schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

nonparametric trellis equalization in the presence of non gaussian interference we consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference cci conventional maximum likelihood sequence estimation mlse and maximum a posteriori probability map trellis equalizers treat the sum of noise and interference as additive white gaussian noise while cci is generally a colored non gaussian process we propose a novel nonparametric approach based on the estimation of the probability density function of the noise plus interference given the availability of a limited volume of data the density is estimated by kernel smoothing techniques the use of a whitening filter in the presence of temporally colored disturbance is also addressed simulation results are provided for the global system for mobile communications gsm showing a significant performance improvement with respect to the equalizer based on the gaussian assumption major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available

on sampling rate analog prefiltering and sufficient statistics for digital receivers we consider the joint sequence estimation timing and phase recovery for linear modulation the paper differs from the classical ones in the sense that time discrete algorithms suitable for fully digital receivers are discussed sufficient conditions are given such that the signal samples represent sufficient statistics these conditions involve signal bandwidth sampling symbol rate and the analog prefilter characteristics it is shown that the sampling rate need not be an exact multiple of the symbol rate i e the samples can be taken from a free running oscillator all subsequent signal processing operations in the receiver then operate with the clock of this free running oscillator timing recovery is then performed by a time variant linear digital interpolator and a decimator carrier recovery and sequence estimation are performed at an average rate of one symbol per sample the digital matched filter for this case is derived for an arbitrary colored noise spectrum

moment problems and orthogonal functions abstract the caratheodory coefficient problem for an infinite sequence c n can be formulated as follows find a caratheodory function f z i e an analytic function mapping the unit disk d z z into the right half plane p w re w 0 whose taylor coefficients at a fixed points in d for convenience the origin are the c n this problem is equivalent to the trigonometric moment problem find a measure on such that e i n d c n for n 0 1 2 these problems are closely related to the theory of szego polynomials i e orthogonal polynomials on the unit circle t z z 1 let n be an arbitrary given sequence of not necessarily distinct points in d and let w n be a given sequence of numbers the nevanlinna pick problem for this situation is to find a caratheodory function f z with the interpolation property f n w n for all n when points n are repeated the interpolation property involves the appropriate number of taylor coefficients also this problem is connected with the problem of finding a measure generating moments the nevanlinna pick problem is related to a theory of rational functions which are orthogonal on t with poles at the points 1 n this relationship is analogous to and generalizes the relationship between the caratheodory coefficient problem or trigonometric moment problem and polynomials orthogonal on t the situation when points n are given on the boundary t or d is also briefly discussed

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

synchronized per survivor mlsd receiver using a differential kalman filter a synchronized per survivor processing psp maximum likelihood sequence detection mlsd receiver is presented for a fast frequency selective rayleigh fading channel and large carrier frequency offset it is shown that by incorporating the synchronization parameters the timing error carrier frequency and phase offsets into the channel impulse response cir and modifying the resulting state space model by a differential approach the time varying carrier frequency offset can be effectively tracked using a simple least mean square lms estimator new criteria are proposed based on the smoothness of the estimated channel derivatives new criteria are proposed based on this fact that for smoothly time varying cir and frequency offset the magnitude of the cir time derivative compared with the magnitude of cir should be very small it is illustrated that the new criteria and the conventional mean square error mse are complementary

joint maximum likelihood parameter estimation for burst ds spread spectrum transmission we first derive the joint optimal maximum likelihood ml estimator of the carrier phase both doppler shift and doppler rate and the spreading code delay for a short burst direct sequence spread spectrum ds ss transmission in the absence of the data modulation the typical burst duration is three data bit periods 60 ms the performance of the joint estimator is analytically derived separately for high and low carrier to noise ratio cnr values a suboptimal ml estimator based on the method of averaged periodogram is proposed for the data modulation present case allowing the joint estimation of the data bit values then the above parameters are assumed correctly estimated and a segmentation approach is adopted deriving the optimal joint ml estimator for the bit synchronization epoch and data simulations show the joint estimators perform reliable down to a cnr of approximately 30 db spl middot hz

favard theorem for reproducing kernels abstract consider for n 0 1 the nested spaces l n of rational functions of degree n at most with given poles 1 i i i 1 n let l 0 l n given a finite positive measure on the unit circle we associate with it an inner product on l by g g d suppose kn z w is the reproducing kernel for l n i e z k n z w w for all l n w then it is known that they satisfy a coupled recurrence relation in this paper we shall prove a favard type theorem which says that if you have a sequence of kernel functions kn z w which are generated by such a recurrence then there will be a measure supported on the unit circle so that kn is the reproducing kernel for ln the measure is unique under certain extra conditions on the points i

twisted condensates of quantised fields the authors construct some quasi free pure states of three quantised fields in 1 1 dimensions that are localised in the sense of knight 1961 they consider massless or massive dirac fields forming a u n n or 1 multiplet and subject it to a local gauge transformation they also subject a doublet of massive klein gordon fields to local so 2 transformations they find the conditions that the resulting automorphisms are spatial in fock space in some cases the conditions turn out to require that certain parameters identified as the winding numbers of the gauge are integers it is argued that this integer labels states of various charge

closed loop least mean square time delay estimator an lms closed loop time delay estimator is presented it uses the error between two samples of the incoming signal the difference between the delayed signal and the reference signal passed through a known delay as a performance index for the estimator the lms algorithm adaptively controls the delay so as to minimize the mean square of this error the controlled delay is implemented using surface acoustic wave devices certain design conditions are applied resulting in a unique minimum for the performance surface it is shown that the proposed estimator is unbiased and has a small variance if the input signal occupies most of the system bandwidth in fact the variance depends on the input noise power and the generalized noise to signal power ratio r n 0 r s 0 as well as on the loop gain the analysis performed also gives a bound on the loop gain required for convergence of the estimator and predicts its rate of convergence computer simulation results show good agreement with the theory

convergence of a ml parameter estimation algorithm for ds ss systems in time varying channels with strong interference an unbiased maximum likelihood ml channel parameter estimation algorithm for direct sequence spread spectrum systems with strong interference is discussed in this paper the algorithm includes correcting terms to the extended kalman filter ekf based on the gradient of the negative log likelihood function of the output of a conventional matched filter by an asymptotic analysis the algorithm is shown to determine the actual parameters a complete implementation of the algorithm is given and its transient behavior is examined by computer simulations results show the ml algorithm albeit optimal in the sense of unbiased parameter estimation is less robust than the modified ekf described in the first reference

sampling and prefiltering effects on blind equalizer design in the development of equalization algorithms for unknown channels the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked in this paper these effects are investigated the relationship between the fractionally spaced output samples of a noise limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time invariant and the time varying channels it is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms thus this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates a case study of the well known subspace method for blind channel identification is presented the effects of the noise color due to the prefilter on equalizers is investigated and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error mse performance criterion is investigated through numerical examples

foreword to the proceedings of the orthoquad 2014 conference orthoquad 2014 was an international symposium on orthogonality quadrature and related topics held on january 20 24 2014 in puerto de la cruz tenerife spain it was held in memory of professor pablo gonzalez vera 1955 2012

sequence detection in nonlinear channels a convenient alternative to analog predistortion a new maximum likelihood sequence detection receiver for spectrally efficient linear modulations on bandlimited bandpass nonlinear channels is proposed the receiver is based on oversampling the received signal corrupted by noise and nonlinear distortion contrary to other solutions in the literature in the proposed technique there is no need for a bank of matched filters and the receiver front end reduces to a single lowpass filter for a given peak power level a performance gain can be achieved over more traditional approaches to transmission on nonlinear channels such as those based on predistortion if a moderate spectral expansion is allowed to analyze the receiver performance the concept of distance spectrum is employed since the minimum distance alone cannot account for a reliable performance evaluation both analysis and simulation are carried out for realistic narrowband nonlinear channels possibly employing reduced state sequence detection appreciable gain margins are confirmed to be possible in these realistic cases

a systematic framework for iterative maximum likelihood receiver design in this paper we link the turbo principle to unconstrained maximum likelihood ml sequence detection and joint ml parameter estimation first we demonstrate for memoryless channels with complete channel state information how the turbo decoder can be systematically derived starting from the ml sequence detection criterion in particular we show that a method to solve the ml sequence detection problem is to iteratively solve the corresponding critical point equations of an equivalent unconstrained estimation problem by means of fixed point iterations the turbo decoding algorithm is obtained by approximating the overall a posteriori probabilities subsequently we show how this general approximative iterative maximum likelihood aiml framework can be applied to general iterative ml receiver design we consider static memoryless channels with unknown channel parameters the time selective fading channels with partial channel state information is the subject of a companion paper

some local covariant representations of the canonical anticommutation relations the authors find some non fock representations of the canonical anticommutation relations in 1 1 dimensions these representations obtained by a bogoliubov transformation of the fock annihilation and creation operators are poincare covariant have positive energy and are labelled by two conserved charges which take on continuous values in the interval 0 2 pi

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

signal detection for orthogonal space time block coding over time selective fading channels a pic approach for the g sub i systems one major assumption in all orthogonal space time block coding o stbc schemes is that the channel remains static over the entire length of the codeword however time selective fading channels do exist and in such case the conventional o stbc detectors can suffer from a large error floor in the high signal to noise ratio snr cases this paper addresses such an issue by introducing a parallel interference cancellation pic based detector for the g sub i coded systems i 3 and 4

design of optimal interpolation filter for symbol timing recovery we propose an optimal interpolation filter for symbol timing recovery in a digital receiver where the input analog to digital a d conversion sampling clock is not synchronized to the transmitter symbol clock the optimal filter is designed by minimizing the mean square error mse at the output of the receiver assuming that the correct timing difference between the nonsynchronized input samples and the correct strobe synchronized to the symbol is given the mse minimization procedure results in a system of linear equations which can easily be solved to yield the optimal filter coefficients we also analyze the symbol tracking performance of a symbol synchronizer that employs the proposed optimal interpolation filter although the proposed optimal filter is designed assuming the availability of the correct timing difference we show that it minimizes the timing estimation error variance even when the computed timing difference values deviate from the ideal we also show that the timing estimation is virtually unbiased if the length of the interpolation filter is greater than or equal to 4 simulation results are included to show the performance improvement realizable by employing the optimal interpolation filter

an ekf based joint estimator for interference multipath and code delay in a ds spread spectrum receiver in direct sequence ds spread spectrum communications it is often necessary to obtain pseudo noise pn code synchronization in the presence of both narrowband interference and frequency selective multipath however conventional delay lock code tracking loops are not optimized for such applications nor are they well suited to digital implementations a code tracking algorithm based on the extended kalman filter ekf is described that provides both code synchronization and joint estimates of interferer and channel parameters it is first assumed that the interference can be modeled by an n th order autoregressive ar process and the multipath by a finite impulse response filter a composite channel equivalent to the convolution of the prewhitening filter and multipath coefficients is then constructed the received waveform is shown to be a linear function of the composite channel parameters that can therefore be directly estimated by an extended kalman filter the code delay spl tau is viewed as a nonlinear parameter that can likewise by estimated after an appropriate linearization using the ekf the performance of the algorithm is first evaluated by computing the average bit error rate ber of a digital rake receiver that employs the joint delay channel and interferer estimates derived from the ekf in addition a nonlinear analysis of the ekf is performed in which the code delay error and error covariance are modeled as a two dimensional markov process the joint probability density function of these parameters and nonlinear delay error variance are obtained via numerical integration of a two dimensional chapman kolmogorov equation

mutual tracking in phase and delay of randomly modulated signals a two parameter tracking loop that mutually locks the phases and delays of two noise contaminated replicas of a randomly phase modulated signal received via different channels is analyzed it is shown that at high snr i e small tracking errors the twoparameter loop can be considered as two uncoupled single parameter loops provided the signals are beaten down to zero center frequency special emphasis is put on the delay error variance it is found that in general the broadening of the phase loop bandwidth provided for more rapid acquisition induces larger delay tracking errors also such broadening decreases the expected time to loss of delay lock the influence of the location of the absorbing boundaries for this problem is investigated quantitative results for a typical configuration are presented in figs 1 9

some covariant representations of massless fermi fields studies the class of pure quasi free gauge invariant states of the fermion algebra the authors show that the question of g covariance of the corresponding representations i e implementability of some group g of one particle symmetry transformations is related to a cohomology group with values in the hilbert schmidt class in four dimensional space time this cohomology is nontrivial thus leading to g covariant non fock representations when g is taken to be the space time translation group together with rotations or space time translations together with boosts in one direction and rotations about it and the fermion mass is zero in two space time dimensions some new fully poincare covariant representations for free massless fermions are constructed

a sequential monte carlo filter for joint linear nonlinear state estimation with application to ds cdma a sequential monte carlo filter is considered which combines previously developed sequential importance sampling sis techniques for conditional linear gaussian models with measurement linearization for construction of approximate simulation densities the resulting sequential monte carlo kalman filter smc kf consists of a bank of conventional kalman filters individually tuned to sampled trajectories of the nonlinear state variables sampling is according to a gaussian distribution with mean and covariance determined by extended kalman filter type equations the smc kf is then applied to joint delay and multipath channel estimation in direct sequence code division multiple access ds cdma a combined analytical simulation technique is employed to compare performance of the smc kf and a previously derived extended kalman filter ekf based ds cdma channel estimator

joint estimation of pn code delay and multipath using the extended kalman filter the problem of delay estimation in the presence of multipath is considered it is shown that the extended kalman filter ekf can be used to obtain joint estimates of time of arrival and multipath coefficients for deterministic signals when the channel can be modeled as a tapped delay line simulation results are presented for the ekf joint estimator used for synchronization in a direct sequence spread spectrum system operating over a frequency selective fading channel a simplified model of the ekf joint estimator is considered for analysis purposes the evolution in time of the tracking error probability density function and the nonlinear tracking error variance are examined through numerical solution of the chapman kolmogorov equation the nonlinear tracking error variance is compared to both the linear error variance estimate directly provided by the ekf and the cramer rao lower bound

iterative multiuser receivers for cdma channels an em based approach maximum likelihood detection for the multiuser code division multiple access cdma channel is prohibitively complex this paper considers new iterative multiuser receivers based on the expectation maximization em algorithm and related more powerful space alternating algorithms the latter algorithms include the sage algorithm and a new missing parameter space alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data application of these em based algorithms to the problem of discrete parameter estimation i e data detection in the gaussian multiple access channel leads to a variety of convergent receiver structures that incorporate soft decision feedback for interference cancellation and or sequential updating of iterative bit estimates convergence and performance analyses are based on well known properties of the em algorithm and on numerical simulation

modified cramer rao bounds for continuous phase modulated signals we consider the estimation of signal amplitude time offset and the parameters of a polynomial phase signal from a continuous phase modulated cpm signal that contains both unknown data symbols and known pilot symbols transformation of the polynomial phase signal into an orthogonal basis allows us to derive the modified cramer rao bounds mcrb for the problem of vector parameter estimation in closed form numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences since our bounds are easy to evaluate they can aid the design of pilot and burst configuration for cpm systems

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

adaptive parameter estimation using parallel kalman filtering for spread spectrum code and doppler tracking we present a new digital direct sequence ds receiver with joint estimation of code delay multipath gains and doppler shift a parameter estimator consisting of a parallel bank of extended kalman filters ekf s extracts estimates of the timing t and the multipath coefficients fl distorting the received signal a detected estimate of the doppler shift vr distorting the received signal is also provided by the estimator we compute the bit error rate that results when a rake matched filter uses the estimated parameters to detect the dpsk encoded binary data in the received signal the bit error rate ber is evaluated and successful performance of the proposed receiver in the presence of doppler shift distortion is observed in many cases we demonstrate that the receiver can operate when the multipath coefficients vary in time doppler spread

effects of multiple access interference on the noncoherent delay lock loop this paper presents a performance analysis of the noncoherent delay lock loop nc dll in the presence of multiple access interference mai a renewal theory approach is applied along with the more familiar linear theory the effect of the mai on performance is evaluated in terms of the mean time to lose lock and the root mean square rms tracking error the analysis is made tractable by approximating the aperiodic cross correlation function between two pseudonoise pn code sequences the results are compared with those which assume that the mai can be approximated as gaussian noise as expected the results indicate a drastic decrease in performance as the number of users in a system is increased the effect of the near far ratio pn code sequence length system load and signal to noise ratio on the performance of the nc dll in mai are also examined

diversity combining for ds ss systems with time varying correlated fading branches diversity combining of multiple time varying and correlated fading branches is investigated for direct sequence spread spectrum systems the correlated branches are modeled and estimated jointly as a vector autoregressive var process the joint estimation is shown to provide performance gain over separate estimation of the fading branches the parameter matrices of the var model are estimated via the method of expectation maximization em with two algorithms the first algorithm using results from kalman smoothing provides a closed form solution to the maximization problem in the iterative em procedure however the iterative em kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays to overcome these disadvantages a new algorithm with only forward time recursions is proposed that approximates the iterative em solution and efficiently adapts to slowly changing doppler spreads as a result the new algorithm significantly reduces memory and training sequence requirements through computer simulations a near ideal bit error rate performance is found for both algorithms and the efficacy of the new adaptive algorithm for channels with changing doppler spreads is demonstrated