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

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

blow up and global solutions to a new integrable model with two components abstract we will discuss a new integrable model which describes the motion of fluid the present work is mainly concerned with global existence and blow up phenomena which are largely due to the application of conservation laws for this integrable equations moreover a new blow up criterion for nonperiodic case is also established via the associated potential some interesting examples are also given to illustrate the application of our results the precise blow up rate is also investigated finally we will emphasize the relations of classical camassa holm equation and our model by analyzing the existence of global solutions

on the wave breaking phenomena for the periodic two component dullin gottwald holm system abstract considered herein is the well posedness problem of the periodic two component dullin gottwald holm dgh system on the circle which can be derived from euler s equation with constant vorticity in shallow water waves moving over a linear shear flow the result of blow up solutions for certain initial profiles in a manner which corresponds to wave breaking is established

performance analysis of multi innovation gradient type identification methods it is well known that the stochastic gradient sg identification algorithm has poor convergence rate in order to improve the convergence rate we extend the sg algorithm from the viewpoint of innovation modification and present multi innovation gradient type identification algorithms including a multi innovation stochastic gradient misg algorithm and a multi innovation forgetting gradient mifg algorithm because the multi innovation gradient type algorithms use not only the current data but also the past data at each iteration parameter estimation accuracy can be improved finally the performance analysis and simulation results show that the proposed misg and mifg algorithms have faster convergence rates and better tracking performance than their corresponding sg algorithms

global weak solutions for a two component camassa holm shallow water system abstract in this paper we prove the existence of global weak solution for an integrable two component camassa holm shallow water system provided the initial data satisfying some certain conditions

optimal minimum distance based precoder for mimo spatial multiplexing systems we describe a new precoder based on optimization of the minimum euclidean distance d sub min between signal points at the receiver side and for use in multiple input multiple output mimo spatial multiplexing systems assuming that channel state information csi can be made available at the transmitter the three steps noise whitening channel diagonalization and dimension reduction which are currently used in investigations on mimo systems are performed thanks to this representation an optimal d sub min precoder is derived in the case of two different transmitted data streams for quadrature phase shift keying qpsk modulation a numerical approach shows that the precoder design depends on the channel characteristics comparisons with maximum signal to noise ratio snr strategy and other precoders based on criteria such as water filling wf minimum mean square error mmse and maximization of the minimum singular value of the global channel matrix are performed to illustrate the significant bit error rate ber improvement of the proposed precoder

generalized linear precoder and decoder design for mimo channels using the weighted mmse criterion we address the problem of designing jointly optimum linear precoder and decoder for a mimo channel possibly with delay spread using a weighted minimum mean squared error mmse criterion subject to a transmit power constraint we show that the optimum linear precoder and decoder diagonalize the mimo channel into eigen subchannels for any set of error weights furthermore we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights we show how to obtain 1 the maximum information rate design 2 qos based design we show how to achieve any set of relative snrs across the subchannels and 3 the unweighted mmse and equal error design for fixed rate systems

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

structure of an optimum linear precoder and its application to ml equalizer the structure of an optimum linear precoder for a rotation invariant performance measure is obtained subject to the constraint of limited input power for a block transmission scheme it is shown that several known performance measures of a communication system are rotation invariant the rotation invariant property provides a unified framework for obtaining the structure of an optimum linear precoder for several criteria such as 1 maximization of minimum distance 2 maximization of channel capacity and 3 optimization of different performance measures such as bit error rate ber mean square error signal to noise ratio of optimum equalizers linear minimum mean square error zero forcing maximum likelihood ml zero forcing block decision feedback minimum mean square error block decision feedback etc this framework provides a method for obtaining the structure of an optimum linear precoder for ber performance measure of the ml equalizer the structure turns out to be a channel diagonalizing structure after a prerotation of the input constellation using this structure the properties of the optimum precoder that minimize the ber of the ml equalizer for two binary phase shift keying symbols transmission under input power constraint are studied

on the usefulness of persistent excitation in arx adaptive tracking the usefulness of persistent excitation is well known in the control community thanks to a persistently excited adaptive tracking control we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional arx framework we establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters a central limit theorem and a law of iterated logarithm are also provided all this asymptotical analysis is related to the schur complement of a suitable limiting matrix

relations between information criteria for model structure selection part 2 modelling by shortest data description the structure selection of stochastic dynamic models by the predictive least squares pls criterion introduced by rissanen and wertz 1985 is investigated in this paper in view of its relations to the bayesian estimator and to information criteria with a penalty term it is shown that in the autoregressive case the strong consistency of the pls criterion can be derived from the strong consistency of the bayesian order estimator

on the well posedness problem and the scattering problem for the dullin gottwald holm equation in this paper we study the well posedness of the cauchy problem and the scattering problem for a new nonlinear dispersive shallow water wave equation the so called dgh equation which was derived by dullin gottwald and holm the issue of passing to the limit as the dispersive parameter tends to zero for the solution of the dgh equation is investigated and the convergence of solutions to the dgh equation as 2 0 is studied and the scattering data of the scattering problem for the equation can be explicitly expressed the new exact peaked solitary wave solutions are obtained in the dgh equation after giving the condition of existing peakon in the dgh equation it turns out to be nonlinearly stable for the peakon in the dgh equation

global existence and blow up solutions for a nonlinear shallow water equation considered herein are the problems of the existence of global solutions and the formation of singularities for a new nonlinear shallow water wave equation derived by dullin gottward and holm blow up can occur only in the form of wave breaking a wave breaking mechanism for solutions with certain initial profiles is described in detail and the exact blow up rate is established the blow up set for a class of initial profiles and lower bounds of the existence time of the solution are also determined

weighted estimation and tracking for branching processes with immigration for branching processes with immigration we propose an approach which allows us to consistently estimate the means m spl lambda and the variances spl sigma sup 2 b sup 2 of the offspring and immigration distributions respectively generally statistical results for branching processes are established under the well known trichotomy m 1 for example no parameters of the immigration distribution can be consistently estimated if m 1 the purpose of the paper is to obtain through the introduction of a suitable adaptive control strongly consistent estimators for all the parameters m spl lambda spl sigma sup 2 and b sup 2 without any restriction on the range of m central limit theorems and laws of iterated logarithm are also provided

will the pls criterion for order estimation work with aml and a posteriori prediction error the general formula of the pls predictive least squares criterion for order estimation is worked out under the assumption that the parameter estimates are calculated via the aml approximate maximum likelihood a particular case is then carefully analysed and it is shown that depending on the system generating the data the pls critetion using the a posteriori prediction error can surprisingly almost surely overestimate the true order

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

toward optimal model averaging in regression models with time series errors abstract consider a regression model with infinitely many parameters and time series errors we are interested in choosing weights for averaging across generalized least squares gls estimators obtained from a set of approximating models however gls estimators depending on the unknown inverse covariance matrix of the errors are usually infeasible we therefore construct feasible generalized least squares fgls estimators using a consistent estimator of the unknown inverse matrix based on this inverse covariance matrix estimator and fgls estimators we develop a feasible autocovariance corrected mallows model averaging criterion to select weights thereby providing an fgls model averaging estimator of the true regression function we show that the generalized squared error loss of our averaging estimator is asymptotically equivalent to the minimum one among those of gls model averaging estimators with the weight vectors belonging to a continuous set which includes the discrete weight set used in hansen 2007 as its proper subset

minimum ber block precoders for zero forcing equalization we determine the linear precoder that minimizes the bit error rate ber at moderate to high signal to noise ratios snrs for block transmission systems with zero forcing zf equalization and threshold detection the design is developed for the two standard schemes for eliminating inter block interference viz zero padding zp and cyclic prefix cp we show that both the zp minimum ber precoder and the cp minimum ber precoder provide substantially lower error rates than standard block transmission schemes such as orthogonal frequency division multiplexing ofdm the corresponding snr gains can be on the order of several decibels we also show that the cp minimum ber precoder can be obtained by a two stage modification of the water filling discrete multitone modulation dmt scheme in which the diagonal water filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete fourier transform dft matrix

wave breaking for a modified two component camassa holm system abstract in this paper we establish sufficient conditions on the initial data to guarantee blow up phenomenon for the modified two component camassa holm mch2 system

adaptive prediction by least squares predictors in stochastic regression models with applications to time series on considere un modele de regression multiple et on etudie la performance asymptotique des predicteurs des moindres carres

performance analysis of estimation algorithms of nonstationary arma processes the correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive ar moving average ma and arma systems by using estimation residuals in place of unmeasurable noise terms in information vector or matrix we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity ergodicity or existence of higher order moments furthermore we derive the conditions for convergence of the parameter estimation the simulation results validate the convergence theorems proposed

singular solutions of a modified two component camassa holm equation the camassa holm ch equation is a well known integrable equation describing the velocity dynamics of shallow water waves this equation exhibits spontaneous emergence of singular solutions peakons from smooth initial conditions the ch equation has been recently extended to a two component integrable system ch2 which includes both velocity and density variables in the dynamics although possessing peakon solutions in the velocity the ch2 equation does not admit singular solutions in the density profile we modify the ch2 system to allow a dependence on the average density as well as the pointwise density the modified ch2 system mch2 does admit peakon solutions in the velocity and average density we analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially confined initial data numerical results for the mch2 system are given and compared with the pure ch2 case these numerics show that the modification in the mch2 system to introduce the average density has little short time effect on the emergent dynamical properties however an analytical and numerical study of pairwise peakon interactions for the mch2 system shows a different asymptotic feature namely besides the expected soliton scattering behavior seen in overtaking and head on peakon collisions the mch2 system also allows the phase shift of the peakon collision to diverge in certain parameter regimes

brief paper a new concept of strong controllability via the schur complement for arx models in adaptive tracking we propose a new concept of strong controllability related to the schur complement of a suitable limiting matrix this new notion allows us to extend the previous convergence results associated with multidimensional arx models in stochastic adaptive tracking on the one hand we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms on the other hand we also provide a central limit theorem and a law of iterated logarithm for these two algorithms

accumulated prediction errors information criteria and optimal forecasting for autoregressive time series the predictive capability of a modification of rissanen s accumulated prediction error ape criterion ape n is investigated in infinite order autoregressive ar oo models instead of accumulating squares of sequential prediction errors from the beginning ape n is obtained by summing these squared errors from stage n n where n is the sample size and 1 n n 1 1 n may depend on n under certain regularity conditions an asymptotic expression is derived for the mean squared prediction error mspe of an ar predictor with order determined by ape n this expression shows that the prediction performance of ape n can vary dramatically depending on the choice of n another interesting finding is that when n approaches 1 at a certain rate ape n can achieve asymptotic efficiency in most practical situations an asymptotic equivalence between ape n and an information criterion with a suitable penalty term is also established from the mspe point of view this offers new perspectives for understanding the information and prediction based model selection criteria finally we provide the first asymptotic efficiency result for the case when the underlying ar oo model is allowed to degenerate to a finite autoregression

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

testing for change points in time series models and limiting theorems for ned sequences this paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near epoch dependent sequences using these limiting theorems we develop a general asymptotic theory on the wald test for change points in a general class of time series models under the no change point hypothesis as an application we verify our assumptions for the long memory fractional arima model

wave breaking phenomenon for a modified two component dullin gottwald holm equation this paper is concerned with the wave breaking phenomenon for a modified two component dullin gottwald holm shallow water system we give sufficient conditions on the initial data to guarantee blow up of solutions in finite time

blow up of solutions to the dgh equation in this paper firstly we find best constants for two convolution problems on the unit circle via a variational method then we apply the best constants on a nonlinear integrable shallow water equation the dgh equation to give sufficient conditions on the initial data which guarantee finite time singularity formation for the corresponding solutions finally we discuss the blow up phenomena for the nonperiodic case

global existence and blow up phenomena for an integrable two component camassa holm shallow water system abstract this paper is concerned with global existence and blow up phenomena for an integrable two component camassa holm shallow water system a new global existence result and several new blow up results of strong solutions to the system are presented our obtained results for the system are sharp and improve considerably earlier results

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

selecting optimal multistep predictors for autoregressive processes of unknown order we consider the problem of choosing the optimal in the sense of mean squared prediction error multistep predictor for an autoregressive ar process of finite but unknown order if a working ar model which is possibly misspecified is adopted for multistep predictions then two competing types of multistep predictors i e plug in and direct predictors can be obtained from this model we provide some interesting examples to show that when both plug in and direct predictors are considered the optimal multistep prediction results cannot be guaranteed by correctly identifying the underlying model s order this finding challenges the traditional model order selection criteria which usually aim to choose the order of the true model a new prediction selection criterion which attempts to seek the best combination of the prediction order and the prediction method is proposed to rectify this difficulty when the underlying model is stationary the validity of the proposed criterion is justified theoretically to obtain this result asymptotic properties of accumulated squares of multistep prediction errors are investigated in addition to overcoming the above difficulty some other advantages of the proposed criterion are also mentioned

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation