an upper bound on the aperiodic autocorrelation function for a maximal length sequence corresp the magnitude of the out of phase aperiodic autocorrelation function for a maximal length linear feedback shift register sequence of period n is at most 1 2 pi n 1 1 2 ln 4n pi previously the best upper bound was n 1 1 2 ln en

the wssus pulse design problem in multicarrier transmission optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering wssus mobile communication channels is still an unsolved problem despite its importance for next generation system design in multicarrier transmission such link adaption is performed by pulse shaping i e by properly adjusting the transmit and receive filters for example pulse shaped offset quadrature amplitude modulation oqam systems have recently been shown to have superior performance over standard cyclic prefix orthogonal frequency division multiplexing ofdm while operating at higher spectral efficiency in this paper we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so called weyl heisenberg or gabor signaling with respect to the scattering function of the wssus channel in our framework the pulse shape optimization problem is translated to an optimization problem over trace class operators which in turn is related to fidelity optimization in quantum information processing by convexity relaxation the problem is shown to be equivalent to a convex constraint quasi convex maximization problem thereby revealing the nonconvex nature of the overall wssus pulse design problem we present several iterative algorithms for optimization providing applicable results even for large scale problem constellations we show that with transmitter side knowledge of the channel statistics a gain of 3 6 db in signal to interference and noise ratio sinr can be expected

orthogonal time frequency signaling over doubly dispersive channels this paper develops a general framework for communication over doubly dispersive fading channels via an orthogonal short time fourier stf basis the stf basis is generated from a prototype pulse via time frequency shifts in general the orthogonality between basis functions is destroyed at the receiver due to channel dispersion the starting point of this work is a pulse scale adaptation rule first proposed by kozek to minimize the interference between the basis functions we show that the average signal to interference and noise sinr ratio associated with different basis functions is identical and is maximized by the scale adaptation rule the results in this paper highlight the critical impact of the channel spread factor the product of multipath and doppler spreads on system performance smaller spread factors result in lesser interference such that a scale adapted stf basis serves as an approximate eigenbasis for the channel a highly effective iterative interference cancellation technique is proposed for mitigating the residual interference for larger spread factors the approximate eigendecomposition leads to an intuitively appealing block fading interpretation of the channel in terms of time frequency coherence subspaces the channel is highly correlated within each coherence subspace whereas it is approximately independent across different subspaces the block fading model also yields an approximate expression for the coherent channel capacity in terms of parallel flat fading channels the deviation of the capacity of doubly dispersive channels from that of flat fading channels is quantified by studying the moments of the channel eigenvalue distribution in particular the difference between the moments of doubly dispersive and flat fading channels is proportional to channel spread factor the results in this paper indicate that the proposed stf signaling framework is applicable for spread factors as large as 0 01

partial period crosscorrelations of geometric sequences for a binary pseudorandom sequence s sub i with period n the partial period autocorrelation function a sub s spl tau k d is defined by correlating the portion of the sequence within a window of size d and start position k with the portion in another window of the same size but starting spl tau steps later in the sequence a distribution of possible partial period autocorrelation values is obtained by allowing the start position k to vary over all possible values o spl les k

dynamic analysis of finite linear elastic solids containing small elastic imperfections theory with application to asymmetric circular plates abstract eigensolutions green s functions and steady state responses of three dimensional homogeneous isotropic finite linear elastic solids containing small linear elastic imperfections are presented in this paper the inhomogeneities are treated as perturbations to otherwise homogeneous solids the spectral eigensolutions of which are known the exact eigensolutions of the imperfect solid formulated through the betti reciprocal theorem satisfy a set of integral equations from which both analytic perturbation formulas and a numerical iteration scheme are developed special emphasis is given to analysis of perfect homogeneous elastic solids that are spectrally degenerate finally the vibration of circular plates with evenly spaced radial inclusions which cause splitting of some of the repeated vibration modes is analyzed both analytically and numerically for the eigensolutions

partial correlation effects in direct sequence spread spectrum multiple access communication systems nearly all previous analytical results on the performance of direct sequence spread spectrum multiple access ds ssma communication systems are restricted to systems in which the period p of the signature sequence is equal to the number n of chips per data symbol in many applications however it is necessary to employ signature sequences whose period p is much larger than n thus successive n chip segments of the signature sequence are used to phase code the carrier during the transmission of successive data symbols the performance of such systems depends on the partial correlation properties of the signature sequences rather than the aperiodic correlation properties as in the case when n p in this paper we consider the performance of a ds ssma system for arbitrary values of p and n as special cases of our results we delermine the effects of partial correlation in three classes of systems those for which n p those for which n and p are relatively prime and those for which n is a divisor of p we also provide two methods for the design of sequences for systems for which n is a divisor of p

theory and applications of q ary interleaved sequences a new class of q ary sequences called interleaved sequence is introduced their periods shift equivalence linear spans and autocorrelation functions are derived the interleaved sequences include a large number of popular sequences such as multiplexed sequences clock controlled sequences kasami 1966 sequences gmw sequences geometric sequences and no 1989 sequences a special class of the interleaved sequences is constructed by mapping gf q sup m sequences into gf q sequences in terms of different bases of gf q sup m over gf q as an application of the theory of interleaved sequences some new families of binary pseudo random sequences are constructed which have large linear spans optimal periodic cross autocorrelation functions balance and the rapidly hopped properties a complete comparison of the new family of sequences with the gold sequence family the kasami small and large set sequence families the bent function sequence family and the no sequence family is discussed this shows that the new sequence families have important advantages for use in spread spectrum multiple access communication systems

ds cdma signature sequences based on pr qmf banks in this paper we propose two classes of multivalued signature sequences for direct sequence code division multiple access ds cdma systems the proposed classes are obtained from the coefficients of the subbands of perfect reconstruction quadrature mirror filterbanks pr qmf the first and second classes are derived from the tree and lattice structure pr qmf banks respectively and they both have perfect correlation properties for synchronous ds cdma systems the second class in addition has generally better correlation properties than other well known sequences in asynchronous ds cdma systems some numerical results for the performance of the asynchronous ds cdma systems with several sequences including the second class of sequences are obtained

on the odd and the aperiodic correlation properties of the kasami sequences derives a new upper bound for the odd and the aperiodic correlations of binary sequences in the small kasami family the approach is based on a technique described in s litsyn and a tietavainen 1994 that is originally due to i m vinogradov 1954 an essential ingredient in this method is a good upper bound on the discrete fourier coefficients of a shifted product of a pair of sequences the author obtains an upper bound of the order o spl radic llnl for the maximal aperiodic and odd correlation magnitudes for sequences of length l

filter design for generalized frequency division multiplexing in this paper optimal filter design for generalized frequency division multiplexing gfdm is considered under two design criteria rate maximization and out of band oob emission minimization first the problem of gfdm filter optimization for rate maximization is formulated by expressing the transmission rate of gfdm as a function of gfdm filter coefficients it is shown that dirichlet filters are rate optimal in additive white gaussian noise channels with no carrier frequency offset cfo under linear zero forcing zf or minimum mean square error mmse receivers but in general channels perturbed by cfo a properly designed nontrivial gfdm filter can yield better performance than dirichlet filters by adjusting the subcarrier waveform to cope with the channel induced cfo next the problem of gfdm filter design for oob emission minimization is formulated by expressing the power spectral density of the gfdm transmit signal as a function of gfdm filter coefficients and it is shown that the oob emission can be reduced significantly by designing the gfdm filter properly and there is a tradeoff between the transmission rate and oob radiation for gfdm with linear receivers finally joint design of gfdm filter and window for the two design criteria is considered

discretized gabor frames of totally positive functions in this paper a large class of universal windows for gabor frames weyl heisenberg frames is constructed these windows have the fundamental property that every overcritical rectangular lattice generates a gabor frame likewise every undercritical rectangular lattice generates a riesz sequence

quantum channels and representation theory in the study of d dimensional quantum channels d 2 an assumption which includes many interesting examples and which has a natural physical interpretation is that the corresponding kraus operators form a representation of a lie algebra physically this is a symmetry algebra for the interaction hamiltonian this paper begins a systematic study of channels defined by representations the famous werner holevo channel is one element of this infinite class we show that the channel derived from the defining representation of su n is a depolarizing channel for all n but for most other representations this is not the case since the standard bloch sphere only exists for the qubit representation of su 2 we develop a consistent generalization of bloch s technique by representing the density matrix as a polynomial in lie algebra generators we determine a class of positive semidefinite matrices which represent quantum states for various channels defined by finite dimensional representations of semisimple

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

eigenvalue eigenvector sensitivity analysis of linear time invariant singular systems this note refers to the eigenvalue eigenvector sensitivity analysis of linear time invariant multivariable singular systems procedures that can be easily programmed on a digital computer are presented for the determination of the deviation of the eigenvalues and the corresponding right and left eigenvectors which are caused by the system s parameter changes about their nominal values the method is illustrated by two examples

maximum likelihood sequence estimation of cpm signals transmitted over rayleigh flat fading channels a method for the sequential updating of log likelihood functions for maximum likelihood sequence estimation is presented it is shown that in a general case this method can be implemented using kalman filtering techniques for the special case of rayleigh flat fading and continuous phase modulation cpm signaling this approach is shown to lead to an attractive receiver structure this type of receiver called the linear predictive receiver can be implemented in the form of the viterbi algorithm with the trellis updates being computed using a bank of finite pulse response fir filter and square operations simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection in the presence of fast fading it is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of rayleigh fading channels used to model terrestrial mobile channels

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

bounds on partial correlations of sequences two approaches to bounding the partial auto and crosscorrelations of binary sequences are considered the first approach uses the discrete fourier transform and bounds for character sums to obtain bounds on partial autocorrelations of m sequences and on the partial auto and crosscorrelations for the small kasami sets and dual bch families of sequences the second approach applies to binary sequences obtained by interleaving m sequences a bound on the peak partial correlation of such sequences is derived in terms of the peak partial autocorrelation of the underlying m sequences the bound is applied to gmw no 1987 and other families of sequences for particular parameters a comparison of the two approaches shows that the elementary method gives generally weaker results but is more widely applicable on the other hand both methods show that well known sequence families can have favorable partial correlation characteristics making them useful in certain spread spectrum applications

d form sequences families of sequences with low correlation values and large linear spans large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems the author describes a method for constructing such families from families of homogeneous functions over finite fields satisfying certain properties he then uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than no sequences no 1988

partial period correlations of zadoff chu sequences and their relatives partial period correlations of sequences are an important performance measure of communication systems employing them but are known to be notoriously difficult to analyze in this paper we present a systematic approach to partial period correlations as a generalization of the paterson lothian approach for a pair of sequences not necessarily distinct we introduce the linear phase shifting sequences of one of them and analyze their full period correlations called the induced correlations with the other one by exploiting the induced correlations we obtain the partial period correlation properties of the given pair we then investigate zadoff chu sequences and give some theoretical results on their partial period autocorrelations including closed form expressions and the first and second moments we also derive an upper bound on the magnitudes of the partial period cross correlations of zadoff chu sequences finally we explore generalized chirp like discrete fourier transform sequences and show that their partial period cross correlations have the same magnitudes as the partial period autocorrelations of the employed zadoff chu sequence up to permutation

eigenvalue tracking due to parameter variation this note describes an efficient eigenvalue tracking algorithm which is applicable in many engineering systems where the effect of parameter variation on system stability is to be determined starting with the original system eigenvalues the algorithm uses determinants to compute first order eigenvalue sensitivities which are used in an iterative method that converges rapidly to the new eigenvalues corresponding to the parameter change the algorithm tracks all the system eigenvalues starting from a given base case it is shown to be less costly than repeated eigenvalue evaluation and is illustrated by means of a simple power system example

adaptive synchronization and channel parameter estimation using an extended kalman filter unified modeling and estimation of the md multiplicative distortion in finite alphabet digital communication systems is presented a simple form of md is the carrier phase exp j theta which has to be estimated and compensated for in a coherent receiver a more general case with fading must however allow for amplitude as well as phase variations of the md the authors assume a state variable model for the md and generally obtain a nonlinear estimation problem with additional randomly varying system parameters such as received signal power frequency offset and doppler spread an extended kalman filter is then applied as a near optimal solution to the adaptive md and channel parameter estimation problem examples are given to show the use and some advantages of this scheme

optimal ofdm design for time frequency dispersive channels transmission over wireless channels is subject to time dispersion due to multipath propagation and to frequency dispersion due to the doppler effect standard orthogonal frequency division multiplexing ofdm systems using a guard time interval or cyclic prefix combat intersymbol interference isi but provide no protection against interchannel interference ici this drawback has led to the introduction of pulse shaping ofdm systems we first present a general framework for pulse shape design our analysis shows that certain pulse shapes proposed in the literature are in fact optimal in a well defined sense furthermore our approach provides a simple way to adapt the pulse shape to varying channel conditions we then show that pulse shaping ofdm systems based on rectangular time frequency lattices are not optimal for time and frequency dispersive wireless channels this motivates the introduction of lattice ofdm lofdm systems which are based on general time frequency lattices using results from sphere packing theory we show how to design lofdm systems lattice and pulse shape optimally for timeand frequency dispersive channels in order to minimize the joint isi ici our theoretical analysis is confirmed by numerical simulations showing that lofdm systems outperform traditional pulse shaping ofdm systems with respect to robustness against isi ici

optimal parametric feedforward estimation of frequency selective fading radio channels estimation of time varying dispersive radio channels is one of the most important tasks of receiver synchronisation state of the art adaptive estimators employing decision feedback suffer from error propagation and limited robustness against faster fading in this paper the optimal feedforward channel estimator using only known training symbols is systematically derived statistical channel information is assumed to be available for moderately rapid fading channels snapshot assumption the optimal estimator is shown to be divided into the two subtasks of maximum likelihood acquisition and subsequent wiener filtering of the acquired quantities if perfect training sequences resulting in optimal performance are used the wiener filtering operation collapses into independent filtering of the individual acquired tap estimates and the resulting channel estimator becomes efficient and flexible the performance of the optimal estimator is evaluated for important cases a design example of a near optimal hf channel estimator receiver is discussed linear interpolation is used to reduce the computational complexity of receiver coefficient adjustment simulation results confirm the superiority and robustness of feedforward synchronization having near optimal performance at reduced complexity

an adaptive maximum likelihood receiver for correlated rayleigh fading channels the paper develops a receiver structure for random gaussian signals in additive noise based on the classic maximum likelihood m l estimator correlator derivation of kailath 1960 and applies it to differential phase shift keying dpsk on the correlated rayleigh fading channel it is shown to lower the error floor found in the performance of conventional dpsk receivers by orders of magnitude in addition the maximum likelihood procedure is shown to make uncorrelated symbol decisions the performance of both conventional and optimal receivers which require knowledge of the channel statistics is examined analytically a recursive channel adaptive version of the optimal receiver utilizing decision feedback to estimate the channel statistics is developed its simulated performance shows no penalty compared to theoretical calculations which require explicit knowledge of the channel statistics

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

concise derivation of scattering function from channel entropy maximization in order to provide a concise time varying siso channel model the principle of maximum entropy is applied to scattering function derivation the resulting model is driven by few parameters that are expressed as moments such as the channel average power or the doppler spread physical interpretations of the model outputs are discussed in particular it is shown that common doppler spectra such as the flat or the jakes spectrum fit well into the maximum entropy framework the matlab code corresponding to the proposed model is available at http perso telecom bretagne eu fxsocheleau software