zeros of the hankel function of real order out of the principal riemann sheet abstract zeros of the hankel function of real order follow as the order varies continuously trajectories across different riemann sheets of the complex plane a discussion of the main features of these trajectories is presented

on the detection and classification of quadrature digital modulations in broad band noise optimal and suboptimal decision rules for the detection of constant envelope quadrature digital modulations in broadband noise are derived and analyzed the effect of various stochastic models for the carrier phase is examined in detail while no epoch or frequency uncertainty is assumed the delay and multiply type of detector is considered a new binary quadrature phase shift keying bpsk qpsk classifier is compared to the more traditional ad hoc techniques of a square law classifier and a phase based classifier weighting on the phase histogram the new classifier is derived by approximating the likelihood ratio functionals of phase modulated digital signals in white gaussian noise hence is named the quasi log likelihood ratio qllr rule it is shown analytically that its performance is significantly better than that of intuitively designed phase based rules or the conventional square law classifier

joint cycle frequencies and lags utilization in cyclostationary feature spectrum sensing cognitive radio cr systems require awareness of spectrum occupancy in order to operate without causing harmful interference to primary users pus cyclostationary feature detection cfd is a preferred method for spectrum sensing under low signal to noise ratio snr or and noise uncertainty scenarios to determine the presence or otherwise of pu signals conventional cfd schemes tend to use test statistics over either multiple cycle frequencies for a fixed lag set or multiple lags for a fixed cycle frequency this paper proposes a new method that jointly utilizes cycle frequencies and lags to produce more reliable test statistics as the optimal way to apply this joint utilization requires prior knowledge of the 4th order cyclic cumulant which can be challenging to obtain an alternative sub optimal scheme independent of this cumulant knowledge will also be provided it will be shown that in the low snr region where it is most critical for cr applications the proposed sub optimal scheme can lead to similar detection performances as the optimal maximum likelihood technique it will also be demonstrated that compared to multi cycle frequency detection with selection combining equal gain combining or maximum ratio combining the proposed provide superior performance

signal activity detection of phase shift keying signals we propose computationally inexpensive and efficient solutions for signal activity detection of phase shift keying psk signals in additive white gaussian noise we consider the complex amplitude of the signal as well as the information sequence as the unknown parameters in addition the noise variance is assumed unknown we derive the generalized likelihood ratio test glrt and suggest a computationally efficient implementation thereof furthermore we develop a new inexpensive detector for binary psk signals which we will refer to as the generalized energy detector to evaluate the performance of these detectors we attempt to derive a uniformly most powerful invariant test umpi as an optimal detector it turns out that the umpi test exists only if the signal to noise ratio is known we use this umpi test in order to obtain an upper bound performance for the evaluation of invariant detectors such as the above mentioned glrt simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors

robust nonparametric cyclic correlation based spectrum sensing for cognitive radio cognitive radios sense the radio spectrum in order to find underutilized spectrum and then exploit it in an agile manner spectrum sensing has to be performed reliably in challenging propagation environments characterized by shadowing and fading effects as well as heavy tailed noise distributions in this paper a robust computationally efficient nonparametric cyclic correlation estimator based on the multivariate spatial sign function is proposed nonparametric statistics provide additional robustness against heavy tailed noise and when the noise statistics are not fully known asymptotic distribution of the spatial sign cyclic correlation estimator under the null hypothesis is established tests using constraint on false alarm rate are derived based on the estimated spatial sign cyclic correlation for single user and collaborative spectrum sensing by multiple secondary users theoretical justification for detecting cyclostationary signals using the spatial sign cyclic correlation is provided a sequential detection scheme for reducing the average detection time is proposed simulation experiments and theoretical results comparing the proposed method with cyclostationary spectrum sensing methods employing the conventional cyclic correlation estimator are presented simulations demonstrate the reliable and highly robust performance of the proposed nonparametric spectrum sensing method in both gaussian and non gaussian noise environments

collaborative cyclostationary spectrum sensing for cognitive radio systems this paper proposes an energy efficient collaborative cyclostationary spectrum sensing approach for cognitive radio systems an existing statistical hypothesis test for the presence of cyclostationarity is extended to multiple cyclic frequencies and its asymptotic distributions are established collaborative test statistics are proposed for the fusion of local test statistics of the secondary users and a censoring technique in which only informative test statistics are transmitted to the fusion center fc during the collaborative detection is further proposed for improving energy efficiency in mobile applications moreover a technique for numerical approximation of the asymptotic distribution of the censored fc test statistic is proposed the proposed tests are nonparametric in the sense that no assumptions on data or noise distributions are required in addition the tests allow dichotomizing between the desired signal and interference simulation experiments are provided that show the benefits of the proposed cyclostationary approach compared to energy detection the importance of collaboration among spatially displaced secondary users for overcoming shadowing and fading effects as well as the reliable performance of the proposed algorithms even in very low signal to noise ratio snr regimes and under strict communication rate constraints for collaboration overhead

shift variance and nonstationarity of linear periodically shift variant systems and applications to generalized sampling reconstruction processes we present a systematic analysis on shift variance of linear t periodically shift variant t lpsv systems with continuous time input and output we first determine how far a t lpsv system h is away from being shift invariant in terms of two measures namely the distance and the angle between h and the subspace of linear shift invariant systems we then consider the level and the index of shift variance svi of h via commutator of h and the shift operator and examine the amount of shift variance of h under particular input all these quantities are characterized in terms of the so called shift variant part and the shift variance kernel of h moreover we study nonstationarity of wide sense cyclostationary random processes possibly induced by t lpsv systems we define and calculate a measure of nonstationarity nst of the output as the svi of the autocorrelation operator the nst can be used to characterize performance loss when the output is treated with a wss approach the expected shift variance of h subject to particular wss random process is also calculated we apply the above results to generalized sampling reconstruction processes gsrps in addition we consider the approximation error of the gsrp and relate it to the shift variance measures three sampling schemes namely the orthogonal the consistent and the minimax regret sampling are examined in detail we show that for both deterministic and wss random inputs the minimax regret gsrp always introduces less shift variance than the consistent counterparts numerical results for the gsrps of b splines of various orders are provided

two alternative philosophies for estimation of the parameters of time series two alternative philosophical frameworks for the two problems of estimating the time invariant or time variant autocorrelation function and its fourier transform for stationary and cyclostationary time series are compared one is based on the stochastic process model and the other is based on the nonstochastic time series model it is then explained that results on estimator bias and variance for these two problems couched within the stochastic process framework have analogs within the nonstochastic framework the bias and variance results for cyclostationary time series that are available within these two frameworks are then summarized

the zeros of special functions from a fixed point method a scheme for the computation of the zeros of special functions and orthogonal polynomials is developed we study the structure of the first order difference differential equations ddes satisfied by two fundamental sets of solutions of second order odes y n prime prime x a n x y n x 0 n being the order of the solutions and an x a family of continuous functions it is proved that with a convenient normalization of the solutions t pm1 z z pm mbox rm sign d arctan y n x z y n pm 1 x z are globally convergent iterations with fixed points z x n i x n i being the zeros of yn x d is one of the coefficients in the ddes and z x is a primitive of d the structure of the ddes is also used to set global bounds on the differences between adjacent zeros of functions of consecutive orders and to find iteration steps which guarantee that all the zeros inside a given interval can be found with certainty as an illustration we describe how to implement this scheme for the calculation of the zeros of arbitrary solutions of the bessel coulomb legendre hermite and laguerre equations

application of galerkin s method to equal width wave equation the non linear equal width equation is solved by galerkin s method using linear finite elements a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found employing the crank nicolson approach including a product approximation the three invariants of the motion are calculated to determine the conservation properties of the system l 2 and l error norms are used to measure differences between the exact and numerical solutions the simulations of solitary wave motion are used to determine the properties of the algorithm finally the development of an undular bore is studied

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

spatial sign cyclic feature detection this paper studies the impact of the spatial sign function on the cyclic features of communication signals and thereby on the performance of cyclic feature detectors it extends the existing results obtained for gaussian signals and provides new insights into the interactions between the cyclic features of a cyclostationary signal sent through a spatial sign filter which lead to the modified cyclic features at the output we apply these results to analytically derive the performance of the spatial sign cyclic correlation sscc detector which filters a received signal by the spatial sign function prior to its processing using a cyclic feature detector these results are extended to variations of the spatial sign function and we further motivate their application to general zero memory non linear zmnl functions

turan type inequalities for struve functions some turan type inequalities for struve functions of the first kind are deduced by using various methods developed in the case of bessel functions of the first and second kind new formulas like mittag leffler expansion infinite product representation for struve functions of the first kind are obtained which may be of independent interest moreover some complete monotonicity results and functional inequalities are deduced for struve functions of the second kind these results complement naturally the known results for a particular case of lommel functions of the first kind and for modified struve functions of the first and second kind

zeros of the hankel function of real order and of its derivative the trajectories followed in the complex plane by all the zeros of the hankel function and those of its derivative when the order varies continuously along real values are discussed

signal interception in non gaussian noise the interception of weak signals in nongaussian noise is discussed the spectral correlation property exhibited by all cyclostationary signals is exploited to synthesize multi cycle and single cycle detectors which assure a superior tolerance as compared to radiometric techniques to one of the most challenging problems in interception namely accommodating unknown and changing noise level and interference activity the proposed detectors perform a maximum likelihood estimate of the noise level and use the estimate to form the detection statistic to obtain some analytical information about the performance of the multi cycle and single cycle detectors the deflection which is a useful measure of the output signal to noise ratio especially appropriate for weak signal snr interception has been evaluated the receiver operating characteristics carried out via computer simulation confirm the superiority of the proposed cycle detector with respect to the traditional radiometer

inequalities involving bessel and modified bessel functions abstract some inequalities for the ratios j v 1 x j v x and i v 1 x i v x of bessel and modified bessel functions of the first kind and order v 1 are given the inequalities are found easily from a different definition of the ratios and improve many results obtained recently by several authors

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

asymptotic performance analysis of cyclic detectors the paper deals with the analytical evaluation of the asymptotic detection and false alarm probabilities of multicycle and single cycle detectors operating in additive white gaussian noise with unknown and nonrandom spectral level which are based on the cyclostationarity properties of the signal to be intercepted the receiver operating characteristics are derived by using the asymptotic complex normality and the covariance expression of the sample average estimator of the cyclic covariance in an observed discrete time series a numerical example for interception of a binary phase shift keying signal is considered

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

algorithms and codes for the macdonald function recent progress and comparisons the modified bessel function kiv x also known as the macdonald function finds application in the kontorovich lebedev integral transform when x and v are real and positive in this paper a comparison of three codes for computing this function is made these codes differ in algorithmic approach timing and regions of validity one of them can be tested independent of the other two through wronskian checks and therefore is used as a standard against which the others are compared

digital implementations of spectral correlation analyzers the issues involved in the design of computationally efficient algorithms for spectral correlation estimation and the resulting impact on high speed digital realization are addressed the spectral correlation analyzer is characterized as a periodically time varying quadratic system with a kernel possessing certain gross properties the mean and variance of the output are expressed in terms of the kernel and the spectral correlation function of the input three realizations are analyzed in detail one is based on the frequency smoothing method of cross spectral analysis the others are variants of the time smoothing method for each of these realizations an exact expression for the quadratic system kernel is given the digital implementation is developed and a detailed complexity analysis is presented high speed pipeline realizations of the algorithms are analyzed and related special issues are discussed examples involving the calculation of the spectral correlation function in near real time for broadband communications signals are discussed

zeros of the macdonald function of complex order the z zeros of the modified bessel function of the third kind k n z also known as modified hankel function or macdonald function are considered for arbitrary complex values of the order n approximate expressions for the zeros applicable in the cases of very small or very large n are given the behaviour of the zeros for varying n or arg n obtained numerically is illustrated by means of some graphics

cyclic statistic estimators with uncertain cycle frequencies for almost cyclostationary processes sufficient conditions are derived such that estimates of the second order cyclic probabilistic functions with estimated cycle frequencies are mean square consistent and asymptotically complex normal cyclic conjugate autocorrelation functions and cyclic conjugate spectra are considered under the derived conditions asymptotically as the data record length approaches infinity the estimates of cyclic statistics with estimated cycle frequencies have the same complex normal distribution as the case of exactly known cycle frequencies the results are applied to the detection of a moving cyclostationary source in the presence of strong doppler effect and for low values of snr

the role of spectral correlation in design and performance analysis of synchronizers the popular class of synchronizers that consist of a quadratic nonlinearity followed by a phase lock loop is investigated and it is shown that the optimum design of the quadratic transformation is characterized in terms of a spectral correlation function for the signal to be synchronized to it is also shown that the snr performance of this quadratic transformation and the mean square phase jitter of the phaselock loop are both characterized in terms of spectral correlation functions the conditions under which the optimum quadratic transformations for symbol synchronization of bpsk qpsk sqpsk and msk and for carrier synchronization of bpsk reduce to the well known matched filter squarer are identified in addition the well known zeromean square phase jitter condition is generalized from pam to all synchronizable signals and is characterized in terms of the spectral correlation function the low snr maximum likelihood synchronizer for all quadratically synchronizable signals is characterized in terms of a multiplicity of maximum snr quadratic spectral line generators a closed form implementation in terms of a matched filter squarer and symbol rate synchronized averager is obtained for bpsk and qpsk signals

application of cubic b splines for numerical solution of the rlw equation cubic b spline functions have been used to develop a collocation method to solve the regularized long wave rlw equation which is used to model solitary waves undular bore development and wave generation performance of the scheme is tested by computing a solitary wave solution of the rlw equation and made comparison with analytical results undular bore development and wave generation is shown to be in good agreement with available results

on the variation with respect to a parameter of zeros of bessel and q bessel functions abstract we apply what is essentially the hellmann feynman theorem in a discrete setting to derive representations for the derivatives with respect to a parameter of the positive zeros of a family of entire functions these representations prove that the zeros are monotone functions of the parameters involved this family includes the bessel functions jv x and their basic analog jv 2 x q as a by product we show that j v 1 2 v 1 increases with v when v 1 jv 1 being the smallest positive zero of jv x we also use the lommel polynomials to derive improved lower bounds for the smallest positive zero of jv x

software needs in special functions abstract currently available software for special functions exhibits gaps and defects in comparison to the needs of moderm high performance scientific computing and also surprisingly in comparison to what could be constructed from current algorithms in this paper we expose some of these deficiencies and identify the related need for user oriented testing software

robust feature detection for signal interception the problem of detecting the presence of direct sequence spread spectrum signals in noise is considered and the detector consisting of a filter followed by a delay and multiply device is optimized with respect to the filter bandwidth and the delay to maximize robustness to errors in assumed values of pulse rate and carrier frequency output snr is used for performance optimization and the results are corroborated by evaluating receiver operating characteristics

letter to the editor note on the complex zeros of h ν x iζh ν x 0 approximations for the complex zeros in the n plane of the hankel functions h n x and h n x are available in terms of the zeros of airy functions the corresponding zeros of a linear combination of hankel functions are of interest when scattering from cylinders with a surface impedance is studied a simple method to compute these zeros efficiently is presented

solving the generalized regularized long wave equation on the basis of a reproducing kernel space on the basis of a reproducing kernel space an iterative algorithm for solving the generalized regularized long wave equation is presented the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u n is constructed by truncating the series to n terms the convergence of u n to the analytical solution is also proved results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations

neumann weber integral transform for complex indices diffusion and heat equations are commonly investigated in mathematical physics and are solvable for potentials in polar coordinates with a separation into a radial and an angular equation while the angular equation can be solved easily a common method for solving the radial part consists in the application of the neumann weber integral transform the neumann weber integral transform however has only been shown to be valid for real indices of bessel functions in this work we generalize the neumann weber transform to complex bessel indices the back transform then becomes dependent on zeros of hankel functions and we provide useful information for its numerical implementation the results are relevant for solving diffusion equations and heat equations around cylindrical objects

detection and source location of weak cyclostationary signals simplifications of the maximum likelihood receiver the problem of dual receiver interception of low snr signals which includes detection of the presence of a particular signal type and location of its source is considered in particular source location based on time difference of arrival tdoa measurements is examined and the low snr maximum likelihood receiver for joint detection and tdoa estimation is taken as a starting point by explicitly revealing the way in which this receiver exploits the spectral correlation properties of the cyclostationary signal several partial implementations with optimality properties of their own are proposed these greatly simplified implementations which require only a one dimensional search over the tdoa parameter are shown by simulation to perform competitively with the relatively complicated maximum likelihood receiver which requires a two or three dimensional search for phase shift keyed psk signals

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

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

corrigendum to least squares quadratic b spline finite element method for the regularized long wave equation comput methods appl mech engrg 182 2000 205 215

evaluation of the modified bessel function of the third kind of imaginary orders the evaluation of the modified bessel function of the third kind of purely imaginary order kia x is discussed we also present analogous results for the derivative the methods are based on the use of maclaurin series nonoscillatory integral representations asymptotic expansions and a continued fraction method depending on the ranges of x and a we discuss the range of applicability of the different approaches considered and conclude that power series the continued fraction method and the nonoscillatory integral representation can be used to accurately compute the function kia x in the range 0 a 200 0 x 100 using a similar scheme the derivative k ia x can also be computed within these ranges

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

second order blind separation of first and second order cyclostationary sources application to am fsk cpfsk and deterministic sources most of the second order so and higher order ho blind source separation bss methods developed this last decade aim at blindly separating statistically independent sources that are assumed zero mean stationary and ergodic nevertheless in many situations of practical interest such as in radiocommunications contexts the sources are nonstationary and very often cyclostationary digital modulations the behavior of the current so and fourth order fo cumulant based bss methods in the presence of cyclostationary sources has been analyzed recently in a previous paper by ferre spl acute ol and chevalier assuming zero mean sources however some cyclostationary sources used in practical situations are not zero mean but have a first order fio cyclostationarity property which is in particular the case for some amplitude modulated am signals and for some nonlinearly modulated digital sources such as frequency shift keying fsk or some continuous phase frequency shift keying cpfsk sources for such sources the results presented in the previous paper by ferre spl acute ol and chevalier no longer hold and the purpose of this paper is to analyze the behavior and to propose adaptations of the current so bss methods for sources that are both fio and so cyclostationary and cyclo ergodic an extension for deterministic sources is also proposed in the paper

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

a petrov galerkin method for solving the generalized regularized long wave grlw equation the generalized regularized long wave grlw equation is solved numerically by the petrov galerkin method which uses a linear hat function as the trial function and a quintic b spline function as the test function product approximation has been used in this method a linear stability analysis of the scheme shows it to be conditionally stable test problems including the single soliton and the interaction of solitons are used to validate the suggested method which is found to be accurate and efficient finally the maxwellian initial condition pulse is studied

on an identity for zeros of bessel functions in this paper our aim is to present an elementary proof of an identity of calogero concerning the zeros of bessel functions of the first kind moreover by using our elementary approach we present a new identity for the zeros of bessel functions of the first kind which in particular reduces to some other new identities we also show that our method can be applied for the zeros of other special functions like struve functions of the first kind and modified bessel functions of the second kind

correlation matching approach for spectrum sensing in open spectrum communications in the new paradigm of open spectrum access the envisioned radio agility calls for fast and accurate spectrum sensing this challenges traditional spectral estimation in this study we propose three new procedures that are able to sense the known spectrum of the candidate or primary user fulfilling the requirements of open spectrum scenarios these procedures are developed by following the framework of correlation matching changing the traditional single frequency scan to a spectral scan with a particular shape and generalizing filter bank designs the proposed techniques are called candidate methods because their goal is to react only when the candidate s spectral shape is present first candidate f is proposed as a spectral detection method where this is based on minimizing the frobenius distance between correlation matrices and can be viewed as an extended version of the weighted overlapped spectrum averaging estimate next candidate g is presented which is a new procedure that is based on a geodesic distance and that presents the lowest complexity lastly a third procedure is studied candidate m which provides the most compliant performance with the demanding open spectrum scenario by generalizing the capon spectral estimator by means of the analytical results simulations of receiver operating characteristics and estimation variance this study shows the advantages of candidate m over the existing filter bank or cyclostationary detector methods

bounds for modified struve functions of the first kind and their ratios abstract we obtain a simple two sided inequality for the ratio l x l 1 x in terms of the ratio i x i 1 x where l x is the modified struve function of the first kind and i x is the modified bessel function of the first kind this result allows one to use the extensive literature on bounds for i x i 1 x to immediately deduce bounds for l x l 1 x we note some consequences and obtain further bounds for l x l 1 x by adapting techniques used to bound the ratio i x i 1 x we apply these results to obtain new bounds for the condition numbers x l x l x the ratio l x l y and the modified struve function l x itself amongst other results we obtain two sided inequalities for x l x l x and l x l y that are given in terms of x i x i x and i x i y respectively which again allows one to exploit the substantial literature on bounds for these quantities the results obtained in this paper complement and improve existing bounds in the literature

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

certain monotonicity properties of bessel functions we prove the absolute monotonicity of various expressions involving bessel functions these results lead to several bessel function inequalities which illuminate and generalize recent results of paris siam j math anal 15 1984 203 205

non data aided symbol rate estimation of linearly modulated signals the estimation of the symbol rate of a linearly modulated signal is addressed with special focus on low signal to noise ratio snr scenarios this problem finds application in automatic modulation classification and signal monitoring a maximum likelihood ml approach is adopted to derive practical estimators exploiting information on the cyclostationarity of the modulated signal as well as knowledge of the received signaling pulse shape the structure of the ml estimator suggests a two step estimation procedure whereby an initial coarse search determines first a neighborhood from which a subsequent fine search yields the final symbol rate estimate links between the ml approach and previous results from the literature in symbol rate estimation are established as well the proposed scheme is applicable even for small excess bandwidths at the cost of a higher complexity with respect to simpler estimators known to fail under such conditions

on the reversion of an asymptotic expansion and the zeros of the airy functions the general theories of the derivation of inverses of functions from their power series and asymptotic expansions are discussed and compared the asymptotic theory is applied to obtain asymptotic expansions of the zeros of the airy functions and their derivatives and also of the associated values of the functions or derivatives a maple code is constructed to generate exactly the coefficients in these expansions the only limits on the number of coefficients are those imposed by the capacity of the computer being used and the execution time that is available the sign patterns of the coefficients suggest open problems pertaining to error bounds for the asymptotic expansions of the zeros and stationary values of the airy functions

completely monotonic functions associated with the gamma function and its q analogues several functions involving the gamma function x and the q gamma function q x are proved to be completely monotonic some of these results are used to establish the infinite divisibility of a number of probability distributions defined via their moment generating functions

frequency domain glr detection of a second order cyclostationary signal over fading channels cyclostationary processes exhibit a form of frequency diversity based on that we show that a digital waveform with symbol period t can be asymptotically represented as a rank 1 frequency domain vector process which exhibits uncorrelation at different frequencies inside the nyquist spectral support of 1 t by resorting to the fast fourier transform fft this formulation obviates the need of estimating a cumbersome covariance matrix to characterize the likelihood function we then derive the generalized likelihood ratio test glrt for the detection of a cyclostationary signal in unknown white noise without the need of a assuming a synchronized receiver this provides a sound theoretical basis for the exploitation of the cyclostationary feature and highlights an explicit link with classical square timing recovery schemes which appear implicitly in the core of the glrt moreover to avoid the well known sensitivity of cyclostationary based detection schemes to frequency selective fading channels a parametric channel model based on a lower bound on the coherence bandwidth is adopted and incorporated into the glrt by exploiting the rank 1 structure of small spectral covariance matrices the obtained detector outperforms the classical spectral correlation magnitude detector

automatic computation of zeros of bessel functions and other special functions an efficient algorithm is developed for the automatic calculation of the zeros of bessel functions of arbitrary order coulomb wave functions and other special functions remarkably this can be done without any actual functional evaluations limitations and generalizations are discussed

consistent estimation of the cyclic autocorrelation the cyclic autocorrelation is often used to describe nonstationary random processes the authors investigate the conditions under which the cyclic autocorrelation can be estimated consistently in mean square for discrete time gaussian processes they extend and generalize results of hurd 1989 and refine results of boyles and gardner 1983 they derive necessary and sufficient conditions for consistency in mean square of an estimator which are in the form of a single sum of autocorrelation coefficients in the form of a double sum of autocorrelation coefficients in the bifrequency domain and in terms of the average spectrum they also discuss the rate of convergence for this estimator

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

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

on the behavior of current second and higher order blind source separation methods for cyclostationary sources most of the second order so and higher order ho blind source separation methods developed in the 1990s aim at blindly separating statistically independent sources that are assumed zero mean stationary and ergodic nevertheless in many situations of practical interest such as in radiocommunication contexts the sources are nonstationary and very often quasi cyclostationary digital modulations in these conditions it becomes important to wonder whether the performance of these current so and ho blind source separation methods which have been developed for stationary sources may be affected by the potential nonstationarity of the latter limiting the analysis to the so and fourth order fo cumulant based blind source separation methods the purpose of this paper is to bring some answers to this important question through the behavior analysis of the empirical so and fo cumulants estimator in the presence of zero mean quasi cyclostationary sources

structural characterization of locally optimum detectors in terms of locally optimum estimators and correlators explicit formulas for locally snr rightarrow 0 optimum mmse signal estimators smoother filter and predictor for discrete time observations of a random signal in additive random noise are derived and used to characterize the locally optimum likelihood ratio signal detector for on off signaling the characterizations are canonical distribution free detector structures involving estimator correlators these structural characterizations provide new interpretations of known detectors for various special cases if the one step signal predictor is recursive and the noise is white possibly non gaussian or nonstationary there is a canonical structure that admits recursive computation the primary motivation for these structural characterizations is to render the estimator correlator design philosophy applicable for the purpose of simplifying implementations and enhancing adaptability unlike the known esfimator correlator structural characterizations for continuous time globally optimum detectors the new characterizations apply for non gaussian as well as gaussian noise and the estimators are explicit rather than implicit

functional inequalities for modified struve functions in this paper by using a general result on the monotonicity of quotients of power series our aim is to prove some monotonicity and convexity results for the modified struve functions moreover as consequences of the above mentioned results we present some functional inequalities as well as lower and upper bounds for modified struve functions our main results complement and improve the results of joshi and nalwaya