interfering source finally simulation results are used to confirm the validity of the analysis for the considered cases of practical interest

on the local convergence study for an efficient k step iterative method research was supported in part by programa de apoyo a ia investigacion de ia fundacion seneca agencia de ciencia y tecnologia de la region de murcia 19374 pi 14 by the project of generalitat valenciana prometeo 2016 089 and the projects mtm2015 64382 p mineco feder mtm2014 52016 c2 1 p and mtm2014 52016 c2 2 p of the spanish ministry of science and innovation