continuous time equivalents of welch bound equality sequences the theory developed on the sequence optimization for equal power code division multiple access cdma systems is generalized in this paper unlike previous works where discrete time or vector channel models are predominantly employed the overloaded channels are modeled as strictly band limited continuous time multiple access channels corrupted by additive white gaussian noise awgn after being posed as a multiple input single output miso joint transmitter and receiver optimization problem with the total mean squared error mse as the objective functional to be minimized the variational problem is solved by using a frequency domain approach it is shown that there exist continuous time equivalents of welch bound equality cte wbe sequences as the jointly optimum transmit waveforms and that the matched filters are the jointly optimum receivers the user capacity of the band limited channels is characterized by a necessary and sufficient condition for the admissibility of users into the system in terms of the channel load the received signal to noise ratio and the signal to interference plus noise ratio sinr requirement it is also shown that cte wbe sequences achieve the lower bound on the continuous time equivalent of total squared correlation cte tsc

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

periodic string response to an impact and a suddenly applied concentrated stationary force an infinite periodic structure unsteady response to a forced excitation is considered any forced excitation can be presented as a sequence or a distribution of impulses the instantaneous impulse is an infinite sum of harmonic forces of the same amplitude and phase whose frequencies fill the infinite band as follows from the fourier transformation of the dirac delta function the solution to the problem of a periodic structure steady state response to excitation by a harmonic concentrated stationary force is obtained by reducing the problem to a difference equation and used to calculate the unsteady response the infinite periodic structure consisting of an infinite stretched string supported by equidistantly spaced identical suspensions is considered each suspension consists of a spring and a dashpot with viscous damping in parallel small transverse oscillations of the string without bending stiffness are considered in order to exclude from the solution the string slope which experience a sudden change at the point where a concentrated force is applied and so at every suspension point the boundary problem is solved over the string unloaded span the string transverse deflection at an arbitrary point of the span as well as its slope are expressed via the deflection values at the beginning and at the end of the span then two neighbour spans are considered together a suspension reaction that depends on the suspension point deflection is connected with the string slopes to the right and to the left of the point the connection involves the string transverse deflection at three successive suspension points and represents the second order difference equations the solution to this equation allows one to express the string deflections at all suspension points via only two which relate to ends of the span where the excitation is applied consideration of this span leads to calculation of the string steady state oscillations and response to an impact to give an example of application the latter is used to calculate the string response to a suddenly applied force

time delay estimation using the cross bispectrum the cross bispectrum phase can be effectively used to estimate the time required for a nongaussian signal to propagate between a pair of spatially separated sensors in the presence of highly correlated gaussian noise the authors present a consistent estimator of the phase of the cross bispectrum derive the exact distribution of the phase of a complex gaussian sample bispectrum and show that in most cases the exact distribution can be approximated by a gaussian distribution using this gaussian approximation the authors derive the variance of the time delay estimate computed from the sample cross bispectrum of a signal in additive correlated noise these results allow the performance of time delay estimators based on the cross bispectrum phase to be quantified as a function of the sample size the skewness of the signal the signal to noise ratio snr and the noise correlation

the k dimensional distribution of combined gfsr sequences we develop an efficient method for analysis of the fc dimensional distribution of combinations of several gfsr sequences by bitwise exclusive or operations first we introduce the notion of a resolution wise lattice structure for gfsr sequences and show that by applying a theorem of couture to this type of lattice we obtain a precise description of a dimensional distribution of combined gfsr sequences in the same way as for combined tausworthe sequences finally we apply this method to the combination of two different twisted gfsr generators which were recently proposed by matsumoto and kurita and investigate the order of equidistribution of the combined sequence

a generalized euclidean algorithm for multisequence shift register synthesis the problem of finding a linear feedback shift register of shortest length capable of generating prescribed multiple sequences is considered a generalized euclidean algorithm which is based on a generalized polynomial division algorithm is presented a necessary and sufficient condition for the uniqueness of the solution is given when the solution is not unique the set of all possible solutions is also derived it is shown that the algorithm can be applied to the decoding of many cyclic codes for which multiple syndrome sequences are available when it is applied to the case of a single sequence the algorithm reduces to that introduced by y sugiyama et al inf control vol 27 p 87 9 feb 1975 in the decoding of bch codes

calculation of force distribution for a periodically supported beam subjected to moving loads abstract in this study a novel model for a periodically supported beam subjected to moving loads was developed using a periodicity condition on reaction forces this condition together with fourier transforms and dirac combs forms a relation between the beam displacement and support reaction forces this relation explains the force distribution at the supports and holds for any type of support and foundation behaviors based on this relation a system equivalence for a periodically supported beam is presented in this paper an application to non ballasted viscoelastic supports is presented as an example and the results clearly match the existing model next an approximation of real time responses was developed for the moving loads as periodic series the comparison shows that this approximation can be used for a limited number of loads if the distances between loads are sufficiently large the system equivalence for a periodically supported beam is efficient for supports with linear behavior and could be extended to other behaviors

blind adaptive fresh filtering for signal extraction a blind adaptive method called the ba fresh optimum frequency shift filtering technique is proposed and its convergence analyzed the ba fresh filter does not require training signals nor knowledge of the statistics of the desired signal it is capable of separating desired signals from spectrally overlapping interference by knowing only the cycle frequencies of the signals

exploitation of cyclostationarity for identifying the volterra kernels of nonlinear systems a class of random time series inputs for nonlinear time invariant systems that permit the analytical specification of a set of operators on the input that are orthonormal over all time to the volterra operators for all orders and all lag sets is introduced the time series in this class are cyclostationary and complex valued the orthonormal operators are used to obtain an input output type of cross correlation formula for identifying the individual volterra kernels of arbitrary order for a nonlinear system of possibly infinite order and possibly infinite memory the real parts of the complex valued inputs in this class comprise a class of real valued inputs for which the same sets of specified operators apply however the orthogonality for different orders holds for these real inputs only for volterra operators of order less than the order of the specified operator thus these real inputs can be used to identify volterra kernels only for finite order systems frequency domain counterparts of the time domain methods that can utilize an fft algorithm are developed

signal reconstruction from the phase of the bispectrum the authors present a simple procedure the bispectrum signal reconstruction bsr algorithm to recover the fourier phase of a signal from the phase of its bispectrum by simple analogy a procedure that recovers the fourier magnitude of a signal from the magnitude of its bispectrum is also presented in addition the authors propose an iterative scheme the bicepstrum iterative reconstruction algorithm bira for the reconstruction of a finite impulse response fir sequence from only the phase of its bispectrum and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the fourier phase of the signal whereas their sums contain the fourier magnitude information

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

an efficient lattice reduction method for f 2 linear pseudorandom number generators using mulders and storjohann algorithm abstract recent simulations often use highly parallel machines with many processors and they need many pseudorandom number generators with distinct parameter sets and hence we need an effective fast assessment of the generator with a given parameter set linear generators over the two element field are good candidates because of the powerful assessment via their dimensions of equidistribution some efficient algorithms to compute these dimensions use reduced bases of lattices associated with the generator in this article we use a fast lattice reduction algorithm by mulders and storjohann instead of schmidt s algorithm and show that the order of computational complexity is lessened experiments show an improvement in the speed by a factor of three we also report that just using a sparsest initial state i e consisting of all 0 bits except one significantly accelerates the lattice computation in the case of mersenne twister generators

blind fsr lptv equalization and interference rejection we address the problem of synthesizing blind channel identification and equalization methods for digital communications systems aimed at counteracting the presence of cochannel or adjacent channel interference owing to the presence of the interfering signal the minimum mean square error equalizer turns out to be linear periodically time varying which is implemented by resorting to its fourier series representation moreover by exploiting the cyclic conjugate second order statistics of the channel output we propose a new weighted subspace based channel identification method which is asymptotically immune to the presence of high level interference computer simulation results confirm the effectiveness of the proposed identification equalization technique

rice s representation for cyclostationary processes the well known formulas relating power spectral densities of a bandpass process and its low pass representors in rice s representation are generalized to accommodate cyclostationary processes which can be more appropriate than stationary processes as models for modulated signals it is explained that improper phase randomization methods for stationarizing cyclostationary processes can yield misleading formulas for power spectral densities in rice s representation in addition the relationships among the spectral correlation functions for a cyclostationary bandpass process and its cyclostationary low pass representors are derived

adaptive fresh filters for compensation of cycle frequency errors this paper deals with the problem of uncertainties in the periodicities of linear almost periodically time variant laptv filters these filters are usually implemented as a set of branches each consisting of a frequency shifter followed by a linear time invariant lti filter this implementation is also known as fresh filters this paper is motivated by the fact that when there exist errors in the frequency shifts the optimum set of lti filters is obtained by canceling the outputs of the corresponding branches the purpose of this paper is to analyze the nonstationary behavior of adaptive filters in order to mitigate this problem our results show that an adaptive filter can offset the errors in the frequency shifts the reason is that the coefficients of the adaptive filter are updated so that the filter actually performs as a linear periodically time variant filter for each branch this allows to track the errors in the frequency shifts when the rate of convergence of the adaptive algorithm is suitably selected an analytical study of the convergence is presented which allows to compute the optimal rate of convergence and the mean squared error attained by the adaptive filter

figures of merit for digital multistep pseudorandom numbers the statistical independence properties of s successive digital multistep pseudorandom numbers are governed by the figure of merit p s i which depends on s and the characteristic polynomial f of the recursion used in the generation procedure we extend previous work for s 2 and describe how to obtain large figures of merit for s 2 thus arriving at digital multistep pseudorandom numbers with attractive statistical independence properties tables of figures of merit for s 3 4 5 and degrees 32 are included

complex valued signal processing the proper way to deal with impropriety complex valued signals occur in many areas of science and engineering and are thus of fundamental interest in the past it has often been assumed usually implicitly that complex random signals are proper or circular a proper complex random variable is uncorrelated with its complex conjugate and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane while these assumptions are convenient because they simplify computations there are many cases where proper and circular random signals are very poor models of the underlying physics when taking impropriety and noncircularity into account the right type of processing can provide significant performance gains there are two key ingredients in the statistical signal processing of complex valued data 1 utilizing the complete statistical characterization of complex valued random signals and 2 the optimization of real valued cost functions with respect to complex parameters in this overview article we review the necessary tools among which are widely linear transformations augmented statistical descriptions and wirtinger calculus we also present some selected recent developments in the field of complex valued signal processing addressing the topics of model selection filtering and source separation

generalized spectral coherences for complex valued harmonizable processes complex valued nonstationary random processes have nonvanishing complementary second order moment functions in this paper we propose generalized dual frequency and time frequency coherence functions for harmonizable processes the proposed generalized spectral coherences are based on widely linear estimators and they result in coherence measures that combine hermitian and complementary moment functions we show that for analytic processes and more surprisingly also for real valued processes additional second order information becomes available through the generalized coherences we offer illuminating geometrical interpretations of the proposed coherences through hilbert space inner product formulations finally we extend the theory to generalized cross coherences between pairs of harmonizable processes

maximally equidistributed combined tausworthe generators tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions however such generators with those restrictions have bad statistical properties unless we combine them a generator is called maximally equidistributed if its vectors of successive values have the best possible equidistribution in all dimensions this paper shows how to find maximally equidistributed combinations in an efficient manner and gives a list of generators with that property such generators have a strong theoretical support and lend themselves to very fast software implementations

free wave propagation in periodically ring stiffened cylindrical shells abstract the free wave propagation characteristics of several periodically ring stiffened cylindrical shells have been investigated using a previously developed finite element based methodology results indicate that predicted stop bands that are associated primarily with shell flexure can be classified into three types the most important stop band type for structurally efficient cylinders is one in which the structural half wavelength or integer multiples there of approaches the stiffener spacing for the cylinders investigated these stop bands are broadband and can be easily tuned to a particular frequency band cylinder designs utilizing double curvature are shown to have significantly more coupling between flexural and longitudinal wave modes this conclusion is reinforced by results from an analytical investigation of a curved beam an axisymmetric formulation for the prediction of propagation constants is also identified

cycloergodic properties of discrete parameter nonstationary stochastic processes it is shown that a large class of nonstationary discrete parameter stochastic processes possess novel ergodic properties which are referred to as em cycloergodic properties specifically it is shown that periodic components of time varying probabilistic parameters can be consistently estimated from time averages on one sample path the cycloergodic theory developed herein extends and generalizes existing ergodic theory for asymptotically mean stationary and n stationary cyclostationary processes and is presented in both wide sense and strict sense contexts

time domain approaches to quadratic phase coupling estimation bicoherence is a quantity used to estimate the contribution of second order nonlinearity to the power in bifrequencies the conventional approach to the problem uses second and third order periodograms for bicoherence estimation time domain approaches that use autocorrelation and third order cumulant samples or their estimates are developed these techniques are suitable for use in situations where high resolution approaches are required for power spectrum and bispectrum estimation

on the oscillations of infinite periodic beams subjected to a moving concentrated force abstract a study is presented of the oscillation of an infinite beam which rests on identical periodic simple elastic supports the study shows how a combination of two different approaches the previous author s 1 and mead s 2 allows one to remove an unnatural restriction on the parameters of the problem the beam s transverse deflection is caused by a harmonic concentrated force moving steadily along the beam it is supposed that the beam had been at rest before the force approached and returned to rest after the force had moved away it is further supposed that the beam deflections at any pair of points separated on the periodic support spacing obey the special condition this condition means that the steady beam oscillations take place and allows one to consider just one beam segment between neighbouring supports the beam deflection is governed within the segment by the euler bernoulli partial differential equation four boundary conditions and the above mentioned suppositions the fourier transformation is used to solve the problem

common pitfalls in the application of stationary process theory to time sampled and modulated signals the common practice of applying the theory of stationary stochastic processes to a cyclostationary process by introducing random phase s into the probabilistic model in order to stationarize the process can lead to erroneous results such as incorrect formulas for power spectral density this is illustrated by showing that commonly used formulas for signals that have undergone frequency conversion or time sampling can be incorrect the source of error is shown to be inappropriate phase randomization procedures the correct procedure is described and corrected formulas are given the problem is further illustrated by showing that commonly used resolution and reliability mean and variance formulas for spectrum analyzers must be corrected for cyclostationary signals it is explained that all corrections to formulas reflect the effects of spectral correlation these effects are inappropriately averaged out by inappropriate phase randomization procedures it is further explained that these inappropriate procedures destroy the important property of ergodicity of the probabilistic model

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

dynamic response of micro periodic composite rods with uncertain parameters under moving random load in this paper axial vibrations of a finite micro periodic composite rod with uncertain parameters under a moving random load are investigated the solution of the problem was found by using the random dynamic influence function and applying the perturbation method the average tolerance approach was also used to pass from differential equations with periodic coefficients to differential equations with constant coefficients two types of the moving random load are considered a normal stationary or non stationary process the continuous load model clm and a random train of moving forces the discrete load model dlm finally a numerical example is provided to demonstrate the algorithm in the context of a computer implementation with slight modification the algorithm for longitudinal vibrations of a rod could also be applied to the dynamics of periodic beams plates and shells with random parameters subjected to stochastic moving loads

nonparametric cyclic polyspectral analysis of am signals and processes with missing observations by viewing discrete time amplitude modulated signals and processes with missing observations as cyclostationary signals nonparametric mean square sense consistent and asymptotically normal single record estimators are developed for their kth order cumulants and polyspectra along with the asymptotic covariances the proposed estimation schemes use cyclic cumulants and polyspectra and are theoretically insensitive to any additive stationary noise in addition schemes of order k or 3 convey complete phase information and are insensitive to additive cyclostationary gaussian noise of unknown covariance the conventional approaches cannot recover mixed phase linear processes are susceptible to additive noise and are a special case of the proposed schemes simulations demonstrate superior performance of the proposed algorithms

the performance of time dependent adaptive filters for interference rejection time dependent adaptive filters tdafs that allow for the cyclostationary nature of communication signals by periodically changing the filter and adaptation parameters are examined the tdaf has an advantage over the conventional time independent adaptive filter in achieving better performance i e reduced mean square error mse for signals with periodic statistics the basic theory of the tdaf is presented the tdaf is shown to be more effective than the time independent adaptive filter for interference rejection this is verified by theoretical analysis and computer simulation of specific cases of extracting a signal in noise or interference the criteria for judging the performance of the tdaf for interference rejection are mse bit error rate measurements and constellation diagrams

acoustic radiation from periodic and sectionally aperiodic rib stiffened plates the far field and near field solutions for the radiated acoustic pressure from a line driven fluid loaded rib stiffened thin elastic plate have been obtained the plate has been configured to have two sets of rib stiffeners though the formulation given has been extended to include additional rib stiffener sets the stiffeners composing a given set are identical and are spaced periodically with distance l however one set of stiffeners is shifted by an amount from the other set in this manner portions of the plate may be configured with periodic repeating sections of arbitrary length l having aperiodic rib spacing the stiffeners exert reactive forces upon the plate but not angular moments fluid loading is included on the upper surface of the plate while the lower surface is unloaded except for a time harmonic line force applied normal to the lower surface the far field radiated pressure has been obtained using the method of stationary phase numerical integration techniques were used to obtain the near field acoustic pressure

capacity of second order cyclostationary complex gaussian noise channels in this paper we derive the capacity of a continuous time single input single output siso frequency selective band limited linear time invariant lti channel whose output is corrupted by a second order cyclostationary socs complex gaussian noise by using a pair of invertible linear conjugate linear time varying operators called a properizing frequency shift p fresh vectorizer and a p fresh scalarizer it is shown that whether the complex noise is proper or improper the siso channel can always be converted to an equivalent multiple input multiple output mimo lti channel whose output is now corrupted by a proper complex vector wide sense stationary noise a variational problem is then formulated in the frequency domain to find the optimal input distribution that maximizes the throughput of the equivalent mimo channel it turns out that the optimal input to the siso channel obtained through a procedure similar to the water filling is an socs complex gaussian random process with the same cycle period as the noise it is shown that this procedure named cyclic water filling significantly outperforms ordinary water filling by effectively utilizing the spectral correlation of the cyclostationary noise

on the lattice basis reduction multisequence synthesis algorithm a lattice basis reduction multisequence synthesis lbrms algorithm was presented with a new intuitive and vector form model in this paper a refined version of the lbrms algorithm is deduced from which massey s conjectured algorithm can be derived moreover if we modify the lattice basis reduction algorithm used in the lbrms algorithm a new synthesis algorithm is deduced which is equivalent to the generalization of the berlekamp massey algorithm proposed by feng and tzeng 1989 therefore the lbrms algorithm provides a unified approach to the multisequence shift register synthesis problem

on the distribution of k dimensional vectors for simple and combined tausworthe sequences the lattice structure of conventional linear congruential random number generators lcgs over integers is well known in this paper we study lcgs in the field of formal laurent series with coefficients in the galois field f2 the state of the generator a laurent series evolves according to a linear recursion and can be mapped to a number between 0 and 1 producing what we call a ls2 sequence in particular the sequences produced by simple or combined tausworthe generators are special cases of ls2 sequences by analyzing the lattice structure of the lcg we obtain a precise description of how all the k dimensional vectors formed by successive values in the ls2 sequence are distributed in the unit hypercube more specifically for any partition of the k dimensional hypercube into 2kl identical subcubes we can quickly compute a table giving the exact number of subcubes that contain exactly n points for each integer n we give numerical examples and discuss the practical implications of our results

nonparametric bispectrum based time delay estimators for multiple sensor data when estimating time delays of signals from sensor outputs the bispectrum has advantages when the signal has a skewed distribution the authors provide nonparametric estimation approaches which exploit the two dimensional nature of the bispectrum when dealing with observations from more than a pair of sensors the new algorithms have computational advantages and in some cases show improved performance compared to the conventional nonparametric bispectrum based time delay estimation approach

spectral correlation of modulated signals part i analog modulation the importance of the concept of cyclostationarity in design and analysis of signal detectors synchronizers and extractors in communication systems is briefly discussed and the central role of spectral correlation in the characterization of random processes that are cyclostationary in the wide sense is explained a spectral correlation function that is a generalization of the power spectral density function is described and a corresponding generalization of the wiener khinchine relation and several other fundamental spectral correlation relations also are described explicit formulas for the spectral correlation function for various types of analog modulated signals are derived this includes pulse and carrier amplitude modulation quadrature amplitude carrier modulation and phase and frequency carrier modulation to illustrate the differing spectral correlation characteristics of different modulation types the magnitudes of the spectral correlation functions are graphed or described in graphical terms as the heights of surfaces above a bifrequency plane

vibration isolation from irregularity in a nearly periodic structure theory and measurements this article describes the theory and a simple experiment carried out to demonstrate the phenomenon of anderson localization in an acoustical context this is an effect whereby the propagation of vibration in a structure which is not entirely regular is impeded by the irregularities giving rise on the average to an exponential decay of vibration level away from the driving point even in the absence of any dissipation the structure used in the experiment was a stretched string with masses attached to it this string was studied with regular spacings of the masses and after the masses had been moved in a controlled way to provide a small degree of irregularity in both cases the transmission of energy from end to end of the string was measured as a function of frequency and also the mode shapes in the second and fourth passbands were measured so as to demonstrate the underlying physics of the localization phenomenon in which the individual modes making up each passband change from being extended throughout the structure in the regular case to being localized in specific areas of the structure in the presence of irregularity all measurements yielded satisfactory agreement with the theoretical predictions

suboptimal detection of non gaussian signals by third order spectral analysis the use of higher order spectra hos is proposed for improving detection performance in non gaussian signals the method comprises two stages first the higher order spectra of the received signal are estimated using conventional spectral estimation techniques then a maximum likelihood ratio test lrt is performed in the higher order spectra domain it is shown that under certain low signal to noise ratio snr conditions the hos based method performs much better than the conventional energy one the required processor is derived and its performance is analyzed while the method is demonstrated using the third order spectrum called bispectrum it can easily be extended to higher order analysis e g trispectrum etc

bearing estimation in the bispectrum domain a new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data the method is based on the asymptotic distribution of cross bispectrum estimates and uses maximum likelihood theory it is demonstrated that when the noise additive sources are spatially correlated gaussian with unknown cross spectral matrix csm the cross bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known csm analytical studies and simulations are given to document the performance of the new method

asymptotic moments of estimated cyclic correlation matrices the first and second moments of the cyclic cross correlogram matrix of two vector valued cyclostationary processes are derived in this paper these results generalize those of hurd 1989 to accommodate incommensurate cycle frequencies and complex vector valued discrete time nongaussian processes as an example application of the results the moments of the left singular vectors of the cyclic cross correlogram matrix are derived which are needed in the performance analysis of subspace fitting methods of direction of arrival estimation for cyclostationary signals including even those methods that do not exploit cyclostationarity but are often applied in practice to cyclostationary signals

randomized polynomial lattice rules for multivariate integration and simulation lattice rules are among the best methods to estimate integrals in a large number of dimensions they are part of the quasi monte carlo set of tools a theoretical framework for a class of lattice rules defined in a space of polynomials with coefficients in a finite field is developed in this paper a randomized version is studied implementations and criteria for selecting the parameters are discussed and examples of its use as a variance reduction tool in stochastic simulation are provided certain types of digital net constructions as well as point sets constructed by taking all vectors of successive output values produced by a tausworthe random number generator are special cases of this method

identification of systems with cyclostationary input and correlated input output measurement noise an alternative approach to wiener s optimum filtering theory for stationary random time series that is applicable when the system input exhibits cyclostationarity is presented this alternative approach can in principle eliminate performance degradation due to input output corruption this method of system identification is called the speccorr spectral correlation ratio method since the cross spectra in the ratio are actually spectral correlation functions an application to interference tolerant time difference of arrival estimation is described and illustrated by simulation results showing its effectiveness for system identification with severely corrupted input output measurements a comparison of wiener s method to the speccorr method shows the superior performance of the latter

asymptotically optimal low complexity sc fde in data like co channel interference in this paper the design of a low complexity linear equalizer is considered for single carrier sc block transmission in the presence of inter symbol interference isi and data like co channel interference cci unlike the linear minimum mean squared error lmmse frequency domain equalizer fde designed to suppress isi only the lmmse fde suffers from high computational complexity due to the cci component in the signal correlation matrix motivated by the fact that the double fourier transform of the autocorrelation function of a wide sense cyclostationary process consists of impulse fences with equal spacing a low complexity fde is proposed that approximates the frequency domain correlation matrix of the cci plus noise by a block matrix with diagonal blocks it is shown that the proposed fde is asymptotically optimal in the sense that the average mean squared error mse converges to that of the lmmse fde as the block length tends to infinity it is also shown that the proposed fde is more numerically stable than the lmmse fde when the receive filter is matched to the transmit filter and its output is over sampled to better capture the cyclostationarity of the cci discussions and numerical results include sc block transmission systems with unique word instead of cyclic prefix and systems with multiple receive antennas

partially blind adaptive mmse interference rejection in asynchronous ds cdma networks over frequency selective fading channels in this work the problem of joint suppression of multiple access and narrow band interference nbi for an asynchronous direct sequence code division multiple access cdma system operating on a frequency selective fading channel is addressed the receiver structure we consider can be deemed as a two stage one the first stage consists of a bank of minimum mean square error mmse filters each keyed to a given replica of the useful signal and aimed at suppressing the overall interference the second stage assuming knowledge of the fading channel coefficients realizations combines the mmse filters outputs according to a maximal ratio combining rule due to the presence of the nbi the resulting structure is in general time varying and becomes periodically time varying if the nbi bit rate has a rational ratio to that of the cdma system moreover enlarging the observation window beyond the signaling interval and oversampling the signal space may yield a noticeable performance improvement for the relevant case that the said ratio is rational a new cyclic blind recursive least squares rls based algorithm is introduced capable of tracking the periodically time varying receiver structure and allowing adaptive interference cancellation with a moderate complexity increase we also come up with a closed form expression for the conditional bit error rate ber which is useful both to evaluate semi analytical methods to assess the unconditional ber and to derive bounds on the system near far resistance the results indicate that the receiver achieves very satisfactory performance in comparison to previously known structures computer simulations also demonstrate that the cyclic blind rls algorithm exhibits quite fast convergence dynamics

on the spectral coherence of nonstationary processes it is shown that for a single path of a nonstationary process reliable i e low variance measurements of the degree of coherence between two spectral bands with substantial separation must be smaller than 1 2 unless the nonstationarity is of a special type that is the nonstationarity must be either of a known form prior to measurement or of a periodic nature which is known as cyclostationarity it is concluded that spectral correlation measurements on single time series are of highly questionable value for detection and characterization of nonstationarity except in the special cases of cyclostationarity

adaptive filtering based on time averaged mse for cyclostationary signals adaptive filters are commonly used in many signal processing and communications systems in many practical digital communications scenarios including for example interference limited wireless and wireline communications as well as narrowband power line communications the considered signals are jointly cyclostationary yet most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals e g the least mean squares lms it is known that these algorithms may not converge for jointly cyclostationary signals in this paper we rigorously study the optimal adaptive filtering of jointly cyclostationary signals we first identify the relevant objective as the time averaged mean squared error criterion ta mse and obtain an adaptive algorithm as the stochastic approximation of the ta mse minimizer when the considered signals are jointly stationary the algorithm specializes to the standard lms algorithm we provide a comprehensive transient and steady state performance analysis without imposing a specific distribution on the considered signals and derive conditions for convergence and stability the algorithm which we call time averaged lms is applied to practical scenarios in a simulations study and an excellent agreement between the theoretical and the empirical performance is observed

signal interception a unifying theoretical framework for feature detection the unifying framework of the spectral correlation theory of cyclostationary signals is used to present a broad treatment of weak random signal detection for interception purposes the relationships among a variety of previously proposed ad hoc detectors optimum detectors and newly proposed detectors are established the spectral correlation plane approach to the interception problem is put forth as especially promising for detection classification and estimation in particularly difficult environments involving unknown and changing noise levels and interference activity a fundamental drawback of the popular radiometric methods in such environments is explained

modulation by means of linear periodic filtering linear periodically time varying filters are considered as modulators and demodulators for the transmission of analog information over a stationary gaussian channel a complete analysis is carried out based on a certain general decomposition of such a filter into a number of branches each containing a linear time invariant filter and a multiplication with a complex sinusoid receiver optimization is carried out under the assumption that the above decomposition is finite finally a joint optimization of transmitter and receiver is derived under the further restriction that the message signal is strictly band limited

lattice computations for random numbers we improve on a lattice algorithm of tezuka for the computation of the k distribution of a class of random number generators based on finite fields we show how this is applied to the problem of constructing for such generators an output mapping yielding optimal k distribution

direction finding algorithms based on high order statistics two direction finding algorithms are presented for nongaussian signals which are based on the fourth order cumulants of the data received by the array the first algorithm is similar to music while the second is asymptotically minimum variance in a certain sense the first algorithm requires singular value decomposition of the cumulant matrix while the second is based on nonlinear minimization of a certain cost function the performance of the minimum variance algorithm can be assessed by analytical means at least for the case of discrete probability distributions of the source signals and spatially uncorrelated gaussian noise the numerical experiments performed seem to confirm the insensitivity of these algorithms to the gaussian noise parameters

the higher order theory of generalized almost cyclostationary time series in this paper the class of generalized almost cyclostationary gacs time series is introduced time series belonging to this class are characterized by multivariate statistical functions that are almost periodic functions of time whose fourier series expansions can exhibit coefficients and frequencies depending on the lag shifts of the time series moreover the union over all the lag shifts of the lag dependent frequency sets is not necessarily countable almost cyclostationary acs time series turn out to be the subclass of gacs time series for which the frequencies do not depend on the lag shifts and the union of the above mentioned sets is countable the higher order characterization of gacs time series in the strict and wide sense is provided it is shown that the characterization in terms of cyclic moment and cumulant functions is inadequate for those gacs time series that are not acs then generalized cyclic moment and cumulant functions in both the time and frequency domains are introduced finally the problem of estimating the introduced generalized cyclic statistics is addressed and two examples of gacs time series are considered

variance reduction via lattice rules this is a review article on lattice methods for multiple integration over the unit hypercube with a variance reduction viewpoint it also contains some new results and ideas the aim is to examine the basic principles supporting these methods and how they can be used effectively for the simulation models that are typically encountered in the area of management science these models can usually be reformulated as integration problems over the unit hypercube with a large sometimes infinite number of dimensions we examine selection criteria for the lattice rules and suggest criteria which take into account the quality of the projections of the lattices over selected low dimensional subspaces the criteria are strongly related to those used for selecting linear congruential and multiple recursive random number generators numerical examples illustrate the effectiveness of the approach

fast lattice reduction for linear pseudorandom number generators sequences generated by an f 2 linear recursion have wide applications in particular pseudorandom number generation the dimension of equidistribution with v bit accuracy is a most important criterion for the uniformity of the generated sequence the fastest known method for computing these dimensions is proposed by couture and l ecuyer based on lenstra s lattice basis reduction and the dual lattice to the lattice of vector valued generating functions with components in the formal power series f2 t 1 associated to the output f 2 vector sequence in this paper we propose a similar but faster algorithm where 1 the state space is used to represent vectors with components in the formal power series 2 the dual lattice is not necessary and 3 lenstra reduction is replaced with a simpler basis reduction the computational complexity of our method is smaller than for the couture l ecuyer method experiments show that our method improves the speed by a factor of 10 for mersenne twister mt19937 and for well generators with state sizes of 19937 bits and 44497 bits

uncertainty in measurements on spectrally correlated stochastic processes in this paper the class of the spectrally correlated stochastic processes is introduced processes belonging to this class exhibit a loe spl grave ve 1963 bifrequency spectrum with spectral masses concentrated on a countable set of support curves in the bifrequency plane thus such processes have spectral components that are correlated the introduced class generalizes the almost cyclostationary acs processes that are obtained as a special case when the separation between correlated spectral components assumes values only in a countable set in such a case the support curves are lines with unit slope for the spectrally correlated processes the amount of spectral correlation existing between two separate spectral components is characterized by the bifrequency spectral correlation density function which is the density of the loe spl grave ve bifrequency spectrum on its support curves it is shown that in general when the location of the support curves is unknown the time smoothed cross periodogram can provide a reliable low bias and variance single sample path based estimate of the bifrequency spectral correlation density function in those points of the bifrequency plane where the slope of the support curves is not too far from unity moreover there exists a tradeoff between the departure of the nonstationarity from the almost cyclostationarity and the reliability of spectral correlation measurements obtainable by a single sample path furthermore in general the estimate accuracy cannot be improved as wished by increasing the data record length and the spectral resolution

cyclic wiener filtering theory and method conventional time and space filtering of stationary random signals which amounts to forming linear combinations of time translates and space translates exploits the temporal and spatial coherence of the signals by including frequency translates as well the spectral coherence that is characteristic of cyclostationary signals can also be exploited some of the theoretical concepts underlying this generalized type of filtering called frequency shift fresh filtering are developed the theory of optimum fresh filtering which is a generalization of wiener filtering called cyclic wiener filtering is summarized and the theory is illustrated with specific examples of separating temporally and spectrally overlapping communications signals including am bpsk and qpsk the structures and performances of optimum fresh filters are presented and adaptive adjustment of the weights in these structures is discussed also specific results on the number of digital qam signals that can be separated as a function of excess bandwidth are obtained

on recursiveness and related topics in linear systems a decomposition of matrix formal power series linear systems is developed the interconnections between formal power series realization pade approximation recursiveness berlekamp massey algorithm feedback interconnections matrix linear fractional representations matrix continued fractions and the matrix euclidean algorithm are thereby revealed

multiuser constrained water pouring for continuous time overloaded gaussian multiple access channels in this paper signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited continuous time overloaded channels corrupted by additive white gaussian noise awgn the total signal power is minimized subject to general asymmetric signal to interference plus noise ratio sinr constraints at the output of linear minimum mean squared error lmmse receivers using vectorized fourier transform vft technique the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain it turns out that every optimal solution performs the same as the optimal frequency division multiple access fdma system a geometric procedure called multiuser constrained water pouring is developed to construct every possible optimal solution of which profiles of signal power and equivalent bandwidth are respectively the same as those of signal power and physical bandwidth of the optimal fdma system it is shown that orthogonal signature waveforms are assigned to oversized users and continuous time equivalents of generalized welch bound equality cte gwbe sequences are assigned to non oversized users

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

steady state response of an infinite string on a non linear visco elastic foundation to moving point loads the steady state response of a long string on a non linear visco elastic foundation to uniformly moving constant point loads is studied the phase plane is employed to construct a phase portrait that determines the string response this portrait consists of trajectories of the autonomous system that represent the string displacement everywhere except at the loading points and vertical segments that satisfy the boundary conditions in these points it is shown that the string response depends crucially on the ratio between the load velocity and the wave speed in the string if the load moves slower than the waves in the string then the response is nearly symmetric with respect to the load and decays exponentially with the distance form the load if the load velocity exceeds the wave speed then the string exhibits a wave pattern which extends well behind the load in front of the load in this case the string is not disturbed

a computationally efficient and interference tolerant nonparametric algorithm for lti system identification based on higher order cyclostationarity a new nonparametric algorithm for the identification of linear time invariant systems is proposed the method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal consequently although it exploits the higher order cyclostationarity properties of the input and output signals its computational complexity is comparable with that of methods based on second order statistics the proposed estimator of the system transfer function is inherently immune to the presence of noise and interference on both input and output signal measurements and turns out to be asymptotically unbiased and consistent moreover bias and variance of the estimate exhibit a rate of convergence to zero equal to that of estimates based on second order statistics finally simulation results show that the proposed algorithm significantly outperforms in terms of both bias and variance of the estimates several nonparametric identification algorithms previously presented in the literature

analysis of self noise in a fourth power clock regenerator a method for computing the power spectra of the in phase and quadrature components of self noise in a fourth power clock recovery scheme is presented this method is shown to be effective if the symbol waveform is time limited or can be so approximated the method applies to baseband signaling schemes such as pulse amplitude modulation and to modulated carrier schemes such as quadrature amplitude modulation comparison is made with the squaring type recovery technique using cosine rolloff nyquist pulses on the binary phase shift keyed mode at several excess bandwidth factors alpha it is shown that when alpha is less than 0 4 the fourth power circuit gives less time jitter than the squarer for a noiseless channel the method for self noise spectrum calculation is verified by computer simulation a prefilter that completely eliminates time jitter in the fourth power clock recovery circuit is described

asymptotic frequency shift properizer for block processing of improper complex second order cyclostationary random processes in this paper the block processing of a discrete time dt improper complex second order cyclostationary socs random process is considered in particular it is of interest to find a preprocessing operation that enables the adoption of conventional signal processing techniques and algorithms developed for the filtering of proper complex signals and that leads to computationally efficient near optimal postprocessing an invertible linear conjugate linear lcl operator named the dt frequency shift fresh properizer is first proposed it is shown that the dt fresh properizer converts a dt improper complex socs random process input to an equivalent dt proper complex socs random process output by utilizing the information only about the cycle period of the input an invertible lcl block processing operator named the asymptotic fresh properizer is then proposed that mimics the operation of the dt fresh properizer but processes a finite number of consecutive samples of a dt improper complex socs random process it is shown that the output of the asymptotic fresh properizer is not proper but asymptotically proper and that its frequency domain covariance matrix converges to a highly structured block matrix with diagonal blocks as the block size tends to infinity two representative estimation and detection problems are presented to demonstrate that asymptotically optimal low complexity postprocessors can be easily designed by exploiting these asymptotic second order properties of the output of the asymptotic fresh properizer

a new method for adaptive time delay estimation for non gaussian signals a novel adaptive scheme for time delay estimation is introduced for signal environments where the signal is non gaussian and the additive noise sources are spatially correlated gaussian with unknown power spectrum characteristics this scheme is based on parametric modeling between two sensor measurements and employs higher order statistics third or fourth order of the data it is demonstrated by means of extensive simulations that this scheme works well for both stationary and nonstationary cases as expected it outperforms the cross correlation based gradient method for time delay adaptation in spatially correlated gaussian noises the proposed scheme is compared to the overdetermined recursive instrumental variable method and is shown to exhibit substantially less computational complexity

fractionally spaced blind equalization using polyperiodic linear filtering performance of fractionally spaced equalizers using polyperiodic linear filtering is depicted the fractionally sampled version of an arbitrary stable channel s outputs with stationary random inputs exhibit cyclostationarity with cycle frequencies being integer multiples of the reciprocal of the oversampling factor by optimally polyperiodic linear filtering the oversampled outputs we can fully utilize the cyclostationary property with some traditional bussgang techniques such as stop and go decision directed method to adaptively update the filter coefficients the convergence rate of the fractionally spaced equalizers proposed is improved while the complexity retains in the same order as original bussgang ones some computer simulation results are shown to demonstrate the improvement we can achieve

two stage interference resistant adaptive periodically time varying cma blind equalization we consider the problem of blindly equalizing a digital communication signal distorted by a linear time invariant channel and contaminated by severe co channel or adjacent channel digital interference under the assumption that the latter exhibits a different symbol rate from the desired signal the proposed equalizer is composed of two stages that are both periodically time varying ptv in order to better match the periodical statistics of the received signal the first stage employs linear ptv filtering to mitigate interference thus allowing the second stage based on the constant modulus algorithm cma to reliably recover the transmitted information symbols computer simulations confirm the effectiveness of the new approach and comparisons with existing blind methods show that a significant performance gain can be attained

free wave propagation relationships of second order and fourth order periodic systems this talk develops an analytical expression for the determinant of two diagonally indexed full matrices when they are zero these matrices originate from second and fourth order periodic system theory the partial differential equations of these systems are solved using a series solution and are converted into closed form analytical expressions the denominators of these expressions are zero when free wave propagation is present and these denominators are equated to the determinants of the system matrices derived from a second analytical method this process develops a relationship between frequency and wavenumber that is explicit for free wave propagation in these systems two examples are included to illustrate this relationship