on totally real cubic fields the authors have constructed a table of the 26440 nonconjugate totally real cubic number fields of discriminant d 500000 thereby extending the existing table of fields with d 100000 by i 0 angell 1 serious defects in angell s table are pointed out for each field running number discriminant coefficients of a generating polynomial integral basis class number and a fundamental pair of units are listed the article contains statistics about the following subjects distribution of class numbers fields in which every norm positive unit is totally positive nonconjugate fields with the same discriminant fields with noncyclic class group the fields are tabulated by means of a method due to davenport and heilbronn 7 8 which leads to a unique normalized generating polynomial the given units are chosen so that the fundamental parallelogram of the unit lattice determined by the corresponding vectors in the logarithmic space is reduced

compressed sensing with basis mismatch performance bounds and sparse based estimator compressed sensing cs is a promising emerging domain that outperforms the classical limit of the shannon sampling theory if the measurement vector can be approximated as the linear combination of few basis vectors extracted from a redundant dictionary matrix unfortunately in realistic scenario the knowledge of this basis or equivalently of the entire dictionary is often uncertain i e corrupted by a basis mismatch bm error the consequence of the bm problem is that the estimation accuracy in terms of bayesian mean square error bmse of popular sparse based estimators collapses even if the support is perfectly estimated and in the high signal to noise ratio snr regime this saturation effect considerably limits the effective viability of these estimation schemes in the first part of this work the bayesian cramer rao bound bcrb is derived for cs model with unstructured bm we show that the bcrb foresees the saturation effect of the estimation accuracy of standard sparse based estimators as for instance the omp cosamp or the bp in addition we provide an approximation of this bmse threshold in the second part and in the context of the structured bm model a new estimation scheme called bias correction estimator bice is proposed and its statistical properties are studied the bice acts as a post processing estimation layer for any sparse based estimator and mitigates considerably the bm degradation finally the bice i is a blind algorithm i e is unaware of the uncorrupted dictionary matrix ii is generic since it can be associated to any sparse based estimator iii is fast i e the additional computational cost remains low and iv has good statistical properties to illustrate our results and propositions the bice is applied in the challenging context of the compressive sampling of non bandlimited impulsive signals

imprimitive ninth degree number fields with small discriminants we present tables of ninth degree nonprimitive i e containing a cubic subfield number fields each table corresponds to one signature except for fields with signature 3 3 for which we give two different tables depending on the signature of the cubic subfield details related to the computation of the tables are given as well as information about the cpu time used the number of polynomials that we deal with etc for each field in the tables we give its discriminant the discriminant of its cubic subfields the relative polynomial generating the field over one of its cubic subfields the corresponding irreducible polynomial over q and the galois group of the galois closure fields having interesting properties are studied in more detail especially those associated with sextic number fields having a class group divisible by 3

convergence of the sign algorithm for adaptive filtering with correlated data convergence of a decreasing gain sign algorithm sa for adaptive filtering is analyzed the presence of the hard limiter in the algorithm makes a rigorous analysis difficult therefore there are few results available such results normally include restrictive assumptions such as the assumptions that successive observation vectors are independent and the new error signal of the adaptive filter has a time invariant probability density function the former assumption is not valid in the context of adaptive filtering since two successive observation vectors share most of their components while the latter assumption is a restriction on the adaptive weights whose evolution is a priori unknown in lieu of using these assumptions an almost sure convergence of the sa is proved under the assumption that the sequence of observation vectors is m dependent this assumption allows strong correlation between successive observations

nonlinear non extensive approach for identification of structured information the problem of separating structured information representing phenomena of differing natures is considered a structure is assumed to be independent of the others if can be represented in a complementary subspace when the concomitant subspaces are well separated the problem is readily solvable by a linear technique otherwise the linear approach fails to correctly discriminate the required information hence a non extensive approach is proposed the resulting nonlinear technique is shown to be suitable for dealing with cases that cannot be tackled by the linear one

minimum ber block based precoder design for zero forcing equalization an oblique projection framework this work devises a minimum bit error rate ber block based precoder used in block transmission systems with the proposed cascaded zero forcing zf equalizer the study framework is developed as follows for a block based precoder a received signal model is formulated for the two redundancy schemes viz trailing zeros tz and cyclic prefix cp by exploiting the property of oblique projection a cascaded equalizer for block transmission systems is proposed and implemented with a scheme in which the inter block interference ibi is completely eliminated by the oblique projection and followed by a matrix degree of freedom for inter symbol interference isi equalization with the available channel state information at the transmitter side the matrix for isi equalization of the cascaded equalizer is utilized to design an optimum block based precoder such that the ber is minimized subject to the isi free and the transmission power constraints accordingly the cascaded equalizer with the isi free constraint yields a cascaded zf equalizer theoretical derivations and simulation results confirm that the proposed framework not only retains identical ber performance to previous works for cases with sufficient redundancy but also allows their results to be extended to the cases of insufficient redundancy

analysis of boundedness and convergence of online gradient method for two layer feedforward neural networks this paper presents a theoretical boundedness and convergence analysis of online gradient method for the training of two layer feedforward neural networks the well known linear difference equation is extended to apply to the general case of linear or nonlinear activation functions based on this extended difference equation we investigate the boundedness and convergence of the parameter sequence of concern which is trained by finite training samples with a constant learning rate we show that the uniform upper bound of the parameter sequence which is very important in the training procedure is the solution of an inequality regarding the bound it is further verified that for the case of linear activation function a solution always exists and moreover the parameter sequence can be uniformly upper bounded while for the case of nonlinear activation function some simple adjustment methods on the training set or the activation function can be derived to improve the boundedness property then for the convergence analysis it is shown that the parameter sequence can converge into a zone around an optimal solution at which the error function attains its global minimum where the size of the zone is associated with the learning rate particularly for the case of perfect modeling a strong global convergence result where the parameter sequence can always converge to an optimal solution is proved

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

a soft switching blind equalization scheme via convex combination of adaptive filters blind equalizers avoid the transmission of pilot sequences allowing a more efficient use of the channel bandwidth normally after a first rough equalization is achieved it is necessary to switch these equalizers to a decision directed dd mode to reduce the steady state mean square error mse to acceptable levels the selection of an appropriate mse threshold for switching between the blind and the dd modes is critical to obtain a good overall performance however this is not an easy task since it depends on several factors such as the signal constellation the communication channel or the signal to noise ratio in this paper we propose an equalization scheme that adaptively combines a blind and a dd equalizers running in parallel the combination is itself adapted in a blind manner and as a result the overall scheme can automatically switch between the component filters avoiding the need to set the transition mse level a priori the performance of our proposal is illustrated both analytically and through an extensive set of simulations where we show its advantages with respect to existing hard and soft switching equalization schemes

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

positivity preserving transformations for q binomial coefficients several new transformations for q binomial coefficients are found which have the special feature that the kernel is a polynomial with nonnegative coefficients by studying the group like properties of these positivity preserving transformations as well as their connection with the bailey lemma many new summation and transformation formulas for basic hypergeometric series are found the new q binomial transformations are also applied to obtain multisum rogers ramanujan identities to find new representations for the rogers szego polynomials and to make some progress on bressoud s generalized borwein conjecture for the original borwein conjecture we formulate a refinement based on new triple sum representations of the borwein polynomials

analysis of mean square error and transient speed of the lms adaptive algorithm for the least mean square lms algorithm we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state we establish the convergence of the second order statistics as the number of iterations increases and we derive the exact asymptotic expressions for the mean square errors in particular the result for the excess signal estimation error gives conditions under which the lms algorithm outperforms the wiener filter with the same number of taps we also analyze a new measure of transient speed we do not assume a linear regression model the desired signal and the data process are allowed to be nonlinearly related the data is assumed to be an instantaneous transformation of a stationary markov process satisfying certain ergodic conditions

quiver diagrams and signed adaptive filters a graphical technique for exploring the behavior of deterministic discrete time adaptive algorithms excited by periodic inputs is examined the constraint to periodic inputs is convenient the underlying concepts used also apply to stationary inputs drawn from finite alphabets the resulting graph is based on plotting single period parameter trajectories in the parameter error space and is essentially a discrete version of flow diagrams associated with continuous time systems for the least mean square lms adaptive fir filter with the algorithm step size sufficiently small the change of adapted parameters from a particular initial value is given by the total update over the input period with the parameterization frozen at its initial value this results in the familiar elliptical hyperparaboloid surface steepest descent interpretation this method can be extended to the lms adaptive infinite input response iir filter with suitable approximations based on a small step size

on convergence analysis of fractionally spaced adaptive blind equalizers in this paper we study the convergence analysis of fractionally spaced adaptive blind equalizers we show that based on the trivial and nontrivial nullspaces of a channel convolution matrix all equilibria can be classified as channel dependent equilibria cde or algorithm dependent equilibria ade because oversampling provides channel diversity the nullspace of the channel convolution matrix is affected we show that fractionally spaced equalizers fses do not possess any cde if a length zero condition is satisfied the convergence behavior of these fse are clearly determined by the specific choice of cost function alone we characterize the global convergence ability of several popular algorithms simply based on their ade we also present an fse implementation of the super exponential algorithm we show that the fse implementation does not introduce any nonideal approximation simulation results are also presented to illustrate the robustness and the improved performance of fse under the super exponential algorithm

stochastic approximation with correlated data new almost sure convergence results for a special form of the multidimensional robbins monro stochastic approximation procedure are developed the results are applicable to cases where the training data is heavily correlated no conditional expectation properties or boundedness assumptions are required to apply the new results for example when the data sequence is normal and i m dependent ii autoregressive moving average or iii band limited the results can be used to establish the almost sure convergence of each algorithm treated the special form of the robbins monro procedure considered is motivated by a consideration of several algorithms that have been proposed for discrete time adaptive signal processing applications most of these algorithms can also be viewed as stochastic gradient following algorithm the ease with which the new results can be applied is illustrated

a table of fundamental pairs of units in totally real cubic fields we apply a method of cusick 5 to tabulate data on the first 250 totally real cubic fields f having discriminant d 6 885 apart from d we list the class number h and the regulator r of f also given are the integer coefficients a b c of a defining polynomial g x x3 ax2 bx c its index i and its largest zero r0 for j 1 2 we also tabulate both the integercoefficients x y z for the two units e x r r2 zj i with norm 1 forming a fundamental pair as well as the e and the integers f trace py2

joint channel and symbol estimation by oblique projections the problem of simultaneous blind channel and symbol estimation of a single input multiple output simo communication channel is considered it is shown that the outer product of the channel vector and the channel input sequence can be obtained by a linear estimator that has the finite sample convergence property furthermore this estimator can be obtained by the use of oblique projections an order detection algorithm that avoids the use of subjective thresholding is also proposed applications to multiuser detection are also considered

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

error energy bounds for adaptive gradient algorithms the paper establishes robustness optimality and convergence properties of the widely used class of instantaneous gradient adaptive algorithms the analysis is carried out in a purely deterministic framework and assumes no a priori statistical information it employs the cauchy schwarz inequality for vectors in an euclidean space and derives local and global error energy bounds that are shown to highlight as well as explain relevant aspects of the robust performance of adaptive gradient filters along the lines of h sup spl infin theory

performance analysis of the minimum variance beamformer in the presence of steering vector errors we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer in the presence of steering vector errors the analysis yields an explicit expression for the sinr in terms of the variance of the steering vector errors and the other parameters affecting performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between desired signal and interference array size and shape correlation between desired signal and interference and finite sample size

the impact of temporal regularization on estimates of the bold hemodynamic response function a comparative analysis in fmri data analysis it has been shown that for a wide range of situations the hemodynamic response function hrf can be reasonably characterized as the impulse response function of a linear and time invariant system an accurate and robust extraction of the hrf is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions when no assumptions are made about the hrf shape it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either fourier or delta basis functions recently regularization methods have been employed to increase the estimation efficiency of the hrf typically these methods produce more accurate hrf estimates than the least squares approach goutte c nielsen f a hansen l k 2000 modeling the haemodynamic response in fmri using smooth fir filters ieee trans med imag 19 12 1188 1201 here we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the hrf such as time to peak ttp height hr and width w of the response we implemented a bayesian approach proposed by marrelec et al marrelec g benali h ciuciu p pelegrini issac m poline j b 2003 robust estimation of the hemodynamic response function in event related bold fmri using basic physiological information hum brain mapp 19 1 17 marrelec g benali h ciuciu p poline j b bayesian estimation of the hemodynamic of the hemodynamic response function in functional mri in r f editor 2001 melville p 229 247 and its deterministic counterpart based on a combination of tikhonov regularization tikhonov a n arsenin v y 1977 solution of ill posed problems washington dc w h winston and generalized cross validation gcv wahba g 1990 spline models for observational data philadelphia siam for selecting the regularization parameter the performance of both methods is compared with least square estimates as a function of temporal resolution color and strength of the noise and the type of stimulus sequences used in almost all situations under the considered assumptions e g linearity time invariance and smooth hrf the regularization based techniques more accurately characterize the hrf compared to the least squares method our results clarify the effects of temporal resolution noise color and experimental design on the accuracy of hrf estimation

on element by element schur complement approximations abstract we discuss a methodology to construct sparse approximations of schur complements of two by two block matrices arising in finite element discretizations of partial differential equations earlier results from 2 are extended to more general symmetric positive definite matrices of two by two block form the applicability of the method for general symmetric and nonsymmetric matrices is analysed the paper demonstrates the applicability of the presented method providing extensive numerical experiments

on identities of the rogers ramanujan type abstract an elementary approach to a number of identities of the rogers ramanujan type is given it is shown that analytic formulas like e g the rogers ramanujan the rogers selberg and the gollnitz gordon identities can be obtained essentially as consequences of the q binomial theorem and the q vandermonde formula

a new subspace identification algorithm for high resolution doa estimation in this paper we propose a new direction of arrival doa estimator for sensor array processing the estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal plus interference model which we develop in this paper the estimator we propose is a signal subspace scaled music algorithm which we call ssmusic it is not a subspace weighted music because the scaling depends on the eigenstructure of the estimated signal subspace ssmusic has the advantage of simultaneously estimating the doa and the power of each source we employ a second order perturbation analysis of the estimator and derive stochastic representations for its bias and squared error we compare the new doa estimator with the music estimator based on these representations numerical results demonstrate the superior performance of ssmusic relative to music and the validity of the perturbation results

detection power estimation efficiency and predictability in event related fmri experimental designs for event related functional magnetic resonance imaging can be characterized by both their detection power a measure of the ability to detect an activation and their estimation efficiency a measure of the ability to estimate the shape of the hemodynamic response randomized designs offer maximum estimation efficiency but poor detection power while block designs offer good detection power at the cost of minimum estimation efficiency periodic single trial designs are poor by both criteria we present here a theoretical model of the relation between estimation efficiency and detection power and show that the observed trade off between efficiency and power is fundamental using the model we explore the properties of semirandom designs that offer intermediate trade offs between efficiency and power these designs can simultaneously achieve the estimation efficiency of randomized designs and the detection power of block designs at the cost of increasing the length of an experiment by less than a factor of 2 experimental designs can also be characterized by their predictability a measure of the ability to circumvent confounds such as habituation and anticipation we examine the relation between detection power estimation efficiency and predictability and show that small increases in predictability can offer significant gains in detection power with only a minor decrease in estimation efficiency

oblique projections for direction of arrival estimation with prior knowledge estimation of directions of arrival doa is an important problem in various applications and a priori knowledge on the source location is sometimes available to exploit this information standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known doa in this paper we derive and analyze the cramer rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown doa are closely spaced and the associated sources are uncorrelated block diagonal source covariance to fill this need we propose to integrate a priori known locations of several sources into the music algorithm based on oblique projection of the steering manifold finally we show that the proposed approach is able to almost completely cancel the influence of the known doa on the unknown ones for block diagonal source covariance and for sufficient signal to noise ratio snr

efficient application of music algorithm under the coexistence of far field and near field sources this correspondence is concerned with source localization and classification for scenarios where both the far field and near field narrowband sources may coexist we propose an efficient music based solution that requires neither a multidimensional search nor high order statistics hos we also derive the stochastic cramer rao bound crb for the problem under consideration the performance of the proposed method is compared with an existing method and with the crb

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

blind equalization based on joint minimum mse criterion a joint minimum mean square error mse criterion is presented for blind adaptive channel equalization of qam signals by jointly estimating the transmitted sequence and the equalizer parameters through the minimization of mse the equalizer parameters can be optimized and the channel input sequence can be restored at the equalizer output to improve computational efficiency a reduced constellation recursive least squares rls algorithm is introduced for blind equalisation simulation results show the success of both the least square and the reduced constellation rls algorithms

orthogonal exactly periodic subspace decomposition the detection and estimation of machine vibration multiperiodic signals of unknown periods in white gaussian noise is investigated new estimates for the subsignals signals making up the received signal and their periods are derived using an orthogonal subspace decomposition approach the concept of exactly periodic signals is introduced this in turn simplifies and enhances the understanding of periodic signals

bi orthonormal polynomial basis function framework with applications in system identification numerical aspects are of central importance in identification and control many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections the aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems the proposed method is built on the introduction of bi orthonormal polynomials with respect to a data dependent bi linear form this bi linear form generalises the conventional inner product and allows for asymmetric and indefinite problems the proposed approach is shown to lead to optimal numerical conditioning kappa 1 in a recent frequency domain instrumental variable system identification algorithm in comparison it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches

robust blind learning algorithm for nonlinear equalization using input decision information in this paper we propose a new blind learning algorithm namely the benveniste goursat input output decision bg iod to enhance the convergence performance of neural network based equalizers for nonlinear channel equalization in contrast to conventional blind learning algorithms where only the output of the equalizer is employed for updating system parameters the bg iod exploits a new type of extra information the input decision information obtained from the input of the equalizer to mitigate the influence of the nonlinear equalizer structure on parameters learning thereby leading to improved convergence performance we prove that with the input decision information a desirable convergence capability that the output symbol error rate ser is always less than the input ser if the input ser is below a threshold can be achieved then the bg soft switching technique is employed to combine the merits of both input and output decision information where the former is used to guarantee ser convergence and the latter is to improve ser performance simulation results show that the proposed algorithm outperforms conventional blind learning algorithms such as stochastic quadratic distance and dual mode constant modulus algorithm in terms of both convergence performance and ser performance for nonlinear equalization

convergence and performance analysis of godard family and multimodulus algorithms for blind equalization we obtain the convergence of the godard family including the sato and constant modulus cm algorithms and the multimodulus algorithms mma in a unified way our analysis also works for cma fractionally spaced equalizer fse our assumptions are quite realistic the channel input can be asymptotically stationary and ergodic the channel impulse response is finite and can be stationary and ergodic this models fading channels and the equalizer length is finite the noise is independent and identically distributed i i d the channel input can be discrete or continuous our approach allows us to approximate the whole trajectory of the equalizer coefficients this provides estimates of the rate of convergence and the system performance symbol error rate can be evaluated under transience and steady state

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

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

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

an a _2 bailey lemma and rogers ramanujan type identities author s andrews george e schilling anne warnaar s ole abstract using new q functions recently introduced by hatayama et al and by two of the authors we obtain an a 2 version of the classical bailey lemma we apply our result which is distinct from the a 2 bailey lemma of milne and lilly to derive rogers ramanujan type identities for characters of the w 3 algebra

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

convergence of an adaptive linear estimation algorithm in this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations two complementary contributions are added to the famous 1977 ljung theorem first we drop the condition of nondivergence of the algorithm assumed by ljung while that condition can be ensured by adding a barrier the convergence of the suitably bounded algorithm itself is not established even on the basis of ljung theorem here the barrier problem is overcome by proving that it is not necessary for the convergence our second contribution is to generalize the model describing the correlated observations no state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed instead we use a decreasing covariance model that agrees with a very wide class of practical applications

on totally real cubic fields with discriminant 10 the authors have constructed a table of the 592923 nonconjugate totally real cubic number fields of discriminant d 107 thereby extending the existing table of fields with d 5 x 105 constructed by ennola and turunen 4 each field is given by its discriminant and the coefficients of a generating polynomial the method used is an improved version of the method developed in 8 the article contains an exposition of the modified method statistics and examples the decomposition of the rational primes is studied and the relative frequency of each type of decomposition is compared with the corresponding density given by davenport and heilbronn 2

analysis and design of perfusion based event related fmri experiments perfusion based functional magnetic resonance imaging fmri using arterial spin labeling asl methods has the potential to provide better localization of the functional signal to the sites of neural activity compared to blood oxygenation level dependent bold contrast fmri at present experiments using asl have been limited to simple block and periodic single trial designs we present here an adaptation of the general linear model to perfusion based fmri that enables the design and analysis of more complicated designs such as random and semirandom event related designs formulas for the least squares estimate of the perfusion response and the f statistic for the detection of a response are derived exact expressions and useful approximations for detection power and estimation efficiency are presented and it is shown that the trade off between power and efficiency for perfusion experiments is similar to that previously observed for bold experiments the least squares estimate is compared with an estimate formed from the running subtraction of tag and control images the running subtraction estimate is shown to be approximately equal to a temporally low pass filtered version of the least squares estimate numerical simulations and results from asl experiments are used to support the theoretical findings

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

constructive updating downdating of oblique projectors a generalization of the gram schmidt process a generalization of the gram schmidt procedure is achieved by providing equations for updating and downdating oblique projectors the work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting the proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

asymptotic properties of sign algorithms for adaptive filtering this paper develops asymptotic properties of a class of sign error algorithms with expanding truncation bounds for adaptive filtering under merely stationary ergodicity and finite second moments of the reference and output signals and using trajectory subsequence ts method it is proved that the algorithm convergers almost surely then a mean squares estimate is derived for the estimation error and a suitably scaled sequence of the estimation error is shown to converge to a diffusion process the scaling factor together with the stationary covariance gives the rate of convergence result moreover an algorithm under mean squares criterion with expanding truncation bounds is also examined compared with the existing results in the literature sufficient conditions for almost sure convergence are much relaxed a simple example is provided for demonstration purpose

convergence analysis of finite alphabet beamformers for digital cochannel signals in this paper we examine the convergence behavior of finite alphabet fa beamformers the two most popular implementations of fa beamformers for digital communication signals are the iterative least squares with projection ilsp and the minimum mean square error mmse beamformer to facilitate the analysis for the binary communications case we derive closed form expressions for the mean weight vector signal to noise ratio and signal to interference ratio for both the ilsp and mmse beamformers in terms of the bit error rate ber performance at each iteration next we generalize the analysis for the m ary pulse amplitude modulation and m ary phase shift keying cases we show that both ilsp and mmse beamformers have previously unreported bias terms in the array response vectors which are functions of the ber for each iteration furthermore as the ber becomes arbitrarily small we show that our solutions converge to the well known asymptotic expressions widely published in the literature next we provide a geometric interpretation of the effects of the noise bias vector in terms of angles between subspaces based on our analysis we were able to develop necessary and sufficient conditions for convergence in the mean we conclude with monte carlo simulations to validate our analysis

an oblique subspace projection approach for mixed pixel classification in hyperspectral images abstract recently oblique projection has been studied for many applications in signal processing in this paper the concept of oblique projection is applied to develop an algorithm for hyperspectral image classification compared with the orthogonal subspace projector osp it can be found that osp is a priori classifier but the oblique subspace projection classifier will be referred to a posterior as a consequence the oblique subspace projector obp can be thought of as a generalized classifier including osp furthermore the estimation error from the obp can be evaluated by applying the neyman pearson detection theory to the corresponding receiver operating characteristic roc curve so the accuracy of the classification can be calculated thereafter finally some computer simulations using real airborne visible infrared image spectrometer aviris data are accomplished to justify and compare the effectiveness of the above algorithms

length and cost dependent local minima of unconstrained blind channel equalizers baud rate linear blind equalizers may converge to undesirable stable equilibria due to different mechanisms one such mechanism is the use of linear fir filters as equalizers it is shown that this type of local minima exist for all unconstrained blind equalizers whose cost functions satisfy two general conditions the local minima generated by this mechanism are thus called length dependent local minima another mechanism is generated by the cost function adopted by the blind algorithm itself this type of local minima are called cost dependent local minima it is shown that several well designed algorithms do not have cost dependent local minimum whereas other algorithms such as the decision directed equalizer and the stop and go algorithm sga do unlike many existing convergence analysis the convergence of the godard 1980 algorithms gas and standard cumulant algorithms scas under gaussian noise is also presented computer simulations are used to verify the analytical results

iterate averaging sign algorithms for adaptive filtering with applications to blind multiuser detection motivated by the developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign error algorithms for adaptive filtering this work develops two stage sign algorithms for adaptive filtering the proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging our main effort is devoted to improving the performance of the algorithms by establishing asymptotic normality of a suitably scaled sequence of the estimation errors the asymptotic covariance is calculated and shown to be the smallest possible hence the asymptotic efficiency or asymptotic optimality is obtained then variants of the algorithm including sign regressor procedures and constant step algorithms are studied the minimal window width of averaging is also dealt with finally iterate averaging algorithms for blind multiuser detection in direct sequence code division multiple access ds cdma systems are proposed and developed and numerical examples are examined

blind equalization by direct examination of the input sequences this paper presents a novel approach to blind equalization deconvolution which is based on direct examination of possible input sequences in contrast to many other approaches it does not rely on a model of the approximative inverse of the channel dynamics to start with the blind equalization identifiability problem for a noise free finite impulse response channel model is investigated a necessary condition for the input which is algorithm independent for blind deconvolution is derived this condition is expressed in an information measure of the input sequence a sufficient condition for identifiability is also inferred which imposes a constraint on the true channel dynamics the analysis motivates a recursive algorithm where all permissible input sequences are examined the exact solution is guaranteed to be found as soon as it is possible an upper bound on the computational complexity of the algorithm is given this algorithm is then generalized to cope with time varying infinite impulse response channel models with additive noise the estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate the proposed method is evaluated on a rayleigh fading communication channel the simulation results indicate fast convergence properties and good tracking abilities

theoremes de convergence presque sure pour une classe d algorithmes stochastiques a pas decroissant the paper studies the pathwise asymptotic behaviour of stochastic algorithms of the following general form theta n 1 theta n gamma n 1 f theta n y n 1 the hypotheses allowing discontinuities on the adaptation termf the process y n n 0 is a markov chain controlled by n for each fixed the markov chain y n n 0 is essentially of positive recurrent type

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

prewhitening for rank deficient noise in subspace methods for noise reduction a fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank in order for the prewhitening step to be defined however there are important cases where this requirement is not fulfilled e g when the noise has narrowband characteristics or in the case of tonal noise we extend the concept of prewhitening to include the case when the noise covariance matrix is rank deficient using a weighted pseudoinverse and the quotient singular value decomposition and we show how to formulate a general rank reduction algorithm that works also for rank deficient noise we also demonstrate how to formulate this algorithm by means of a quotient ulv decomposition which allows for faster computation and updating finally we apply our algorithm to a problem involving a speech signal contaminated by narrowband noise

observations on oblique projectors and pseudoinverses oblique projectors which were examined by behrens and scharf see ibid vol 42 no 6 p 1413 24 1994 are related to earlier work on oblique pseudoinverses and constrained least squares methods and are reconsidered from the standpoint of orthogonal basis vectors and qr factorizations construction algorithms are presented that are numerically more stable than the normal equations constructions previously used

blind separation of synchronous co channel digital signals using an antenna array i algorithms we propose a maximum likelihood ml approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site the spatial response of the array is assumed to be known imprecisely or unknown we exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal uniqueness of the estimates is established for bpsk signals we introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner computationally efficient algorithms for both block and recursive estimation of the signals are presented this new approach is applicable to an unknown array geometry and propagation environment which is particularly useful in wireless communication systems simulation results demonstrate its promising performance

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

non unitary minimal models bailey s lemma and n 1 2 superconformal algebras using the bailey flow construction we derive character identities for the n 1 superconformal models sm p 2p p and sm p 3p 2p and the n 2 superconformal model with central charge c 3 open image in new window from the nonunitary minimal models m p p a new ramond sector character formula for representations of n 2 superconformal algebras with central element c 3 open image in new window is given

spatial spectrum estimation in a location sector multiple narrowband source localization using arbitrarily configured arrays and spatial spectrum estimation is considered a new eigenspace based approach which uses projections onto a particular vector or vector set in the estimated noise only subspace is described several closest vector estimators are developed by using different measures of closeness first closest is a novel full dimensional element space approach to spatial spectrum estimation which has important performance advantages relative to pertinent established spatial spectrum estimators it incorporates a priori knowledge of the array manifold over a location sector of interest to provide snr spectral resolution thresholds which are lower than those of min norm for some arrays substantially lower second relationships between the closest approach and several established approaches to spatial spectrum estimation are established for a linear equispaced array min norm is shown to be a special case of the closest approach one which is based on projection onto a noise only subspace vector which is close to the array manifold over the entire field of view

time frequency formulation design and implementation of time varying optimal filters for signal estimation this paper presents a time frequency framework for optimal linear filters signal estimators in nonstationary environments we develop time frequency formulations for the optimal linear filter time varying wiener filter and the optimal linear time varying filter under a projection side constraint these time frequency formulations extend the simple and intuitive spectral representations that are valid in the stationary case to the practically important case of underspread nonstationary processes furthermore we propose an approximate time frequency design of both optimal filters and we present bounds that show that for underspread processes the time frequency designed filters are nearly optimal we also introduce extended filter design schemes using a weighted error criterion and we discuss an efficient time frequency implementation of optimal filters using multiwindow short time fourier transforms our theoretical results are illustrated by numerical simulations

balanced3ϕ2summation theorems foru n basic hypergeometric series abstract in this paper we begin the theory and application of the u n 1 generalization of the classical bailey transform and bailey lemma we work in the setting of multiple basic hypergeometric series very well poised on unitary groups u n 1 the u n 1 bailey transform is obtained from a suitably modified u n 1 terminating very well poised 4 3 summation theorem and termwise transformations it is then interpreted as a matrix inversion result for two infinite lower triangular matrices this provides a higher dimensional generalization of andrews matrix inversion formulation of the bailey transform as in the classical case the concept of a u n 1 bailey pair is introduced and then inverted this u n 1 inversion enables us to derive u n 1 terminating balanced 3 2 summations directly from suitable u n 1 terminating very well poised 6 5 summations and vice versa these pairs of u n 1 dual identities extend the classical one variable case of andrews special limiting cases of the u n 1 terminating balanced 3 2 summation yield u n 1 q gauss summations several u n 1 q chu vandermonde summations u n 1 q binomial theorems and a u n 1 cauchy identity many other consequences of the u n 1 6 2 and 3 2 summations and the u n 1 bailey transform are further developed in our subsequent papers these include a derivation of the u n 1 bailey lemma several terminating u n 1 q whipple transformations u n 1 10 9 transformations and nonterminating u n 1 q whipple transformations the classical case of all this work corresponding to a 1 or equivalently u 2 contains a substantial amount of the theory and application of one variable basic hypergeometric series

nonlinear and nonideal sampling theory and methods we study a sampling setup where a continuous time signal is mapped by a memoryless invertible and nonlinear transformation and then sampled in a nonideal manner such scenarios appear for example in acquisition systems where a sensor introduces static nonlinearity before the signal is sampled by a practical analog to digital converter we develop the theory and a concrete algorithm to perfectly recover a signal within a subspace from its nonlinear and nonideal samples three alternative formulations of the algorithm are described that provide different insights into the structure of the solution a series of oblique projections approximated projections onto convex sets and quasi newton iterations using classical analysis techniques of descent based methods and recent results on frame perturbation theory we prove convergence of our algorithm to the true input signal we demonstrate our method by simulations and explain the applicability of our theory to wiener hammerstein analog to digital hybrid systems

on the real cubic fields in this paper the authors announce a table of the 4753 totally real nonconjugate nonabelian cubic fields with discriminant less than 100000 each field is given by its discriminant the coefficients of a generating polynomial and the index of this polynomial over the field a basis of the integers of the field is also given some differences with other tables are pointed out godwin and samet 3 have described the construction of a table of real cubic fields with discriminants d 20000 using similar methods angell 1 extends these results up to d 100000 using a different method the authors 5 have constructed a table of the 4753 real nonabelian cubic fields with discriminants d 100000 here and in the sequel triplets of conjugate fields are counted once only the method developed in 5 generalizes the one used in 4 and the table constructed there gives for each cubic field k its discriminant an irreducible polynomial f x which defines k the index of f x over k and a basis for the integers of k in this work we present some consequences derived from 5 in particular we have discovered that ten fields are missing from angell s table in table 1 we give each of these ten fields and its corresponding class numbers h the field k with discriminant d is generated by a root 0 of the polynomial f x x3 ax b s is the index of 0 and 1 0 a is a basis of the integers of k where 02 to t 2 a a

estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to nmr spectroscopy data we present fast maximum likelihood fml estimation of parameters of multiple exponentially damped sinusoids the fml algorithm was motivated by the desire to analyze data that have many closely spaced components such as the nmr spectroscopy data of human blood plasma the computational efficiency of fml lies in reducing the multidimensional search involved in ml estimation into multiple 1 d searches this is achieved by using our knowledge of the shape of the compressed likelihood function clf in the parameter space the proposed fml algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the clf the other striking features of the proposed algorithm are that it provides procedures for initialization has a fast converging iteration stage and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal to noise ratio snr the computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction kiss iqml alternating projections ap and expectation maximization em

further bibasic hypergeometric transformations and their applications abstract in this paper we give several new transformation formulae and generalize one result obtained by singh u b singh certain bibasic hypergeometric transformations and their applications j math anal appl 201 1996 44 56 with the help of bailey s transform further some new multiple series identities of the rogers ramanujan type are established

joint signal detection and parameter estimation in multiuser communications the problem of simultaneously detecting the information bits and estimating signal amplitudes and phases in a k user asynchronous direct sequence spread spectrum multiple access communication system is addressed the joint maximum likelihood ml estimator has a computational complexity that is exponential in the total number of bits transmitted and thus does not represent a practical solution to the problem an estimator that combines a suboptimum tree search algorithm with a recursive least squares estimator of complex signal amplitude is considered the complexity of this estimator is o k sup 2 computations per decoded bit and its performance is very close to that of the joint ml receiver this receiver has the advantage that the transmitted signal powers and phases are extracted from the received signal in an adaptive fashion without using a test sequence

on the convergence of blind adaptive equalizers for constant modulus signals this paper studies the behavior of the error sequence of stop anti go variants of two adaptive blind equalizers namely cma2 2 and sato s 1975 algorithm it is shown that for transmitted signals with constant modulus spl gamma the equalizer output can be made to lie within the circle of radius spl gamma spl radic c infinitely often for some value of c that is only slightly larger than one

partial theta functions i beyond the lost notebook it is shown how many of the partial theta function identities in ramanujan s lost notebook can be generalized to infinite families of such identities key in our construction is the bailey lemma and a new generalization of the jacobi triple product identity by computing residues around the poles of our identities we find a surprising connection between partial theta function identities and garrett ismail stanton type extensions of multisum rogers ramanujan identities

constrained maximum likelihood solution of linear equations the total least squares tls is used to solve a set of inconsistent linear equations ax spl ap y when there are errors not only in the observations y but in the modeling matrix a as well the tls seeks the least squares perturbation of both y and a that leads to a consistent set of equations when y and a have a defined structure we usually want the perturbations to also have this structure unfortunately standard tls does not generally preserve the perturbation structure so other methods are required we examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations given an a priori perturbation probability density function while our approach is applicable to both gaussian and non gaussian distributions we show in the uncorrelated gaussian case that our method is equivalent to several existing methods our approach is therefore more general and can be applied to a wider variety of signal processing problems

blind adaptation of zero forcing projections and oblique pseudo inverses for subspace detection and estimation when interference dominates noise in much of modern radar sonar and wireless communication it seems more reasonable to model measurement noise as subspace interference plus broadband noise than as colored noise this observation leads naturally to a variety of detection and estimation problems in the linear statistical model to solve these problems one requires oblique pseudo inverses oblique projections and zero forcing orthogonal projections the problem is that these operators depend on knowledge of signal and interference subspaces and this information is often not at hand more typically the signal subspace is known but the interference subspace is unknown we prove a theorem that allows these operators to be estimated directly from experimental data without knowledge of the interference subspace as a byproduct the theorem shows how signal subspace covariance may be estimated when the strict identities of the theorem are approximated then the detectors estimators and beamformers of this paper take on the form of adaptive subspace estimators detectors and capon beamformers all of which are reduced in rank the fundamental operator turns out to be a certain reduced rank wiener filter which we clarify in the course of our derivations the results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation they may be applied to detection and estimation in radar sonar and hyperspectral imaging and to data decoding in multiuser communication receivers

complexity reduction for sign configurations through the kp ii equation and its information theoretic aspects we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed

a deflation procedure for subspace decomposition a general deflation framework is described for the separation of a desired signal subspace of arbitrary dimensions from noisy multichannel observations the method simultaneously uses single and multichannel priors to split the desired and undesired subspaces even for coplanar intersecting subspaces by appropriate use of signal priors it can even extract signals from degenerate mixtures of signals and noise recorded from a few number of channels in low snr scenarios without the reduction of the data dimensions as a case study the performance of the proposed method is studied for the problem of extracting fetal cardiac signals from maternal abdominal recordings over simulated and real data a second case study deals with the degenerate problem of extracting diaphragmatic electromyogram from electrocardiograph artifacts a provisional patent application based on this method has been filed

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

certain bibasic hypergeometric transformations and their applications abstract we have obtained two new transformation formulae with the help of bailey s transform one of which contains series involving two independent bases it has also been shown that some very interesting new multiple series identities of the rogers ramanujan type can be established

static and dynamic convergence behavior of adaptive blind equalizers this paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers we first study the properties of prediction error functions of blind equalization algorithms and then we use these properties to analyze the static and dynamic convergence behavior based on the independence assumption we prove in this paper that with a small step size the ensemble average of equalizer coefficients will converge to the minimum of the cost function near the channel inverse however the convergence is not consistent the correlation matrix or equalizer coefficients at equilibrium are determined by a lyapunov equation according to our analysis results for a given channel and stepsize there is an optimal length for an equalizer to minimize the intersymbol interference this result implies that a longer length blind equalizer does not necessarily outperform a shorter one which is contrary to what is conventionally conjectured the theoretical analysis results are confirmed by computer simulations

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

continuous time tracking algorithms involving two time scale markov chains this work is concerned with least mean squares lms algorithms in continuous time for tracking a time varying parameter process a distinctive feature is that the true parameter process is changing at a fast pace driven by a finite state markov chain the states of the markov chain are divisible into a number of groups within each group the transitions take place rapidly among different groups the transitions are infrequent introducing a small parameter into the generator of the markov chain leads to a two time scale formulation the tracking objective is difficult to achieve nevertheless a limit result is derived yielding algorithms for limit systems moreover the rates of variation of the tracking error sequence are analyzed under simple conditions it is shown that a scaled sequence of the tracking errors converges weakly to a switching diffusion in addition a numerical example is provided and an adaptive step size algorithm developed

application of manifold separation to polarimetric capon beamformer and source tracking two adaptive capon methods that jointly estimate the azimuth angle and polarization of the sources in a closed form are proposed it is shown that the azimuth angles of the sources may be estimated from the roots of a complex valued polynomial or by rooting a real valued polynomial instead the latter method is particularly useful in tracking arbitrarily polarized sources in a sequential snapshot by snapshot manner using root tracking techniques the proposed polynomial rooting based methods are applicable to polarization sensitive arrays regardless of the array geometry including conformal arrays and take into account array nonidealities a large sample analysis of the polarimetric capon method is also provided showing that it converges up to a multiplicative factor that depends on the interference plus noise power to the polarimetric music method in the high sinr regime such a result gives a new insight into the well known capon and music methods this paper also shows that employing manifold separation in robust capon beamforming as well as in transmit beamforming schemes leads to improved performance in terms of received sinr when array calibration measurements are used extensive numerical results employing real world polarimetric arrays are given results show that employing manifold separation leads to improved performance in many array processing tasks

two channel constrained least squares problems solutions using power methods and connections with canonical coordinates the problem of two channel constrained least squares cls filtering under various sets of constraints is considered and a general set of solutions is derived for each set of constraints the solution is determined by a coupled asymmetric generalized eigenvalue problem this eigenvalue problem establishes a connection between two channel cls filtering and transform methods for resolving channel measurements into canonical or half canonical coordinates based on this connection a unified framework for reduced rank wiener filtering is presented then various representations of reduced rank wiener filters in canonical and half canonical coordinates are introduced an alternating power method is proposed to recursively compute the canonical coordinate and half canonical coordinate mappings a deflation process is introduced to extract the mappings associated with the dominant coordinates the correctness of the alternating power method is demonstrated on a synthesized data set and conclusions are drawn

nonlinear blind equalization schemes using complex valued multilayer feedforward neural networks among the useful blind equalization algorithms stochastic gradient iterative equalization schemes are based on minimizing a nonconvex and nonlinear cost function however as they use a linear fir filter with a convex decision region their residual estimation error is high in the paper four nonlinear blind equalization schemes that employ a complex valued multilayer perceptron instead of the linear filter are proposed and their learning algorithms are derived after the important properties that a suitable complex valued activation function must possess are discussed a new complex valued activation function is developed for the proposed schemes to deal with qam signals of any constellation sizes it has been further proven that by the nonlinear transformation of the proposed function the correlation coefficient between the real and imaginary parts of input data decreases when they are jointly gaussian random variables last the effectiveness of the proposed schemes is verified in terms of initial convergence speed and mse in the steady state in particular even without carrier phase tracking procedure the proposed schemes correct an arbitrary phase rotation caused by channel distortion