a kernel adaptive algorithm for quaternion valued inputs the use of quaternion data can provide benefit in applications like robotics and image recognition and particularly for performing transforms in 3 d space here we describe a kernel adaptive algorithm for quaternions a least mean square lms based method was used resulting in the derivation of the quaternion kernel lms quat klms algorithm deriving this algorithm required describing the idea of a quaternion reproducing kernel hilbert space rkhs as well as kernel functions suitable with quaternions a modified hr calculus for hilbert spaces was used to find the gradient of cost functions defined on a quaternion rkhs in addition the use of widely linear or augmented filtering is proposed to improve performance the benefit of the quat klms and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations

an algebraic translation of cayley dickson linear systems and its applications to online learning the m dimensional cayley dickson number system am is a standard extension of real m 1 complex m 2 quaternion m 22 octonion m 23 and sedenion m 24 etc in this paper we present a systematic algebraic translation of the cayley dickson hypercomplex valued linear systems into a real vector valued linear model this translation is designed by using jointly two new isomorphisms between real vector spaces and enables us to straightforwardly apply the well established schemes in real domain to problems for the hypercomplex linear model we also clarify useful algebraic properties of the proposed translation as an example of many potential algorithms through the proposed algebraic translation we present am adaptive projected subgradient method am apsm for am valued adaptive system identification and show that many hypercomplex adaptive filtering algorithms can be viewed as special cases of this algorithm moreover we also apply the am apsm to nonlinear adaptive filtering by using the kernel trick numerical examples show that the effectiveness of the am apsm in many cayley dickson valued linear system identification and nonlinear channel equalization problems

optimization of quiescent response in partially adaptive beamformers the adaptive weights utilize only a fraction of the available degrees of freedom in partially adaptive lcmv linearly constrained minimum invariance beamformers two procedures are presented for incorporating unused degrees of freedom into the beamformer s quiescent response in one case the quiescent response is chosen to approximate a desired quiescent response and in the other case it is chosen to maximize the average interference cancellation over a set of likely interference scenarios a sidelobe canceling interpretation indicates that maximization of average interference cancellation results in quiescent weights that optimize the sum of the white noise gain and the error between the quiescent response and the class of responses which the adaptive branch can synthesize simulations illustrate the utility of the methods

design of asymptotically optimal improper constellations with hexagonal packing this paper addresses the problem of designing asymptotically optimal improper constellations with a given circularity coefficient correlation coefficient between the constellation and its complex conjugate the designed constellations are optimal in the sense that at high signal to noise ratio snr and for a large number of symbols yield the lowest probability of error under an average power constraint for additive white gaussian noise channels as the number of symbols grows the optimal constellation is the intersection of the hexagonal lattice with an ellipse whose eccentricity determines the circularity coefficient based on this asymptotic result we propose an algorithm to design finite improper constellations the proposed constellations provide significant snr gains with respect to previous improper designs which were generated through a widely linear transformation of a standard m ary quadrature amplitude modulation constellation as an application example we study the use of these improper constellations by a secondary user in an underlay cognitive radio network

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

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

numerical normal forms for codim 2 bifurcations of fixed points with at most two critical eigenvalues in this paper we derive explicit formulas for the normal form coefficients to verify the nondegeneracy of eight codimension two bifurcations of fixed points with one or two critical eigenvalues these include all strong resonances as well as the degenerate flip and neimark sacker bifurcations applying our results to n dimensional maps one avoids the computation of the center manifold but one can directly evaluate the critical normal form coefficients in the original basis the formulas remain valid also for n 2 and allow one to avoid the transformation of the linear part of the map into jordan form the developed techniques are tested on two examples 1 a three dimensional map appearing in adaptive control 2 a periodically forced epidemic model we compute numerically the critical normal form coefficients for several codim 2 bifurcations occurring in these models to compute the required derivatives of the poincare map for the epidemic model the automatic differentiation package adol c is used

on maximum linearly achievable degrees of freedom region of 2 times 2 times 2 interference network with arbitrary antenna configurations we obtain the exact maximum degrees of freedom dof region achieved by linear transceivers without symbol extensions of the 2 times 2 times 2 multiple input multiple output mimo interference network which is comprised of two sources two relays and two destinations each with arbitrary number of antennas we prove that the maximum achievable dof region for the networks under some antenna configurations coincide with the cut set bound of the networks while there is only one dof gap from the bound for the networks under other configurations which can not be bridged by linear transceivers the basic idea of the proof is to construct a two tier transceiver where the first tier decomposes the general networks to several basic networks with special configurations and the second tier achieves the maximal dof tuples for these basic networks a mechanism for constructing the second tier transceiver is proposed which is referred to as channel scaling assisted interference elimination combined with interference avoidance at sources and interference cancelation at destinations depending on the antenna configurations interference free transmission can be ensured

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

orthogonal weight perturbation algorithms in partially adaptive arrays single port adaptive algorithms have been proposed to circumvent the need to implement a separate receiver for each adaptive element in an adpative antenna in this paper transient and steady state performance of a bounded single port perturbation algorithm is obtained and compared with that of the least mean square lms algorithm results are developed both with and without a hardlimiter on one input to the correlator techniques for adaptively changing both the algorithm step size and perturbation amplitude are given simulation results are presented and compared with theoretical results

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

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

block skew circulant matrices in complex valued signal processing two main lines of approach can be identified in the recent literature on improper signals and widely linear operations the augmented complex formulation based on the signal and its complex conjugate is considered as more insightful since it leads to convenient mathematical formulations for many considered problems moreover it allows an easy distinction between proper and improper signals as well as between linear and widely linear operations on the other hand the composite real representation using the real and imaginary parts of the signal is closer to the actual implementation and it allows to readily reuse results that have originally been derived for real valued signals or proper complex signals in this work we aim at getting the best of both worlds by introducing mathematical tools that make the composite real representation more powerful and elegant the proposed approach relies on a decomposition of real matrices into a block skew circulant and a block hankel skew circulant component by means of various application examples from the field of signal processing for communications we demonstrate the usefulness of the proposed framework

numerical periodic normalization for codim 1 bifurcations of limit cycles explicit computational formulas for the coefficients of the periodic normal forms for all codim 1 bifurcations of limit cycles in generic autonomous odes are derived they include second order coefficients for the fold limit point bifurcation as well as third order coefficients for the flip period doubling and neimark sacker torus bifurcations the formulas are independent of the dimension of the phase space and involve solutions of certain boundary value problems on the interval 0 t where t is the period of the critical cycle as well as multilinear functions from the taylor expansion of the right hand sides near the cycle the formulas allow us to distinguish between sub and supercritical bifurcations in agreement with earlier asymptotic expansions of the bifurcating solutions our formulation makes it possible to use robust numerical boundary value algorithms based on orthogonal collocation rather than shooting techniques which greatly expands its applicability the actual implementation is described in detail we include three numerical examples in which codim 2 singularities are detected along branches of codim 1 bifurcations of limit cycles as zeros of the periodic normal form coefficients

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

systolic preprocessors for linearly constrained beamforming systolic preprocessors for linearly constrained beamforming are developed using factorizations of the generalized sidelobe canceller these preprocessors transform linearly constrained beamformers into unconstrained form which permits unconstrained adaptive processors to be used for computing the beamformer output two preprocessors are developed for small numbers of constraints relative to the data dimension and two for partially adaptive beamforming where the number of effective constraints is often large relative to the data dimension all four preprocessors are applicable to arbitrary constraint sets tradeoffs between the various preprocessors are discussed

improper complex valued multiple model adaptive estimation motivated by the problem of estimating the discrete and continuous states of an improper complex valued stochastic hybrid system the paper proposes a class of widely linear augmented multiple model adaptive estimation algorithms referred to as the c mmae we show that for an improper complex valued signal pseudo covariance of the innovation sequence is not zero and therefore carries useful statistical information regarding the unknown behaviour mode of the hybrid system a new bayesian law is therefore derived as a function of the pseudo covariance of the innovation sequence and used to compute the probability that a hypothesized model is in effect at a certain time we show that the c mmae which uses the new bayesian law and utilizes the complete second order statistical characterization of the complex valued innovation sequence convergences faster than its counterpart which only uses the conventional covariance of the innovation sequence in order to simplify the computational complexity we develop two circularized versions of the c mmae using a preprocessing step referred to as the circularizing filter cf the cf is incorporated to convert the improper observations innovations into the proper ones in order to reduce the computational complexity of the hypothesis testing step finally an interacting version of the c mmae referred to as c imm is developed for improper complex valued systems with markovian switching coefficients simulation results indicate that the proposed hybrid estimators provide improved performance and convergence properties over their traditional counterparts

improper signaling for symbol error rate minimization in k user interference channel the rate maximization for the k user interference channels ics has been investigated extensively in the literature however the practical problem of minimizing the error probability with given signal modulations and or data rates of the users is less studied in this paper by utilizing additional degrees of freedom from the improper signaling versus the conventional proper signaling we seek to optimize the precoding matrices for the k user single input single output siso ics to minimize pair wise error probability pep and symbol error rate ser with two proposed algorithms respectively compared with conventional proper signaling and other state of the art improper signaling designs our proposed improper signaling schemes achieve notable error rate improvement in siso ics under both the additive white gaussian noise awgn and cellular system setups with or without channel coding our study provides another viewpoint for optimizing transmissions in ics and further justifies the practical benefit of improper signaling in interference limited communication systems

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

class of widely linear complex kalman filters recently a class of widely linear augmented complex valued kalman filters kfs that make use of augmented complex statistics have been proposed for sequential state space estimation of the generality of complex signals this was achieved in the context of neural network training and has allowed for a unified treatment of both second order circular and noncircular signals that is both those with rotation invariant and rotation dependent distributions in this paper we revisit the augmented complex kf augmented complex extended kf and augmented complex unscented kf in a more general context and analyze their performances for different degrees of noncircularity of input and the state and measurement noises for rigor a theoretical bound for the performance advantage of widely linear kfs over their strictly linear counterparts is provided the analysis also addresses the duality with bivariate real valued kfs together with several issues of implementation simulations using both synthetic and real world proper and improper signals support the analysis

receivers with widely linear processing for frequency selective channels we propose several equalization schemes based on widely linear processing wlp the received signal and its complex conjugate are separately filtered and the results are linearly combined it is shown that wlp yields a gain in performance if the noiseless received signal can be interpreted as the convolution of a real valued data sequence and an equivalent complex valued intersymbol interference channel impulse response such a model applies to e g amplitude shift keying offset quadrature amplitude modulation and binary minimum shift keying type modulation we consider receivers without and with decision feedback finite impulse response filters are derived for these structures which are optimum with respect to the zero forcing and minimum mean squared error mmse criteria respectively in the mmse case adaptive algorithms for filter adjustment are given infinite filter orders are investigated in order to obtain analytical performance results furthermore suboptimum trellis based detection with widely linear preprocessing is briefly discussed it is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly depending on the considered application

efficient optimization of the merit factor of long binary sequences autocorrelation sidelobes are a form of self noise that reduce the effectiveness of phase coding in radar and communication systems the merit factor is a well known measure related to the autocorrelation sidelobe energy of a sequence in this paper an equation is derived that allows the change in the merit factor of a binary sequence to be computed for all single element changes with o nlogn operations where n is the sequence length the approach is then extended to multiple element changes allowing the merit factor change to be calculated with an additional o ns3 operations where nsis the number of changed elements irrespective of sequence length the multiple element calculations can be used to update the single element calculations so that in iterative use only o n operations are required per element change to keep the single element calculations current a steep descent algorithm a variation on the steepest descent method employing these two techniques was developed and applied to quarter rotated periodically extended legendre sequences producing optimized sequences with an apparent asymptotic merit factor of approximately 6 3758 modestly higher than the best known prior result of approximately 6 3421 modified jacobi sequences improve after steep descent to an approximate asymptotic merit factor of 6 4382 three prime and four prime jacobi sequences converge very slowly making a determination difficult but appear to have a higher post steep descent asymptotic merit factor than legendre or modified jacobi sequences

switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in odes the paper provides full algorithmic details on switching to the continuation of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium bifurcation points in n dimensional odes we discuss the implementation and the performance of the algorithm in several examples including an extended lorenz 84 model and a laser system

widely linear versus conventional subspace based estimation of simo flat fading channels mean squared error analysis we analyze the mean squared error mse performance of widely linear wl and conventional subspace based channel estimation for single input multiple output simo flat fading channels employing binary phase shift keying bpsk modulation when the covariance matrix is estimated using a finite number of samples the conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the wl estimator we derive accurate closed form expressions for the mse of the two estimators under four ambiguity resolution scenarios in the first three scenarios the receiver resolves the ambiguity using some clairvoyant knowledge about the channel the first scenario used as a reference is the ideal case of optimal resolution the second scenario assumes that one of the channel coefficients is known and the third assumes knowledge of the coefficient with the largest magnitude the fourth scenario considers the more realistic case where pilot symbols are employed for ambiguity resolution our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of wl and conventional subspace based estimators showing that the wl estimator performs better when partial or inaccurate channel information is employed for ambiguity resolution

analysis and design of ofdm oqam systems based on filterbank theory a discrete time analysis of the orthogonal frequency division multiplex offset qam ofdm oqam multicarrier modulation technique leading to a modulated transmultiplexer is presented the conditions of discrete orthogonality are established with respect to the polyphase components of the ofdm oqam prototype filter which is assumed to be symmetrical and with arbitrary length fast implementation schemes of the ofdm oqam modulator and demodulator are provided which are based on the inverse fast fourier transform non orthogonal prototypes create intersymbol and interchannel interferences isi and ici that in the case of a distortion free transmission are expressed by a closed form expression a large set of design examples is presented for ofdm oqam systems with the number of subcarriers going from four up to 2048 which also allows a comparison between different approaches to get well localized prototypes

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

complex support vector machines for regression and quaternary classification the paper presents a new framework for complex support vector regression svr as well as support vector machines svm for quaternary classification the method exploits the notion of widely linear estimation to model the input out relation for complex valued data and considers two cases 1 the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and 2 a pure complex kernel is used to directly map the data to the induced complex feature space the recently developed wirtinger s calculus on complex reproducing kernel hilbert spaces is employed to compute the lagrangian and derive the dual optimization problem as one of our major results we prove that any complex svm svr task is equivalent with solving two real svm svr tasks exploiting a specific real kernel which is generated by the chosen complex kernel in particular the case of pure complex kernels leads to the generation of new kernels which have not been considered before in the classification case the proposed framework inherently splits the complex space into four parts this leads naturally to solving the four class task quaternary classification instead of the typical two classes of the real svm in turn this rationale can be used in a multiclass problem as a split class scenario based on four classes as opposed to the one versus all method this can lead to significant computational savings experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

computation of the phase response curve a direct numerical approach neurons are often modeled by dynamical systems parameterized systems of differential equations a typical behavioral pattern of neurons is periodic spiking this corresponds to the presence of stable limit cycles in the dynamical systems model the phase resetting and phase response curves prcs describe the reaction of the spiking neuron to an input pulse at each point of the cycle we develop a new method for computing these curves as a by product of the solution of the boundary value problem for the stable limit cycle the method is mathematically equivalent to the adjoint method but our implementation is computationally much faster and more robust than any existing method in fact it can compute prcs even where the limit cycle can hardly be found by time integration for example because it is close to another stable limit cycle in addition we obtain the discretized phase response curve in a form that is ideally suited for most applications we present several examples and provide the implementation in a freely available matlab code

models of complex dynamics in nonlinear systems abstract a study of complex dynamics in a simple important class of nonlinear systems has been developed the well known phenomena of period doubling and homoclinic orbit have been analysed and simple conditions approximate in nature for their occurrence are derived they allow one to establish some connections of such complex behaviours with structural characteristics of the considered systems as shown by two detailed application examples

analysis of bifurcations of limit cycles with lyapunov exponents and numerical normal forms in this paper we focus on the combination of normal form and lyapunov exponent computations in the numerical study of the three codim 2 bifurcations of limit cycles with dimension of the center manifold equal to 4 or to 5 in generic autonomous odes the normal form formulas are independent of the dimension of the phase space and involve solutions of certain linear boundary value problems the formulas allow one to distinguish between the complicated bifurcation scenarios which can happen near these codim 2 bifurcations where 3 tori and 4 tori can be present we apply our techniques to the study of a known laser model a novel model from population biology and a model of mechanical vibrations these models exhibit limit point neimark sacker period doubling neimark sacker and double neimark sacker bifurcations lyapunov exponents are computed to numerically confirm the results of the normal form analysis in particular with respect to the existence of stable invariant tori of various dimensions conversely the normal forms are essential to understand the significance of the lyapunov exponents

harmonic balance analysis of period doubling bifurcations with implications for control of nonlinear dynamics the harmonic balance method is applied to the analysis of period doubling bifurcations in a general class of nonlinear feedback systems compact conditions for the prediction and stability analysis of period doubling bifurcations are obtained specializations of these conditions for systems in which the nonlinear subsystem is static are given the implications of the results to control design are illustrated through the development of a design procedure for solving a representative control problem the objectives of the control design can include delay of a given period doubling bifurcation as well as stability objectives the results are illustrated with a detailed example

signed frames and hadamard products of gram matrices abstract this paper concerns redundant representations in a hilbert space h of the form f j c j f j j f h these are more general than those obtained from a tight frame and we develop a general theory based on what are called signed frames we are particularly interested in the cases where the scaling factors cj are unique and the geometric interpretation of negative cj this is related to results about the invertibility of certain hadamard products of gram matrices which are of independent interest e g we show for almost every v 1 v n c d rank v i v j r v i v j s min r d 1 d 1 s d 1 d 1 n r s 0 applications include the construction of tight frames of bivariate jacobi polynomials on a triangle which preserve symmetries and numerical results and conjectures about the class of tight signed frames in a finite dimensional space

asymptotically locally optimal weight vector design for a tighter correlation lower bound of quasi complementary sequence sets a quasi complementary sequence set qcss refers to a set of two dimensional matrices with low nontrivial aperiodic auto and cross correlation sums for multicarrier code division multiple access applications the availability of large qcsss with low correlation sums is desirable the generalized levenshtein bound glb is a lower bound on the maximum aperiodic correlation sum of qcsss the bounding expression of glb is a fractional quadratic function of a weight vector mathbf w and is expressed in terms of three additional parameters associated with qcss the set size k the number of channels m and the sequence length n it is known that a tighter glb compared to the welch bound is possible only if the condition m geq 2 and k geq overline k 1 where overline k is a certain function of m and n is satisfied a challenging research problem is to determine if there exists a weight vector that gives rise to a tighter glb for all not just some k geq overline k 1 and m geq 2 especially for large n i e the condition is asymptotically both necessary and sufficient to achieve this we analytically optimize the glb which is in general nonconvex as the numerator term is an indefinite quadratic function of the weight vector our key idea is to apply the frequency domain decomposition of the circulant matrix in the numerator term to convert the nonconvex problem into a convex one following this optimization approach we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the glb under certain conditions

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

optimal codebooks from binary codes meeting the levenshtein bound in this paper a generic construction of codebooks based on binary codes is introduced with this generic construction a few previous constructions of optimal codebooks are extended and a new class of codebooks almost meeting the levenshtein bound is presented exponentially many codebooks meeting or almost meeting the levenshtein bound from binary codes are obtained in this paper the codebooks constructed in this paper have alphabet size 4 as a byproduct three bounds on the parameters of binary codes are derived

a subband selective broadband gsc with cosine modulated blocking matrix a novel subband selective generalized sidelobe canceller gsc for partially adaptive broadband beamforming is proposed the columns of the blocking matrix are derived from a prototype vector by cosine modulation and the broadside constraint is incorporated by imposing zeros on the prototype vector appropriately these columns constitute a series of bandpass filters which select signals with specific directions of arrival and frequencies this results in a high pass type bandlimited spectra of the blocking matrix outputs which is further exploited by subband decomposition and suitably discarding the low pass subbands prior to running independent unconstrained adaptive filters in each nonredundant subband by these steps the computational complexity of a gsc implementation is greatly reduced compared to fully adaptive gsc schemes while performance is comparable or even enhanced due to subband decorrelation in both spatial and temporal domains

transmit optimization with improper gaussian signaling for interference channels this paper studies the achievable rates of gaussian interference channels with additive white gaussian noise awgn when improper or circularly asymmetric complex gaussian signaling is applied for the gaussian multiple input multiple output interference channel mimo ic with the interference treated as gaussian noise we show that the user s achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex gaussian signaling in terms of the users transmit covariance matrices and an additional term which is a function of both the users transmit covariance and pseudo covariance matrices the additional degrees of freedom in the pseudo covariance matrix which is conventionally set to be zero for the case of proper gaussian signaling provide an opportunity to further improve the achievable rates of gaussian mimo ics by employing improper gaussian signaling to this end this paper proposes widely linear precoding which efficiently maps proper information bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo covariance matrices in particular for the case of two user gaussian single input single output interference channel siso ic we propose a joint covariance and pseudo covariance optimization algorithm with improper gaussian signaling to achieve the pareto optimal rates by utilizing the separable structure of the achievable rate expression an alternative algorithm with separate covariance and pseudo covariance optimization is also proposed which guarantees the rate improvement over conventional proper gaussian signaling

fir zero forcing multiuser detection and code designs for downlink mc cdma this paper focuses on multiuser detection for multicarrier code division multiple access mc cdma systems employing cyclic prefixed cp or zero padded zp transmission techniques for both systems we consider either the classical linear finite impulse response l fir receiving structures or when the transmitted symbols are improper the proposed widely linear fir wl fir ones which process both the received signal and its complex conjugate version with regard to both cp and zp based downlink configurations it is shown that if the number of users does not exceed a given threshold and their codes are appropriately designed l fir and wl fir universal zero forcing zf multiuser detectors can be synthesized which in the absence of noise guarantee perfect symbol recovery for each user regardless of the underlying frequency selective channel in particular some spreading code examples are provided which satisfy the design rules finally numerical simulations are carried out to show that the theoretical considerations developed herein provide useful guidelines for practical mc cdma system designs

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

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

a new lower bound on the maximum correlation of a set with mismatched filters a new lower bound is proposed in this article like levenshtein bound it relates to the maximum correlation value autocorrelation and cross correlation a set of sequences can achieve the novelty introduced here is that each sequence is associated with a mismatched filter the proposed bound is inspired from levenshtein s holds for any set of unimodular sequences and can be applied in both aperiodic and periodic cases it appears that the obtained expression does not deviate a lot from the matched levenshtein which indicates that the use of a mismatched filter will not guarantee much better sidelobe performance as the number fo sequences is significant contrary to the popular belief

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

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

design of partially adaptive arrays using the singular value decomposition the objective of partially adaptive array design is to reduce the number of adaptive weights without significantly degrading the performance of the adaptive array previous work includes numerical techniques for approximately minimizing the average generalized sidelobe canceller gsc output power for a desired number of adaptive weights where the average is over a range of jammer parameters our new power space method also attempts to minimize the average gsc output power but under a constraint that the reduced dimensional solutions for all of the scenario trials lie in the same subspace this constraint allows us to use the singular value decomposition to get the rank reducing transformation thereby simplifying the optimization problem using computer simulation we show that our transformation yields lower output power in comparison with a previously reported example that used the numerical methods the simplicity of the method allows large ranges of jammer parameters to be considered using our transformation we consider how closely the reduced rank solutions match the full rank solutions and how the quality of this match relates to the output power of the partially adaptive array

harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems abstract the paper considers the problem of determining the conditions under which a nonlinear dynamical system can give rise to a chaotic behaviour on the basis of the harmonic balance principle which is widely used in the frequency analysis of nonlinear control systems two practical methods are presented for predicting the existence and the location of chaotic motions this is formulated as a function of the system parameters when the system structure is fixed by rather general input output or state equation models several examples of application are presented to show the rather straightforward computations involved in the proposed methods the kind of results which can be obtained and due to the heuristic approach to the problem their corresponding approximation

shrinkage linear and widely linear complex valued least mean squares algorithms for adaptive beamforming in this paper shrinkage linear complex valued least mean squares sl clms and shrinkage widely linear complex valued least mean squares swl clms algorithms are devised for adaptive beamforming by exploiting the relationship between the noise free a posteriori and a priori error signals the sl clms method is able to provide a variable step size to update the weight vector for the adaptive beamformer significantly enhancing the convergence speed and decreasing the steady state misadjustment on the other hand besides adopting a variable step size determined by minimizing the square of the augmented noise free a posteriori errors the swl clms approach exploits the noncircular properties of the signal of interest which considerably improves the steady state performance simulation results are presented to illustrate their superiority over the clms complex valued normalized lms variable step size recursive least squares rls algorithms and their corresponding widely linear based schemes additionally our proposed algorithms are more computationally efficient than the rls solutions though they may have a slightly slower convergence rate

a separability theorem for 2m conjugate symmetric signals impinging on an m element sensor array we show under reasonable assumptions that an m sensor linear conjugate linear lcl processor can separate up to 2m conjugate symmetric signals including the cases in which up to m of the signals each share the same direction of arrival as each of m other signals numerical evaluations illustrate ways in which the performance of the m sensor lcl processor is superior to that of a conventional 2m sensor linear processor when 2m conjugate symmetric signals are received

complex valued filtering based on the minimization of complex error entropy in this paper we consider the training of complex valued filter based on the information theoretic method we first generalize the error entropy criterion to complex domain to present the complex error entropy criterion ceec due to the difficulty in estimating the entropy of complex valued error directly the entropy bound minimization ebm method is used to compute the upper bounds of the entropy of the complex valued error and the tightest bound selected by the ebm algorithm is used as the estimator of the complex error entropy then based on the minimization of complex error entropy mcee and the complex gradient descent approach complex valued learning algorithms for both the linear transverse filter and the nonlinear neural network are derived the algorithms are applied to complex valued linear filtering and complex valued nonlinear channel equalization to demonstrate their effectiveness and advantages

a simple proof of a known blind channel identifiability result an alternative simple proof for a well known result encountered in blind identification and equalization of communication channels is derived it is shown that the coprimeness condition of a number of fir channels is equivalent to the full column rank condition of a certain block sylvester matrix whose entries are the channel coefficients as a corollary it is also shown that in general the null space of a block sylvester matrix is spanned by the set of generalized vandermonde vectors associated with the common zeros present in all the channels

sparse lcmv beamformer design for suppression of ground clutter in airborne radar cancellation of the ground clutter received at an airborne phased array radar is an inherently two dimensional problem clutter returns are doppler shifted due to platform motion forcing the use of processors that can resolve targets in both velocity doppler and azimuth fully adaptive processors that operate in both dimensions require prohibitively large computation so that reduced adaptive dimension or partially adaptive processors must be considered in conventional partially adaptive linearly constrained minimum variance lcmv beamformer design the approach taken has been to represent the interference subspace with some reduced set of vectors typically the eigenvectors associated with the largest eigenvalues of the interference covariance matrix this technique does yield good performance but will not give the optimum performance for a given partially adaptive dimension in this paper an off line method for selecting the best degrees of freedom to be retained in a partially adaptive design is presented the sequential algorithm described selects those degrees of freedom that best minimize the beamformer output mean square error this approach leads to a sparse structure for the transformation matrix which when implemented in a generalized sidelobe canceller gsc structure results in a reduction in the computational load this approach also allows a reduction in the required adaptive dimension as compared to the eigenvector based approach illustrative examples demonstrate the effectiveness of this method

eigenstructure based partially adaptive array design a procedure is presented for designing partially adaptive arrays having nearly fully adaptive performance under steady state conditions theory predicts that the required adaptive dimension is less than or equal to the rank of the spatially temporally correlated portion of the interference correlation matrix for arbitrary linearly constrained minimum variance beamformers knowledge of the eigenstructure of the interference correlation matrix is required to implement a beamformer with this adaptive dimension to avoid adaptive estimation of the eigenstructure the eigenstructure of an averaged correlation matrix which spans the interference scenarios of interest is utilized and the adaptive dimension is given by the rank of the averaged correlation matrix construction of a transformation for reducing adaptive dimension is addressed simulations illustrating the utility of the eigenstructure approach are provided

numerical normalization techniques for all codim 2 bifurcations of equilibria in ode s explicit computational formulas for the coefficients of the normal forms for all codim 2 equilibrium bifurcations of equilibria in autonomous odes are derived they include second order coefficients for the bogdanov takens bifurcation third order coefficients for the cusp and fold hopf bifurcations and coefficients of the fifth order terms for the generalized hopf bautin and double hopf bifurcations the formulas are independent on the dimension of the phase space and involve only critical eigenvectors of the jacobian matrix of the right hand sides and its transpose as well as multilinear functions from the taylor expansion of the right hand sides at the critical equilibrium the normal form coefficients for the fold hopf bifurcation in the new lorenz model are computed using the derived formulas proving the existence of a nontrivial invariant set in the system

a unifying discussion of correlation analysis for complex random vectors the assessment of multivariate association between two complex random vectors is considered a number of correlation coefficients based on three popular correlation analysis techniques namely canonical correlation analysis multivariate linear regression and partial least squares are reviewed and connected to performance measures in signal processing and communications such as mean squared estimation error mutual information and signal to noise ratio snr for complex data there are three types of correlation coefficients which account for rotational reflectional and total i e rotational and reflectional dependencies between two random vectors these three types are defined and analyzed for different correlation coefficients and a numerical example is given it is often required to compare two complex random vectors in a lower dimensional subspace for the large class of increasing schur convex correlation coefficients it is shown that the low rank approximations of two random vectors maximizing a particular correlation coefficient are determined only by the constraints imposed on the correlation analysis technique in this context the correlation spread is defined as a normalized measure of how much of the overall correlation is contained in a low dimensional subspace

computing periodic orbits and their bifurcations with automatic differentiation this paper formulates several algorithms for the direct computation of periodic orbits as solutions of boundary value problems the algorithms emphasize the use of coarse meshes and high orders of accuracy convergence theorems are given in the limit of increasing order with a fixed mesh the algorithms are implemented with the use of matlab and adol c a software package for automatic differentiation automatic differentiation enables accurate computation of high order derivatives of functions without the truncation errors inherent in finite difference calculations we embed the algorithms in a continuation framework and extend them to compute saddle node bifurcations of periodic orbits directly we present data from numerical studies of four test problems making some comparisons with other methods for computing periodic orbits these results demonstrate that high order methods based upon automatic differentiation are capable of high precision with small meshes

a generic construction of complex codebooks meeting the welch bound codebooks also called signal sets meeting the welch bound on the maximum correlation amplitude are called mwbe codebooks and are desirable in code division multiple access systems two different but related constructions of mwbe codebooks from difference sets were developed by xia and ding recently the objectives of this correspondence are to present a generic construction of mwbe codebooks that contains the previous two constructions as special cases and describe new mwbe codebooks that cannot be produced by the earlier two constructions

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

interpolation of complex stationary processes the problem of minimum mean square infinite extent interpolation for discrete time stationary complex stochastic processes is studied the interpolator consists of linear combinations of samples of the process and of their complex conjugate the expressions of the interpolator and of the approximation error are derived and various consequences are examined it is shown in particular that the approximation error may be zero while the interpolation error obtained when using only linear combinations of the samples is maximum

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

computation of periodic solution bifurcations in odes using bordered systems we consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous odes namely the fold the period doubling or flip bifurcation and the torus or neimark sacker bifurcation in the fold and flip cases we append one scalar equation to the standard periodic bvp that defines the periodic solution in the torus case four scalar equations are appended evaluation of these scalar equations and their derivatives requires the solution of linear bvps whose sparsity structure after discretization is identical to that of the linearization of the periodic bvp therefore the calculations can be done using existing numerical linear algebra techniques such as those implemented in the software auto and colsys

using spectral estimation techniques in adaptive processing antenna systems improved spectral estimation techniques hold promise for becoming a valuable asset in adaptive processing array antenna systems their value lies in the considerable amount of additional useful information which they can provide about the interference environment utilizing a relatively small number of degrees of freedom dof the superresolution capabilities estimation of coherence and relative power level determination serve to complement and refine the data from faster conventional estimation techniques two conceptual application area examples for using such techniques are discussed partially adaptive low sidelobe arrays and fully adaptive tracking arrays for the partially adaptive area the information is utilized for efficient assignment of a limited number of dof in a beamspace constrained adaptive system in order to obtain a stable main beam retention of low sidelobes considerably faster response and reduction in overall cost these benefits are demonstrated via simulation examples computed for a 16 element linear array for the fully adaptive tracking array area the information is utilized in an all digital processing system concept to permit stable hulling of coherent interference sources in the main beam region efficient assignment control of the available dof and greater flexibility in time domain adaptive filtering strategy

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

generalization and improvement of the levenshtein lower bound for aperiodic correlation this paper deals with lower bounds on aperiodic correlation of sequences it intends to solve two open questions the first one is on the validity of the levenshtein bound for a set of sequences other than binary sequences or those over the roots of unity although this result could be a priori extended to polyphase sequences a formal demonstration is presented here proving that it does actually hold for these sequences the second open question is on the possibility to find a bound tighter than welch s in the case of a set consisting of two sequences m 2 by including the specific structure of correlation sequences a tighter lower bound is introduced for this case besides this method also provides in the cases m 3 and m 4 a tighter bound than the up to now tightest bound provided by liu et al

design of partially adaptive array beamformers based on information theoretic criteria in this paper two basic problems in designing partially adaptive array beamformers based on the structure of generalized sidelobe canceller gsc are considered the first problem is to decide the proper dimension of the required adaptive weight vector using the information of the array output power we develop the detection formulas for the information theoretic criteria aic and mdl to decide the proper dimension of the adaptive weight vector if the input noise power is unknown a priori efficient methods are proposed for estimating the input noise power in both cases with and without the desired signal to make the detection formulas still feasible the second problem is to find the most appropriate channel signals for weight adaptation for efficiently canceling interference an efficient method based on the maximum power reduction criterion is presented for selecting the most desired channel signals from the output of the signal blocking matrix theoretical analysis concerning the performance of the proposed methods is made computer simulations showing the effectiveness of the proposed methods are also provided

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

global characterization of the normal form for a vector field near a closed orbit on deduit une generalisation naturelle de la caracterisation globale de elphick pour des champs de vecteurs pres d une orbite fermee

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

a simple global characterization for normal forms of singular vector fields we derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems using an appropriate scalar product in the space of homogeneous vector polynomials we show that the resonant terms commute with the group generated by the adjoint of the original critical linear operator this leads to a very efficient constructive method to compute both the nonlinear coefficients and the unfolding of the normal form explicit examples and results obtained when there are additional symmetries are also presented

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

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

a neural mass model with direct and indirect excitatory feedback loops identification of bifurcations and temporal dynamics neural mass modeling is a part of computational neuroscience that was developed to study the general behavior of a neuronal population this type of mesoscopic model is able to generate output signals that are comparable to experimental data such as electroencephalograms classically neural mass models consider two interconnected populations excitatory pyramidal cells and inhibitory interneurons however many authors have included an excitatory feedback on the pyramidal cell population two distinct approaches have been developed a direct feedback on the main pyramidal cell population and an indirect feedback via a secondary pyramidal cell population in this letter we propose a new neural mass model that couples these two approaches we perform a detailed bifurcation analysis and present a glossary of dynamical behaviors and associated time series our study reveals that the model is able to generate particular realistic time series that were never pointed out in either simulated or experimental data finally we aim to evaluate the effect of balance between both excitatory feedbacks on the dynamical behavior of the model for this purpose we compute the codimension 2 bifurcation diagrams of the system to establish a map of the repartition of dynamical behaviors in a direct versus indirect feedback parameter space a perspective of this work is from a given temporal series to estimate the parameter value range especially in terms of direct versus indirect excitatory feedback

a new weight vector for a tighter levenshtein bound on aperiodic correlation the levenshtein bound on aperiodic correlation which is a function of the weight vector is tighter than the welch bound for sequence sets over the complex roots of unity when m 4 and n 2 where m denotes the set size and n the sequence length although it is known that the tightest levenshtein bound is equal to the welch bound for m 1 2 it is unknown whether the levenshtein bound can be tightened for m 3 and levenshtein in his paper published in 1999 postulated that the answer may be negative a new weight vector is proposed in this paper which leads to a tighter levenshtein bound for m 3 n 3 and m 4 n 2 in addition the explicit form of the weight vector which is derived by relating the quadratic minimization to the chebyshev polynomials of the second kind in levenshtein s paper is given interestingly this weight vector also yields a tighter levenshtein bound for m 3 n 3 and m 4 n m a fact not noticed by levenshtein