adaptive detection in gaussian interference with unknown covariance after reduction by invariance in this paper we address the problem of adaptive detection in homogeneous gaussian interference with unknown covariance matrix after reduction by invariance starting from a maximal invariant statistic which contains all the information for the synthesis of an invariant detector we devise the rao test generalized likelihood ratio test glrt and durbin test moreover we compare their decision statistics with those of the receivers designed according to the same criteria from the raw data i e before reduction by invariance we prove that the glrt in the original data space is statistically equivalent to the glrt designed after reduction by invariance under a very mild assumption and coincide with the conditional uniformly most powerful invariant c umpi test obtained conditioning on an ancillary part of the maximal invariant statistic as to the rao and durbin criteria when they are applied after reduction by invariance lead to detectors different from the counterparts devised in the raw data domain at the analysis stage the performance of the receivers devised in the invariant domain is analyzed in comparison with that of the counterparts synthesized from the original observations

maximum likelihood based estimation of frequency and phase offset in dct ofdm systems under non circular transmissions algorithms analysis and comparisons recently the advantages of the discrete cosine transform dct based orthogonal frequency division multiplexing ofdm have come to the light we thus consider dct ofdm with non circular transmission our results cover circular transmission as well and present two blind joint maximum likelihood frequency offset and phase offset estimators both our theoretical analysis and numerical comparisons reveal new advantages of dct ofdm over the traditional discrete fourier transform dft based ofdm these advantages as well as those already uncovered in the early works on dct ofdm support the belief that dct ofdm is a promising multi carrier modulation scheme

variance and correlation of square law detected allpass channels with bandpass harmonic signals in gaussian noise a bandpass harmonic signal consists of a multiple tone complex with uniform spacing of the frequencies this paper considers the correlation of square law detected allpass channels with such signals in gaussian noise the square law mixing terms of each allpass filtered channel are low pass filtered to produce the detector output components and then are synchronously demodulated at the tone difference frequency to form output components in this paper we derive the theoretical variance and cross correlation between the different channels before and after synchronous demodulation simulations for a three tone signal demonstrate excellent agreement with the exact and approximate theoretical results applications of this work include wide band system identification an example of which is detailed in this paper for the estimation of differential phase

complex elliptically symmetric random variables generation characterization and circularity tests complex elliptically symmetric ces distributions constitute a flexible and broad class of distributions for many engineering applications and include the widely used complex gaussian complex complex generalized gaussian and symmetric stable distributions for example their careful statistical characterization is needed moreover the mechanisms for generating random variables from these distributions are not well defined in literature in this paper we provide such treatment in order to provide a better insight on their statistical properties and simplifying proofs and derivations for example insightful expressions for complex kurtosis coefficients of ces distributions are derived providing an interpretation on what complex kurtosis really measures also derived are asymptotic distributions of circularity measures the sample circularity quotient and coefficient assuming i i d samples from an unspecified ces distribution also new wald s type detectors of circularity are proposed that are valid within ces distributions with finite fourth order moments these results are accompanied with examples that are of interest in developing signal processing algorithms for complex valued signals

associated laguerre konhauser polynomials quasi monomiality and operational identities abstract in this paper we exploit the monomiality principle to discuss and introduce a new class of laguerre konhauser polynomials we study their properties differential equations generating functions recurrence relations expansions and so on and discuss the link with ordinary case

properness and widely linear processing of quaternion random vectors in this paper the second order circularity of quaternion random vectors is analyzed unlike the case of complex vectors there exist three different kinds of quaternion properness which are based on the vanishing of three different complementary covariance matrices the different kinds of properness have direct implications on the cayley dickson representation of the quaternion vector and also on several well known multivariate statistical analysis methods in particular the quaternion extensions of the partial least squares pls multiple linear regression mlr and canonical correlation analysis cca techniques are analyzed showing that in general the optimal linear processing is full widely linear however in the case of jointly q proper or c proper vectors the optimal processing reduces respectively to the conventional or semi widely linear processing finally a measure for the degree of improperness of a quaternion random vector is proposed which is based on the kullback leibler divergence between two zero mean gaussian distributions one of them with the actual augmented covariance matrix and the other with its closest proper version this measure quantifies the entropy loss due to the improperness of the quaternion vector and it admits an intuitive geometrical interpretation based on kullback leibler projections onto sets of proper augmented covariance matrices

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

a complex generalized gaussian distribution characterization generation and estimation the generalized gaussian distribution ggd provides a flexible and suitable tool for data modeling and simulation however the characterization of the complex valued ggd in particular generation of samples from a complex ggd have not been well defined in the literature in this correspondence we provide a thorough presentation of the complex valued ggd by i constructing the probability density function pdf ii defining a procedure for generating random numbers from the complex valued ggd and iii implementing a maximum likelihood estimation mle procedure for the shape and covariance parameters in the complex domain we quantify the performance of the mle with simulations and actual radar data

complex noise analysis of dmt in this paper we consider discrete multitone dmt or baseband orthogonal frequency division multiplexing ofdm modulation and perform a detailed noise analysis which takes into account dependencies and power variance differences of real and imaginary part after the complex valued discrete fourier transform dft the derivation is based on the so called pseudocovariance matrix of a complex random vector which was introduced by neeser and massey 1993 we show that the relevant pseudocovariance matrix is not the zero matrix in general in contrast to pass band ofdm for which it can be proven under certain assumptions that all occurring pseudocovariance matrices are vanishing we show that for colored noise rotated rectangular symbol constellations are more appropriate than the common quadratic quadrature amplitude modulation qam symbol constellations with respect to capacity and symbol error probability and we derive formulas for the rotation angles and constellation sizes densities finally we extend the results to a multitransceiver multiple input multiple output mimo scenario for which we assume a very general noise model at the inputs of the receivers allowing correlations between the noise signals of different receivers this requires the introduction of pseudocross covariance matrices of complex random vectors which are the important objects together with cross covariance matrices in the mimo situation

asymptotic normality of sample covariance matrix for mixed spectra time series application to sinusoidal frequencies estimation this correspondence addresses the asymptotic normal distribution of the sample mean and the sample covariance matrix of mixed spectra time series containing a sum of sinusoids and a moving average ma process two central limit cl theorems are proved as an application of this result the asymptotic normal distribution of any sinusoidal frequencies estimator of such time series based on second order statistics is deduced

blind frequency offset estimation for ofdm oqam systems this paper deals with the problem of blind carrier frequency offset cfo estimation in orthogonal frequency division multiplexing ofdm systems based on offset quadrature amplitude modulation ofdm oqam specifically by assuming that the number of subcarriers is sufficiently large the received signal is modeled as a complex gaussian random vector cgrv since the ofdm oqam signal results to be a noncircular nc process i e its relation function is different from zero by exploiting the generalized probability density function for nc cgrvs the unconditional maximum likelihood algorithm for cfo estimation in nondispersive channel is derived moreover due to its computational complexity a more feasible estimator is considered the performance of the proposed estimators assessed via computer simulation is compared with that of recently proposed cfo estimators exploiting second order cyclostationarity and with the gaussian crameacuter rao bound

augmented performance bounds on strictly linear and widely linear estimators with complex data novel physical insights are provided into the performances of strictly linear sl and widely linear wl estimators of the generality of complex valued data both proper second order circular and improper second order noncircular this is achieved by first performing a novel complementary mean square error cmse analysis in order to quantify the degrees of improperness second order noncircularity of the sl and wl estimation errors the exact bounds on the cmse difference between the sl and wl estimators are investigated to show that only a joint consideration of the standard mse analysis and the proposed cmse analysis has enough degrees of freedom for a rigorous account of the performance of wl and sl estimators this also makes it possible to rigourously quantify the contributions to the wl performance advantage from the individual real and imaginary channels an important finding not possible to obtain by using the standard mse analysis only

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

the multivariate complex normal distribution a generalization the multivariate complex normal distribution usually employed in the literature is a special case since certain restrictions have been imposed on the covariances of the real and imaginary parts of its variables a more general distribution is proposed of which the usual distribution is shown to be a special case

semiparametric crb and slepian bangs formulas for complex elliptically symmetric distributions the main aim of this paper is to extend the semiparametric inference methodology recently investigated for real elliptically symmetric res distributions to complex elliptically symmetric ces distributions the generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data moreover the ces distributions has been widely recognized as a valuable and general model to statistically describe the non gaussian behaviour of datasets originated from a wide variety of physical measurement processes the paper is divided in two parts in the first part a closed form expression of the constrained semiparametric cramer rao bound cscrb for the joint estimation of complex mean vector and complex scatter matrix of a set of ces distributed random vectors is obtained by exploiting the so called wirtinger or mathbb c mathbb r calculus the second part deals with the derivation of the semiparametric version of the slepian bangs formula in the context of the ces model specifically the proposed semiparametric slepian bangs ssb formula provides us with a useful and ready to use expression of the semiparametric fisher information matrix sfim for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a ces distributed vector in the presence of unknown nuisance density generator furthermore we show how to exploit the derived ssb formula to obtain the semiparametric counterpart of the stochastic crb for direction of arrival doa estimation under a random signal model assumption simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications

kinematics of complex valued time series the contribution to a stationary complex valued time series at a single frequency magnitude takes the form of a random ellipse and its properties such as aspect ratio which includes rotational direction and orientation are of great interest in science a case when both the aspect ratio and orientation are fixed is found and their variability in general results from the additional influence of an orthogonal ellipse it is shown how a magnitude squared coherence coefficient controls both the relative influences of these components and the variation of both the orientation and aspect ratio of the resultant ellipse realizations of random ellipses are recovered very accurately from simulated time series the mean orientation of the random ellipse is formally derived

second order analysis of improper complex random vectors and processes we present a comprehensive treatment of the second order theory of complex random vectors and wide sense stationary wss signals the main focus is on the improper case in which the complementary covariance does not vanish accounting for the information present in the complementary covariance requires the use of widely linear transformations based on these we present the eigenanalysis of complex vectors and apply it to the problem of rank reduction through principal components we also investigate joint properties of two complex vectors by introducing canonical correlations which paves the way for a discussion of the wiener filter and its rank reduced version we link the concepts of propriety and joint propriety to eigenanalysis and canonical correlation analysis respectively our treatment is extended to wss signals in particular we give a result on the asymptotic distribution of eigenvalues and examine the connection between wss proper and analytic signals

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

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

on testing the extent of noncircularity in this correspondence we provide a multiple hypothesis test to detect the number of latent noncircular signals in a complex gaussian random vector our method sequentially tests the results of individual generalized likelihood ratio test glrt statistics with known asymptotic distributions to form the multiple hypothesis detector specifically we are able to set a threshold yielding a precise probability of error this test can be used to statistically determine if a given complex observation is circular gaussian and if not how many latent signals in the observation are noncircular simulations are used to quantify the performance of the detector as compared to a detector based on the minimum description length mdl criterion the utility of the detector is shown by applying it to a beamforming application using independent component analysis ica

stochastic time frequency analysis using the analytic signal why the complementary distribution matters we challenge the perception that we live in a proper world where complex random signals can always be assumed to be proper also called circularly symmetric rather we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper which means that its complementary correlation function is nonzero we explore the consequences of this finding in the context of stochastic time frequency analysis in cohen s class there the analytic signal plays a prominent role because it reduces interference terms however the usual time frequency representation tfr based on the analytic signal gives only an incomplete signal description it must be augmented by a complementary tfr whose properties we develop in detail we show why it is still advantageous to use the pair of standard and complementary tfrs of the analytic signal rather than the tfr of the corresponding real signal

identification of closed loop linear systems via cyclic spectral analysis given noisy input output time domain data the problem of closed loop system identification given noisy time domain input output measurements is considered it is assumed that the various disturbances affecting the system are zero mean stationary whereas the closed loop system operates under an external cyclostationary input which is not measured noisy measurements of the direct input and output of the plant are assumed to be available the closed loop system must be stable but it is allowed to be unstable in open loop no knowledge about the linear feedback mechanism is assumed two identification algorithms are investigated using cyclic spectral analysis of noisy input output data for both approaches the open loop transfer function is first estimated using the cyclic spectrum and cyclic cross spectrum of the input output data these transfer function estimates are then used as data for the proposed algorithms both classes of parameter estimators are shown to be weakly consistent in any stationary noise both at input as well as output asymptotic performance analysis of the proposed parameter estimators is also provided computer simulation examples are presented in support of the proposed approaches

on a singular integral equation including a set of multivariate polynomials suggested by laguerre polynomials in this paper we introduce the class of polynomials z n 1 n j a x 1 x j r 1 r j suggested by the multivariate laguerre polynomials we give schlafli s contour integral representation and calculate the fractional order integral of these polynomials furthermore we obtain linear multilinear and mixed multilateral generating functions for them finally we construct a singular integral equation with z n 1 n j a x 1 x j r 1 r j in the kernel and obtain the solution in terms of multivariate analogue of the mittag leffler functions

detection and estimation of improper complex random signals nonstationary complex random signals are in general improper not circularly symmetric which means that their complementary covariance is nonzero since the karhunen loeve k l expansion in its known form is only valid for proper processes we derive the improper version of this expansion it produces two sets of eigenvalues and improper observable coordinates we then use the k l expansion to solve the problems of detection and estimation of improper complex random signals in additive white gaussian noise we derive a general result comparing the performance of conventional processing which ignores complementary covariances with processing that takes these into account in particular for the detection and estimation problems considered we find that the performance gain as measured by deflection and mean squared error mse respectively can be as large as a factor of 2 in a communications example we show how this finding generalizes the result that coherent processing enjoys a 3 db gain over noncoherent processing

estimation of second order cross moments of generalized almost cyclostationary processes in this paper the problem of estimating second order cross moments of generalized almost cyclostationary gacs processes is addressed gacs processes have statistical functions that are almost periodic functions of time whose generalized fourier series expansions have both frequencies and coefficients that depend on the lag shifts of the processes the class of such nonstationary processes includes the almost cyclostationary acs processes which are obtained as a special case when the frequencies do not depend on the lag shifts acs processes filtered by doppler channels and communications signals with time varying parameters are further examples it is shown that the second order cross moment of two jointly gacs processes is completely characterized by the cyclic cross correlation function moreover it is proved that the cyclic cross correlogram is an asymptotically normal mean square consistent estimator of the cyclic cross correlation function furthermore it is shown that well known consistency results for acs processes can be obtained by specializing the results of this paper

a cfar adaptive subspace detector for first order or second order gaussian signals based on a single observation in this paper we consider the problem of detecting a signal in gaussian noise with unknown covariance matrix in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor one solution to this problem is the adaptive subspace detector asd with a single or multiple observations however the probabilities of false alarm and detection of this asd have not been obtained yet in this paper these expressions are derived on the basis of a single observation which are confirmed with monte carlo simulations it is shown that the asd has a constant false alarm rate property with respect to both the shared noise covariance matrix structure and the independent scaling of the noise in the test data in addition we prove that for the first order model where the signal of interest is assumed to be a deterministic but unknown vector the asd derived with the generalized likelihood ratio test is consistent with that derived with an ad hoc two step design procedure

iterative hos sos ihoss algorithm for direction of arrival estimation and sensor localization a new method for joint direction of arrival doa and sensor position estimation is introduced the sensors are assumed to be randomly deployed except two reference sensors the proposed method exploits the advantages of both higher order statistics hos and second order statistics sos with an iterative algorithm namely iterative higher order second order statistics ihoss a new cumulant matrix estimation technique is proposed for the hos approach by converting the multisource problem into a single source one ihoss performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate a cost function is defined for the joint doa and position estimation the iterative procedure is guaranteed to converge the ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies the conditions on these frequencies are presented closed form expressions are derived for the deterministic cramer rao bound crb for doa and unknown sensor positions for noncircular complex gaussian noise with unknown covariance matrix simulation results show that the performance of ihoss is significantly better than the hos approaches for doa estimation and closely follows the crb for both doa and sensor position estimations

perturbations on the antidiagonals of hankel matrices given a strongly regular hankel matrix and its associated sequence of moments which defines a quasi definite moment linear functional we study the perturbation of a fixed moment i e a perturbation of one antidiagonal of the hankel matrix we define a linear functional whose action results in such a perturbation and establish necessary and sufficient conditions in order to preserve the quasi definite character a relation between the corresponding sequences of orthogonal polynomials is obtained as well as the asymptotic behavior of their zeros we also study the invariance of the laguerre hahn class of linear functionals under such perturbation and determine its relation with the so called canonical linear spectral transformations

tapering promotes propriety for fourier transforms of real valued time series we examine fourier transforms of real valued stationary time series from the point of view of the statistical propriety processes with a large dynamic range spectrum have transforms that are very significantly improper for some frequencies the real and imaginary parts can be highly correlated and the periodogram will not have the standard chi square distribution at these frequencies nor have two degrees of freedom use of a taper reduces impropriety to just frequencies close to zero and nyquist only and frequency ranges where the propriety breaks down can be quite accurately and easily predicted by half the autocorrelation width of h h 2f denoted by c where h f is the fourier transform of the taper and denotes convolution for vector time series we derive an improved distributional approximation for minus twice the log of the generalized likelihood ratio test statistic for testing for propriety of the fourier transform at any frequency and compare frequency range cutoffs for propriety determined by the hypothesis test with those determined by c

generalized polynomials and associated operational identities we use operational identities to introduce multivariable laguerre polynomials we explore the wealth of differential equations they satisfy we analyze their properties and the link with legendre type polynomials

transfer function and transient estimation by gaussian process regression in the frequency domain inspired by the recent promising developments of bayesian learning techniques in the context of system identification this paper proposes a transfer function estimator based on gaussian process regression contrary to existing kernel based impulse response estimators a frequency domain approach is adopted this leads to a formulation and implementation which is seamlessly valid for both continuous and discrete time systems and which conveniently enables the selection of the frequency band of interest a pragmatic approach is proposed in an output error framework from sampled input and output data the transient is dealt with by estimating it simultaneously with the transfer function modelling the transfer function and the transient as gaussian processes allows for the incorporation of relevant prior knowledge on the system in the form of suitably designed kernels the ss stable spline and dc diagonal correlated kernels from the literature are translated to the frequency domain and are proven to impose the stability of the estimated transfer function specifically the estimates are shown to be stable rational functions in the frequency variable the hyperparameters of the kernel are tuned via marginal likelihood maximisation the comparison between the proposed method and three existing methods from the literature the regularised finite impulse response rfir estimator the local polynomial method lpm and the local rational method for frequency response function estimation is illustrated on simulations on multiple case studies

the approximation properties of generalized bernstein polynomials of two variables the positive linear operators of bernstein type of two variables are considered and the theorems about approximation and about the order of approximation of the sequence of these operators are established

blind symbol timing estimation for ofdm oqam systems in this correspondence we consider the problem of blind symbol timing st estimation for pulse shaping orthogonal frequency division multiplexing ofdm systems based on offset quadrature amplitude modulation oqam in particular under the assumption of low signal to noise ratio the joint maximum likelihood ml phase offset and st estimator for additive white gaussian noise awgn channel is derived since the phase estimate is in closed form the st estimate requires a one dimensional maximization procedure with respect to a continuous parameter specifically the st estimate depends on both the unconjugate and the conjugate correlation function of the transmitted ofdm oqam signal and exploits the cyclostationarity of the ofdm oqam signal that is related to the bandwidth of the considered pulse shaping filter in particular for the adopted pulse shaping filter the ofdm oqam signal results to be stationary with respect to its unconjugate correlation function and then the ml cost function depends only on the conjugate correlation function the performance of the proposed ml estimator is assessed via computer simulations both in awgn and multipath channel

asymptotic analysis and tight performance bounds of diversity receptions over beckmann fading channels with arbitrary correlation prior results on exact error rates and outage probabilities of diversity receptions over arbitrarily correlated fading channels involve intractable nested integrals which makes the performance analyses challenging to carry out in this paper we derive asymptotic expressions and asymptotically tight bounds for error rates and outage probabilities of diversity receptions including maximal ratio combining selection combining and equal gain combining over arbitrarily correlated beckmann fading channels these new asymptotic performance expressions reveal insights into the diversity systems over arbitrarily correlated beckmann fading channels and the accuracy of the asymptotic performance expressions is explicitly quantified by the performance bounds using these analytical tools one can assess the performance of the diversity reception systems over arbitrarily correlated beckmann fading channels without resorting to time consuming monte carlo simulation or numerical multifold integration

an integrable system connected with the uvarov chihara problem for orthogonal polynomials a new non local integrable chain with continuous time and discrete space variable is considered in contrast to the case of toda and volterra chains the general solution can be presented in explicit form in terms of two arbitrary sequences it is shown that this solution is connected with the so called uvarov chihara problem inserting a discrete mass at the centre of the spectral interval of symmetric orthogonal polynomials the asymptotic behaviour of the recurrence coefficients of such polynomials is considered

stochastic crame spl acute r rao bound for noncircular signals with application to doa estimation after providing an extension of the slepian bangs formula for general noncircular complex gaussian distributions this paper focuses on the stochastic crame spl acute r rao bound crb on direction of arrival doa estimation accuracy for noncircular sources we derive an explicit expression of the crb for doa parameters alone in the case of noncircular complex gaussian sources by two different methods one of them consists of computing the asymptotic covariance matrix of the maximum likelihood ml estimator and the other is obtained directly from our extended slepian bangs formula some properties of this crb are proved and finally it is numerically compared with the crbs under circular complex gaussian and complex discrete distributions of sources

bivariate mittag leffler functions arising in the solutions of convolution integral equation with 2d laguerre konhauser polynomials in the kernel abstract recently the 2d laguerre konhauser polynomials were introduced in 1 in the present paper first of all we propose another bivariate polynomial family which is bi orthonormal with the 2d laguerre konhauser polynomials then we consider a convolution integral equation with 2d laguerre konhauser polynomials in the kernel and we obtain its solution by introducing a new family of bivariate mittag leffler functions furthermore we introduce a double fractional integral operator including bivariate mittag leffler functions in the kernel this integral operator includes the double riemann liouville fractional integral operator we investigate its transformation properties on the continuous function and lebesgue summable function spaces also the semigroup property of the operator is investigated we further study some miscelenenous properties of 2d laguerre konhauser polynomials and bivariate mittag leffler functions such as generating function schlafli s integral represantation finally we approximate to the image of any bivariate continuous function under the action of the proposed double integral operators

widely linear alamouti receiver for the reception of real valued constellations corrupted by interferences the alamouti saic maic concept orthogonal space time block codes stbc and the alamouti scheme in particular are of particular interest in multiple input multiple output mimo systems since they achieve full spatial diversity over fading channels and are decoded from linear processing at the receiver nevertheless due to the expensive spectral resource increasing network capacity requires the development of interference cancellation ic techniques allowing several users to share the same spectral resources without impacting the transmission quality in this context several ic schemes have been developed during this last decade where each user is equipped with multiple antennas and employs stbc at transmission however these ic techniques require multiple antennas at reception which remains a challenge at the handset level due to cost and size limitations for this reason low complexity single antenna interference cancellation saic techniques currently operational in gsm handsets have been developed recently for single antenna users using real valued modulations or complex filtering of real valued modulations by using a widely linear wl filtering at reception extension to multiple antennas at reception is called multiple antenna interference cancellation maic technique the purpose of this paper is to extend the saic maic technology to users using both real valued constellations such as amplitude shift keying ask constellations and the alamouti scheme at transmission a wl minimum mean square error mmse receiver completely new for ic purposes in the context of radio communications systems using the alamouti scheme is proposed and analyzed this receiver which corresponds to the maximum likelihood ml receiver for synchronous intranetwork interferences is able to separate up to 2 n alamouti users from n antennas at reception hence saic capability for n 1

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

block sparse bayesian learning based nb iot interference elimination in lte advanced systems narrowband internet of things nb iot is one of the emerging 5g technologies but might introduce narrowband interference nbi to existing broadband systems such as long term evolution advanced lte a systems thus the mitigation of the nb iot interference to lte a is an important issue for the harmonic coexistence and compatibility between 4g and 5g in this paper a newly emerged sparse approximation technique block sparse bayesian learning bsbl is utilized to estimate the nb iot interference in lte a systems the block sparse representation of the nbi is constituted through the proposed temporal differential measuring approach and the bsbl theory is utilized to recover the practical block sparse nbi a bsbl based method partition estimated bsbl is proposed with the aid of the estimated block partition beforehand the bayesian parameters are obtained to yield the nbi estimation the intra block correlation ibc is considered to facilitate the recovery moreover exploiting the inherent structure of the identical ibc matrix another method of informative bsbl is proposed to further improve the accuracy which does not require prior estimation of the block partition reported simulation results demonstrate that the proposed methods are effective in canceling the nb iot interference in lte a systems and significantly outperform other conventional methods

on probability density functions for complex variables complex random variables arise naturally in many settings and their properties are of general interest past work on complex variables has mainly focused on their second order structure as well as that of their conjugates whereas the main purpose of this correspondence is to clarify the concept of a density function for a complex random variable and to discuss its properties two different functions play the role that the density of a real univariate random variable holds only one of these two functions can be correctly interpreted as a density but both functions clarify the nature of a complex variable the role played by the complex conjugate of the variable in this formulation is clarified and the complex scalar nature of z is discussed as the properties of complex random variables are most naturally specified in terms of the complex quantities directly and given in terms of the distribution of the complex variables rather than formulated in terms of the real and imaginary parts ensuring that an interpretable complex formulation exists is important

spectral transformations self similar reductions and orthogonal polynomials we study spectral transformations in the theory of orthogonal polynomials which are similar to darboux transformations for the schr dinger equation linear transformations of the stieltjes function with coefficients that are rational in the argument are constructed as iterations of the christoffel and geronimus transformations we describe a characteristic property of semi classical orthogonal polynomials scop on the uniform and the exponential lattice namely that all these polynomials can be obtained through simple quasi periodic and q periodic self similar closures of the chain of linear spectral transformations in the self similar setting a characterization of the laguerre hahn polynomials on linear and q linear lattices is obtained by considering rational transformations of the stieltjes function generated by transitions to the associated polynomials

sieved orthogonal polynomials vii generalized polynomial mappings systems of symmetric orthogonal polynomials whose recurrence relations are given by compatible blocks of second order difference equations are studied in detail applications are given to the theory of the recently discovered sieved orthogonal polynomials the connection with polynomial mappings is examined an example of a family of orthogonal polynomials having discrete masses in the interior of the spectrum is included

generalized likelihood ratios for testing the properness of quaternion gaussian vectors in a recent paper the second order statistical analysis of quaternion random vectors has shown that there exist two different kinds of quaternion widely linear processing which are associated with the two main types of quaternion properness in this paper we consider the problem of determining from a finite number of independent vector observations whether a quaternion gaussian vector is proper or not specifically we derive three generalized likelihood ratio tests glrts for testing the two main kinds of quaternion properness and show that the glrts reduce to the estimation of three previously proposed quaternion improperness measures interestingly the three glrt statistics improperness measures can be interpreted as an estimate of the entropy loss due to the quaternion improperness additionally we analyze the case in which the orthogonal basis for the representation of the quaternion vector is unknown which results in the problem of estimating the principal bbc properness direction i e the pure unit quaternion minimizing the bbc improperness measure although this estimation problem is not convex we propose a technique based on successive convex approximations which can be solved in closed form finally some simulation examples illustrate the performance and practical application of the proposed tests

a rank reduced lmmse canceller for narrowband interference suppression in ofdm based systems we present a narrowband interference nbi canceller that suppresses spectral leakage in an orthogonal frequency division multiplexing ofdm based system caused by a narrowband nb signal we assume that the spectrum of the nb signal is within the spectrum of the ofdm signal this can be the case e g on digital subscriber lines dsl and in new unlicensed frequency bands for radio transmission the canceller makes linear minimum mean square error estimates of the spectral leakage by measuring the nbi on a few modulated or unmodulated ofdm subcarriers it uses a model of the nb signal s power spectral density as a priori information using a frequency invariant design it is possible to cancel nbi from signals that are changing their frequency location with significantly reduced complexity overhead the operational complexity of the canceller can be lowered by using the theory of optimal rank reduction and using the time bandwidth product of the nb signal analytical performance evaluations as well as monte carlo simulations show that without perfect a priori information this canceller can suppress the spectral leakage from a strong nb signal e g with equal power as the ofdm signal to well below the background noise floor for typical applications where it causes negligible signal to noise ratio and symbol error rate degradation

arma prediction of widely linear systems by using the innovations algorithm a new autoregressive moving average arma predictor for widely linear systems is presented by using the innovations algorithm and under an improper treatment the main characteristics of this predictor are its facility of implementation from a practical standpoint and a better performance with respect to the conventional predictor obtained from a proper processing

ml based symbol timing and frequency offset estimation for ofdm systems with noncircular transmissions this paper deals with the problem of joint symbol timing and carrier frequency offset cfo estimation in orthogonal frequency division multiplexing ofdm systems with noncircular nc transmissions maximum likelihood ml estimators of symbol timing and cfo have been derived under the assumption of nondispersive channel and by modeling the ofdm signal vector as a circular complex gaussian random vector c cgrv the gaussian assumption is reasonable when the number of subcarriers is sufficiently large however if the data symbols belong to an nc constellation the received signal vector becomes an nc cgrv i e a cgrv whose relation matrix defined as the statistical expectation of the product between the vector and its transpose is not identically zero hence in this case previously mentioned estimators termed mlc estimators are not ml estimators in this paper by exploiting the joint probability density function for nc cgrvs ml estimators are derived moreover since their implementation complexity is high feasible computational algorithms are considered finally refined symbol timing estimators apt to counteract the degrading effects of intersymbol interference isi in dispersive channels are suggested the performance of the derived estimators is assessed via computer simulation and compared with that of mlc estimators and that of modified mlc mmlc estimators exploiting only isi free samples of the cyclic prefix

second order complex random vectors and normal distributions complex random vectors are usually described by their covariance matrix this is insufficient for a complete description of second order statistics and another matrix called the relation matrix is necessary some of its properties are analyzed and used to express the probability density function of normal complex vectors various consequences are presented

complex random vectors and ica models identifiability uniqueness and separability in this paper the conditions for identifiability separability and uniqueness of linear complex valued independent component analysis ica models are established these results extend the well known conditions for solving real valued ica problems to complex valued models relevant properties of complex random vectors are described in order to extend the darmois skitovich theorem for complex valued models this theorem is used to construct a proof of a theorem for each of the above ica model concepts both circular and noncircular complex random vectors are covered examples clarifying the above concepts are presented

glrt based adaptive detection algorithms for range spread targets we address adaptive detection of a range spread target or targets embedded in gaussian noise with unknown covariance matrix to this end we assume that cells referred to in the following as secondary data that are free of signal components are available those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test in this context we design detectors relying on the generalized likelihood ratio test glrt and on a two step glrt based design procedure remarkably both criteria lead to receivers ensuring the constant false alarm rate cfar property with respect to the unknown quantities a thorough performance assessment of the proposed detection strategies together with the evaluation of their processing cost highlights that the two step design procedure is to be preferred with respect to the plain glrt in fact the former leads to detectors that achieve satisfactory performance under several situations of practical interest and are simpler to implement than those designed resorting to the latter

on testing for impropriety of multivariate complex valued random sequences we consider the problem of testing whether a complex valued vector random sequence is proper i e if the sequence is uncorrelated with its complex conjugate previous nonparametric approaches to impropriety testing are limited to a sequence of independent random vectors typically assumed to be gaussian in this paper we extend the results to stationary vector sequences that can be non gaussian a binary hypothesis testing approach is formulated and a generalized likelihood ratio test glrt is derived using the power spectral density estimator of an augmented sequence an asymptotic analytical solution for calculating the test threshold is provided the performance of the glrt is analyzed by deriving an approximate asymptotic distribution of the glrt statistic under the alternative hypothesis the results are illustrated via simulations

discrete time estimation of second order statistics of generalized almost cyclostationary processes in this paper the problem of estimating second order statistics of continuous time generalized almost cyclostationary gacs processes is addressed gacs processes in the wide sense have autocorrelation function almost periodic in time whose generalized fourier series expansion has both frequencies and coefficients that depend on the lag shifts almost cyclostationary acs processes are obtained as a special case when the frequencies do not depend on the lag shifts acs processes filtered by doppler channels and communications signals with time varying parameters are further examples it is shown that continuous time gacs processes do not have a discrete time counterpart the discrete time cyclic cross correlogram of the discrete time acs processes obtained by uniformly sampling gacs processes is considered as estimator of samples of the continuous time cyclic cross correlation function the asymptotic performance analysis is carried out by resorting to the hybrid cyclic cross correlogram which is partially continuous time and partially discrete time its mean square consistency and asymptotic complex normality as the number of data samples approaches infinity and the sampling period approaches zero are proved under mild conditions on the regularity of the fourier series coefficients and the finite or practically finite memory of the processes expressed in terms of summability of cumulants it is shown that the asymptotic properties of the hybrid cyclic cross correlogram are coincident with those of the continuous time cyclic cross correlogram hence discrete time estimation does not give rise to any loss in asymptotic performance with respect to continuous time estimation