robust shrinkage affine projection sign adaptive filtering algorithms for impulsive noise environments two robust affine projection sign raps algorithms both of which minimize the mixed norm of l 1 and l 2 of the error signal are proposed the direction vector of the raps algorithms is obtained from the gradient of an l 1 norm based objective function while two related l 2 norm based minimization problems are solved to obtain the line search of the two raps algorithms the l 1 norm based direction vector reduces the impact of impulsive noise whereas the l 2 norm based line search produces an unbiased solution in the proposed algorithms in addition one of the two raps algorithms shares the data selective adaptation used in the set membership sm affine projection smap algorithm the proposed algorithms are shown to offer a significant improvement in the convergence speed as well as a significant reduction in the steady state misalignment relative to the pseudo affine projection sign paps algorithm in addition the proposed algorithms offer robust performance with respect to impulsive noise and improved tracking of the unknown system in comparison to that provided by the paps and affine projection sign aps algorithms these features of the proposed algorithms are demonstrated using simulation results in system identification and echo cancellation applications

minimax length links of a dissimilarity matrix and minimum spanning trees a theorem is proved stating that the set of all minimax links defined as links minimizing over paths the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph comprise the union of all minimum spanning trees of that graph this theorem is related to methods of fitting network models to dissimilarity data particularly a method called pathfinder due to schvaneveldt and his colleagues as well as to single linkage clustering and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees

maximum likelihood priority first search decodable codes for combined channel estimation and error correction the coding technique that combines channel estimation and error correction has received attention recently and has been regarded as a promising approach to counter the effects of multipath fading it has been shown by simulation that a proper code design that jointly considers channel estimation can improve the system performance subject to a fixed code rate as compared to a conventional system which performs channel estimation and error correction separately nevertheless the major obstacle that prevents the practice of such coding technique is that the existing codes are mostly searched by computers and subsequently exhibit no apparent structure for efficient decoding hence the operation intensive exhaustive search becomes the only decoding option and the decoding complexity increases dramatically with codeword length in this paper a systematic construction is derived for a class of structured codes that support joint channel estimation and error correction it is confirmed by simulation that these codes have comparable performance to the best simulated annealing based computer searched codes moreover the systematically constructed codes can now be maximum likelihoodly decoded with respect to the unknown channel criterion in terms of a newly derived recursive metric for use by the priority first search decoding algorithm thus the decoding complexity is significantly reduced as compared with that of an exhaustive decoder

a feedback approach to the steady state performance of fractionally spaced blind adaptive equalizers this paper proposes a new approach to the analysis of the steady state performance of constant modulus algorithms cma which are among the most popular adaptive schemes for blind equalization a major feature of the proposed feedback approach is that it bypasses the need for working directly with the weight error covariance matrix in so doing approximate expressions for the steady state mean square error of several cm algorithms are derived including cma2 2 cma1 2 normalized cma and a new normalized cma variant with less bias a comparison among the various algorithms is also performed along with several simulation results the conclusions confirm the superior performance of cma2 2

paper tracking error bounds of adaptive nonstationary filtering adaptive filtering with error gradient algorithm and constant step size is analyzed for a deterministic time variable optimum filtering vector the unrealistic assumption of independent observations is replaced by a bounded memory model largely justifiable in applications then the mean square tracking deviation msd between the optimum vector and the algorithm output is proved to include two contributions the stationary mode error characteristic of convergence accuracy which is proportional to the step size and the transient mode error reflecting the rapidity of tracking which is proportional to the squared ratio of the maximum optimum estimator increment to the step size this result agrees with the common intuition that there exists an optimum step size which compromises between convergence accuracy and tracking speed

steady state performance of spline adaptive filters recently a novel class of nonlinear adaptive filters called spline adaptive filters safs has been introduced and demonstrated to be very effective in many practical applications the learning rules of these architectures are based on the least mean square lms algorithm in order to provide theoretical foundation to the saf in this paper we provide a steady state performance evaluation in particular after the stochastic analysis of the mean behavior of the saf approach under the gaussian assumption the analytical derivation of the theoretical excess mean square error emse and the normalized misadjustment are derived and discussed the proposed analysis of emse and misadjustment is based on the energy conservation approach that has been extended to saf architecture the derived theoretical analysis allows to accurately predict the steady state performance therefore some properties for the correct choice of filter parameters are also provided experimental results demonstrate the effectiveness of the analysis results

analysis of error gradient adaptive linear estimators for a class of stationary dependent processes in many applications the training data to be processed by an adaptive linear estimator can be assumed to have a finite correlation length an exact analysis for this class of problems that yields the coefficient bias coefficient correlation matrix and mean square estimation error is obtained via a stochastic imbedding procedure a power series expansion in the gain parameter is used to obtain simplified expressions of order one for the above statistical moments these new expressions are shown to contain the terms that would result from an analysis based upon the assumption of independent training data plus additional terms arising from data correlation algorithm convergence properties are studied by identifying the appropriate matrix eigenvalues from the first order theory

optimal joint detection estimation in fading channels with polynomial complexity the problem of sequence detection in frequency nonselective time selective fading channels when channel state information csi is not available at the transmitter and receiver is considered in this paper the traditional belief is that exact maximum likelihood sequence detection mlsd of an uncoded sequence over this channel has exponential complexity in the channel coherence time thus for slowly varying channels i e channels having coherence time on the order of the sequence length the complexity appears to be exponential in the sequence length in the first part of this work it is shown that exact mlsd can be computed with only polynomial worst case complexity in the sequence length regardless of the operating signal to noise ratio snr for equal energy signal constellations by establishing a relationship between the aforementioned complexity and the rank of the correlation matrix of the fading process an understanding of how complexity of the optimal mlsd receiver varies as the channel dynamics change is provided in the second part of this paper the problem of decoding turbo like codes in frequency nonselective time selective fading channels without receiver csi is examined using arguments similar to the ones used for the mlsd case it is shown that the exact symbol by symbol soft decision metrics sbssdms implied by the min sum algorithm can be evaluated with polynomial worst case complexity in the sequence length regardless of snr for equal energy signal constellations finally by simplifying some key steps in the polynomial complexity algorithm a family of fast approximate algorithms is derived which yield near optimal performance

a unified approach to dynamic length algorithms for adaptive linear equalizers the number of taps is an important factor which affects nearly all the performance and complexity measures of adaptive equalizers recently dynamic length algorithms for the adaptive finite impulse response fir filters have attracted considerable attention and several methods have been proposed nevertheless the relationship among these techniques is still unclear which makes the performance comparison remaining difficult in this paper a unified explanation of these techniques is presented which summarizes all proposed algorithms and provides a platform for their performance comparison moreover a new type of dynamic length algorithms the varying threshold dynamic length algorithm vt dla is proposed simulation results show that the performance of the new algorithm outperforms that of existing algorithms

tracking analysis of the sign algorithm in nonstationary environments a tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented under the assumption that the nonstationary can be modeled using a random disturbance it is shown that the long term time average of the mean absolute error is bounded and that there exists an optimal choice of the convergence constant mu which minimizes this quality applying the commonly used independence assumption and under the assumption that the nonstationarity is solely due to the time varying behavior of the optimal coefficients it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode finally under the additional assumption that the signals involved are zero mean and gaussian a set of nonlinear difference equations is derived that characterizes the mean and mean squared behavior of the filter coefficients and the mean squared estimation error during adaptation and tracking results of several experiments that show very good correlation with the theoretical analyses are presented

transient and steady state analysis of the affine combination of two adaptive filters in this paper we propose an approach to the transient and steady state analysis of the affine combination of one fast and one slow adaptive filters the theoretical models are based on expressions for the excess mean square error emse and cross emse of the component filters which allows their application to different combinations of algorithms such as least mean squares lms normalized lms nlms and constant modulus algorithm cma considering white or colored inputs and stationary or nonstationary environments since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant its adaptation is also taken into account in the transient analysis furthermore we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance good agreement between analysis and simulation results is always observed

sampling and prefiltering effects on blind equalizer design in the development of equalization algorithms for unknown channels the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked in this paper these effects are investigated the relationship between the fractionally spaced output samples of a noise limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time invariant and the time varying channels it is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms thus this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates a case study of the well known subspace method for blind channel identification is presented the effects of the noise color due to the prefilter on equalizers is investigated and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error mse performance criterion is investigated through numerical examples

tracking properties and steady state performance of rls adaptive filter algorithms adaptive signal processing algorithms derived from ls least squares cost functions are known to converge extremely fast and have excellent capabilities to track an unknown parameter vector this paper treats analytically and experimentally the steady state operation of rls recursive least squares adaptive filters with exponential windows for stationary and nonstationary inputs a new formula for the estimation noise has been derived involving second and fourth order statistics of the filter input as well as the exponential windowing factor and filter length furthermore it is shown that the adaptation process associated with lag effects depends solely on the exponential weighting parameter in addition the calculation of the excess mean square error due to the lag for an assumed markov channel provides the necessary information about tradeoffs between speed of adaptation and steady state error it is also the basis for comparison to the simple lms algorithm in a simple case of channel identification it is shown that the lms and rls adaptive filters have the same tracking behavior finally in the last part we present new rls restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise namely finite precision arithmetic

generalized app detection of continuous phase modulation over unknown isi channels techniques for computing soft information in the presence of unknown intersymbol interference are presented with a particular focus on iterative detection of serially concatenated continuous phase modulation the techniques are centered around the recursive least squares algorithm thus enabling unsupervised detection in particular we employ bidirectional estimation

mean square performance of a family of affine projection algorithms affine projection algorithms are useful adaptive filters whose main purpose is to speed the convergence of lms type filters most analytical results on affine projection algorithms assume special regression models or gaussian regression data the available analysis also treat different affine projection filters separately this paper provides a unified treatment of the mean square error tracking and transient performances of a family of affine projection algorithms the treatment relies on energy conservation arguments and does not restrict the regressors to specific models or to a gaussian distribution simulation results illustrate the analysis and the derived performance expressions

steady state mean square performance of the multichannel filtered x affine projection algorithm this paper provides a unified analysis of the steady state behavior of different multichannel filtered x affine projection algorithms when used in active noise control anc systems the analysis deals with two different filtering schemes the modified filtered x affine projection mfxap algorithm with the modified filtered x structure embedded that has been studied in previous works and the filtered x affine projection cfxap algorithm with the conventional filtered x structure embedded that becomes the main contribution of this work this study is based on energy conservation principles and does not require a specific signal distribution the derived theoretical models allow to accurately predict the steady state performance of the considered algorithms for moderate ap orders and low step sizes simulation results obtained in practical anc systems validate both the analysis and the achieved expressions showing a relative good match between theory and practice

mlse for an unknown channel i optimality considerations the problem of performing joint maximum likelihood ml estimation of a digital sequence and unknown dispersive channel impulse response is considered starting from a continuous time ct model previous investigations of this problem have not considered the front end fe processing in detail rather a discrete time signal model has been assumed we show that a fractionally spaced whitened matched filter matched to the known data pulse provides a set of sufficient statistics when a tapped delay line channel model is assumed and that the problem is ill posed when the channel impulse response is generalized to a ct finite length model practical approximations are considered that circumvent this ill posed condition recursive computation of the joint ml metric is developed together the fe processing and metric recursion provide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per survivor processing and they lead directly to generalizations several fe processors representative of those suggested in the literature are developed and related to the practically optimal fe

optimized variable selection via repeated data splitting model selection in high dimensional settings has received substantial attention in recent years however similar advancements in the low dimensional setting have been lacking in this article we introduce a new variable selection procedure for low to moderate scale regressions n p this method repeatedly splits the data into two sets one for estimation and one for validation to obtain an empirically optimized threshold which is then used to screen for variables to include in the final model in an extensive simulation study we show that the proposed variable selection technique enjoys superior performance compared with candidate methods backward elimination via repeated data splitting univariate screening at 0 05 level adaptive lasso scad being amongst those with the lowest inclusion of noisy predictors while having the highest power to detect the correct model and being unaffected by correlations among the predictors we illustrate the methods by applying them to a cohort of patients undergoing hepatectomy at our institution

analysis of the normalized lms algorithm with gaussian inputs the lms adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter for stability and convergence since the input power level is usually one of the statistical unknowns it is normally estimated from the data prior to beginning the adaptation process it is then assumed that the estimate is perfect in any subsequent analysis of the lms algorithm behavior in this paper the effects of the power level estimate are incorporated in a data dependent that appears explicitly within the algorithm the transient mean and second moment behavior of the modified lms nlms algorithm are evaluated taking into account the explicit statistical dependence of upon the input data the mean behavior of the algorithm is shown to converge to the wiener weight a constant coefficient matrix difference equation is derived for the weight fluctuations about the wiener weight the equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single frequency input in steady state for small expressions for the misadjustment error are also presented it is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the lms algorithm in the ale application the steady state weight fluctuations are shown to be mode dependent being largest at the frequency of the input

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

the least mean fourth lmf adaptive algorithm and its family new steepest descent algorithms for adaptive filtering and have been devised which allow error minimization in the mean fourth and mean sixth etc sense during adaptation the weights undergo exponential relaxation toward their optimal solutions time constants have been derived and surprisingly they turn out to be proportional to the time constants that would have been obtained if the steepest descent least mean square lms algorithm of widrow and hoff had been used the new gradient algorithms are insignificantly more complicated to program and to compute than the lms algorithm their general form is w j 1 w j 2 mu k epsilon j 2k 1 x j where w j is the present weight vector w j 1 is the next weight vector epsilon j is the present error x j is the present input vector mu is a constant controlling stability and rate of convergence and 2k is the exponent of the error being minimized conditions have been derived for weight vector convergence of the mean and of the variance for the new gradient algorithms the behavior of the least mean fourth lmf algorithm is of special interest in comparing this algorithm to the lms algorithm when both are set to have exactly the same time constants for the weight relaxation process the lmf algorithm under some circumstances will have a substantially lower weight noise than the lms algorithm it is possible therefore that a minimum mean fourth error algorithm can do a better job of least squares estimation than a mean square error algorithm this intriguing concept has implications for all forms of adaptive algorithms whether they are based on steepest descent or otherwise

improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm convergence analysis of stochastic gradient adaptive filters using the sign algorithm is presented in this paper the methods of analysis currently available in literature assume that the input signals to the filter are white this restriction is removed for gaussian signals in our analysis expressions for the second moment of the coefficient vector and the steady state error power are also derived simulation results are presented and the theoretical and empirical curves show a very good match

analysis of the gradient descent total least squares adaptive filtering algorithm the gradient descent total least squares gd tls algorithm is a stochastic gradient adaptive filtering algorithm that compensates for error in both input and output data we study the local convergence of the gd tls algoritlun and find bounds for its step size that ensure its stability we also analyze the steady state performance of the gd tls algorithm and calculate its steady state mean square deviation our steady state analysis is inspired by the energy conservation based approach to the performance analysis of adaptive filters the results predicted by the analysis show good agreement with the simulation experiments

blind adaptive interference suppression based on set membership constrained constant modulus algorithms with dynamic bounds this work presents blind constrained constant modulus ccm adaptive algorithms based on the set membership filtering smf concept and incorporates dynamic bounds for interference suppression applications we develop stochastic gradient and recursive least squares type algorithms based on the ccm design criterion in accordance with the specifications of the smf concept we also propose a blind framework that includes channel and amplitude estimators that take into account parameter estimation dependency multiple access interference mai and inter symbol interference isi to address the important issue of bound specification in multiuser communications a convergence and tracking analysis of the proposed algorithms is carried out along with the development of analytical expressions to predict their performance simulations for a number of scenarios of interest with a ds cdma system show that the proposed algorithms outperform previously reported techniques with a smaller number of parameter updates and a reduced risk of overbounding or underbounding

adaptive recovery of a chirped sinusoid in noise ii performance of the lms algorithm the authors study the ability of the exponentially weighted recursive least square rls algorithm to track a complex chirped exponential signal buried in additive white gaussian noise power p sub n the signal is a sinusoid whose frequency is drifting at a constant rate psi lt is recovered using an m tap adaptive predictor five principal aspects of the study are presented the methodology of the analysis proof of the quasi deterministic nature of the data covariance estimate r k a new analysis of rls for an inverse system modeling problem a new analysis of rls for a deterministic time varying model for the optimum filter and an evaluation of the residual output mean square error mse resulting from the nonoptimality of the adaptive predictor the misadjustment in terms of the forgetting rate beta of the rls algorithm it is shown that the misadjustment is dominated by a lag term of order beta sup 2 and a noise term of order beta thus a value beta sub opt exists which yields a minimum misadjustment it is proved that beta sub opt m 1 rho psi sup 2 sup 1 3 and the minimum misadjustment is equal to 3 4 p sub n m 1 beta sub opt where rho is the input signal to noise ratio snr

a theory on the convergence behavior of the affine projection algorithm in this paper we present a theoretical convergence analysis of the affine projection algorithm apa based on the arguments of energy conservation although the apa and its convergence analysis have been widely studied the dependency of weight error vector on past noise is usually neglected for simplicity to obtain accurate theoretical results for the apa we here consider the dependency between the weight error vector and past noise in the mean square analysis presented by shin and sayed in mean square performance of a family of affine projection algorithms ieee transactions on signal processing vol 52 no 1 pp 90 102 january 2004 through this work we can also theoretically analyze the behavior of the periodic apa which updates its weights periodically simulation results show that our theoretical results coincide closely with simulations

data detection and kalman estimation for multiple space time trellis codes this work presents a joint channel estimation and data detection algorithm over high doppler fading channels for space time trellis codes sttcs having more than one code vector per trellis branch such codes are referred to as multiple sttcs msttcs this algorithm belongs to the per survivor processing psp family where a survivor sequence associated with a trellis state can be considered as the data sequence aiding per path channel estimation in a joint detection and estimation procedure we propose a smoothed data detection technique that utilizes past present and future received symbols to increase the probability of the survivor being a correct data sequence a symbol by symbol maximum a posteriori probability map criterion with a fixed delay d is employed for data detection combined with a kalman predictor kp for channel estimation this novel algorithm called smoothed data detection and kalman estimation sdd ke provides a significant performance gain when d 0 over d 0 with a linear increase in complexity when d increases comparison with the delayed mixture kalman filtering d mkf technique shows that the sdd ke algorithm provides important performance and complexity advantages

approximate ml decoding of coded psk with no explicit carrier phase reference an approximate method is discussed for maximum likelihood estimation of coded psk sequences in the presence of an unknown carrier phase this method makes use of the viterbi algorithm to find an optimum path in the encoder trellis diagram phase estimation is embedded into the structure of the detection algorithm and the branch metrics in the trellis are modified with respect to those employed with known carrier phase comparisons with traditional decoding schemes show that the proposed solution has better performance in terms of acquisition time and cycle slips

adaptive fractionally spaced blind cma equalization excess mse the performance of the constant modulus algorithm cma a reference algorithm for adaptive blind equalization is studied in terms of the excess mean square error emse due to the nonvanishing step size of the gradient descent algorithm an analytical approximation of emse is provided emphasizing the effect of the constellation size and resulting in design guidelines

upper and lower bounds of the misadjustment in the lms algorithm the misadjustment is a dimensionless measure of the difference between the optimal weiner performance and the actual performance of the lms least mean squares algorithm this difference is attributed to the gradient noise in the adaptive process present estimates relate the misadjustment to the convergence gain and the trace of the autocorrelation matrix the authors establish tighter lower bounds on the estimate of this misadjustment an upper bound on the misadjustment as a function of the convergence gain is found

nonparametric trellis equalization in the presence of non gaussian interference we consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference cci conventional maximum likelihood sequence estimation mlse and maximum a posteriori probability map trellis equalizers treat the sum of noise and interference as additive white gaussian noise while cci is generally a colored non gaussian process we propose a novel nonparametric approach based on the estimation of the probability density function of the noise plus interference given the availability of a limited volume of data the density is estimated by kernel smoothing techniques the use of a whitening filter in the presence of temporally colored disturbance is also addressed simulation results are provided for the global system for mobile communications gsm showing a significant performance improvement with respect to the equalizer based on the gaussian assumption major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available

ordinal network representation representing proximities by graphs ordinal network representations are graph theoretic representations of proximity data they seek to provide parsimonious representations of the ordinal nonmetric information in observed proximity data by means of the minimum path length distance of a connected and weighted graph in contrast to traditional tree based graph theoretic approaches ordinal network representation is not limited to but includes the representation by trees asymmetry in the proximity data and violations of zero minimality are allowed for the paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations a simple strategy for handling the problem of errors in the data is described and illustrated

tracking of time varying mobile radio channels 1 the wiener lms algorithm adaptation algorithms with constant gains are designed for tracking smoothly time varying parameters of linear regression models in particular channel models occurring in mobile radio communications in a companion paper an application to channel tracking in the is 136 tdma system is discussed the proposed algorithms are based on two key concepts first the design is transformed into a wiener filtering problem second the parameters are modeled as correlated arima processes with known dynamics this leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information the algorithms can be realized as wiener filters called learning filters or as lms newton updates complemented by filters that provide predictions or smoothing estimates the simplest algorithm named the wiener lms is presented all parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known the computational complexity is of the same order of magnitude as that of lms for regressors which are either white or have autoregressive statistics the tracking performance is however substantially improved

improving the tracking capability of adaptive filters via convex combination as is well known hessian based adaptive filters such as the recursive least squares algorithm rls for supervised adaptive filtering or the shalvi weinstein algorithm swa for blind equalization converge much faster than gradient based algorithms such as the least mean squares algorithm lms or the constant modulus algorithm cma however when the problem is tracking a time variant filter the issue is not so clear cut there are environments for which each family presents better performance given this we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability we show the potential of this combination and provide a unified theoretical model for the steady state excess mean square error for convex combinations of gradient and hessian based algorithms assuming a random walk model for the parameter variations the proposed model is valid for algorithms of the same or different families and for supervised lms and rls or blind cma and swa algorithms

maximum likelihood synchronization equalization and sequence estimation for unknown time varying frequency selective rician channels this paper develops a receiver structure to perform jointly maximum likelihood ml synchronization equalization and detection of a linearly modulated signal transmitted over a time varying frequency selective rician faded channel corrupted by additive white gaussian noise awgn the receiver is particularly suited to a fast fading channel where other receivers that rely on estimating the channel cannot track it quickly enough the signal mean and autocovariance are needed and a scheme is proposed for estimating these quantities adaptively the receiver processes the specular and diffuse components corresponding to the signal mean and autocovariance separately processing the known specular component is the classical detection problem the unknown diffuse component is processed by predictors we show that the predictors can achieve synchronization in a novel manner if synchronization is required a union bound on the receiver s bit error rate ber is derived and it tightly bounds simulated bers in fast fading at high signal to noise ratios snrs

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

combined coding and training for unknown isi channels the traditional method of sending a training signal to identify a channel followed by data may be viewed as a simple code for the unknown channel results in blind sequence detection suggest that performance similar to this traditional approach can be obtained without training however for short packets and or time recursive algorithms significant error floors exist due to the presence of sequences that are indistinguishable without knowledge of the channel in this paper we reconsider training signal design in light of recent results in blind sequence detection specifically we consider the tradeoff between the complexity of receiver processing and the amount of training overhead required more generally we design training codes which combine modulation and training in order to design these codes we find an expression for the pairwise error probability of the joint maximum likelihood jml channel and sequence estimator this expression motivates a pairwise distance for the jml receiver based on principal angles between the range spaces of data matrices the general code design problem generalized sphere packing is formulated as the clique problem associated with an unweighted undirected graph we provide optimal and heuristic algorithms for this clique problem for both long and short packets we demonstrate that significant improvements are possible by jointly considering the design of the training modulation and receiver processing

tracking of time varying channels using two step lms type adaptive algorithm this paper presents a modified version of the two step least mean square lms type adaptive algorithm motivated by the work of gazor we describe the nonstationary adaptation characteristics of this modified two step lms mg lms algorithm for the system identification problem it ensures stable behavior during convergence as well as improved tracking performance in the smoothly time varying environments the estimated weight increment vector is used for the prediction of weight vector for the next iteration the proposed modification includes the use of a control parameter to scale the estimated weight increment vector in addition to a smoothing parameter used in the two step lms g lms algorithm which controls the initial oscillatory behavior of the algorithm the analysis focuses on the effects of these parameters on the lag misadjustment in the tracking process the mathematical analysis for a nonstationary case where the plant coefficients are assumed to follow a first order markov process shows that the mg lms algorithm contributes less lag misadjustment than the conventional lms and g lms algorithms further the stability criterion imposes upper bound on the value of the control parameter these derived analytical results are verified and demonstrated with simulation examples which clearly show that the lag misadjustment reduces with increasing values of the smoothing and control parameters under permissible limits

performance analysis of the deficient length lms adaptive algorithm in almost all analyzes of the least mean square lms finite impulse response fir adaptive algorithm it is assumed that the length of the adaptive filter is equal to that of the unknown system impulse response however in many practical situations a deficient length adaptive filter whose length is less than that of the unknown system is employed and analysis results for the sufficient length lms algorithm are not necessarily applicable to the deficient length case therefore there is an essential need to accurately quantify the behavior of the lms algorithm for realistic situations where the length of the adaptive filter is deficient in this paper we present a performance analysis for the deficient length lms adaptive algorithm for correlated gaussian input data and using the common independence assumption exact expressions that completely characterize the transient and steady state mean square performances of the algorithm are developed which lead to new insights into the statistical behavior of the deficient length lms algorithm simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm

a unified approach to the steady state and tracking analyses of adaptive filters most adaptive filters are inherently nonlinear and time variant systems the nonlinearities in the update equations tend to lead to difficulties in the study of their steady state performance as a limiting case of their transient performance this paper develops a unified approach to the steady state and tracking analyses of adaptive algorithms that bypasses many of these difficulties the approach is based on the study of the energy flow through each iteration of an adaptive filter and it relies on a fundamental error variance relation

a full mean square analysis of clms for second order noncircular inputs a full mean square transient and steady state analysis of the complex least mean square clms algorithm is provided for strictly linear estimation of general second order noncircular improper gaussian inputs to this end we also consider the performance assessment in terms of the evolution of the complementary mean square error cmse and the complementary covariance pseudocovariance matrix of the weight error vector of clms this makes it possible to measure the degrees of noncircularity of the output error and the weight error vector which arise due to second order noncircularity improperness of the system input and system noise the recently introduced approximate uncorrelating transform which allows for joint direct diagonalization of both the input covariance and complementary covariance matrices with a single singular value decomposition is then employed in order to derive a unified bound on the step size which guarantees the convergence of both the standard mse and the proposed cmse a joint consideration of the standard mean square performance analysis and the proposed complementary performance analysis is shown to provide full second order closed form statistical descriptions of both the transient and steady state performances of clms for second order noncircular improper gaussian input data simulations in the system identification setting support the analysis

distributed estimation over an adaptive incremental network based on the affine projection algorithm we study the problem of distributed estimation based on the affine projection algorithm apa which is developed from newton s method for minimizing a cost function the proposed solution is formulated to ameliorate the limited convergence properties of least mean square lms type distributed adaptive filters with colored inputs the analysis of transient and steady state performances at each individual node within the network is developed by using a weighted spatial temporal energy conservation relation and confirmed by computer simulations the simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady state performance as compared to an lms based scheme in addition the new approach attains an acceptable misadjustment performance with lower computational and memory cost provided the number of regressor vectors and filter length parameters are appropriately chosen as compared to a distributed recursive least squares rls based method

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

on the statistical efficiency of the lms algorithm with nonstationary inputs a fundamental relationship exists between the quality of an adaptive solution and the amount of data used in obtaining it quality is defined here in terms of misadjustment the ratio of the excess mean square error mse in an adaptive solution to the minimum possible mse the higher the misadjustment the lower the quality is the quality of the exact least squares solution is compared with the quality of the solutions obtained by the orthogonalized and the conventional least mean square lms algorithms with stationary and nonstationary input data when adapting with noisy observations a filter trained with a finite data sample using an exact least squares algorithms will have a misadjustment given by m frac n n frac number of weights number of training samples if the same adaptive filter were trained with a steady flow of data using an ideal orthogonalized lms algorithm the misadjustment would be m frac n 4 tau mse frac number of weights number of training samples thus for a given time constant tau mse of the learning process the ideal orthogonalized lms algorithm will have about as low a misadjustment as can be achieved since this algorithm performs essentially as an exact least squares algorithm with exponential data weighting it is well known that when rapid convergence with stationary data is required exact least squares algorithms can in certain cases outperform the conventional widrow hoff lms algorithm it is shown here however that for an important class of nonstationary problems the misadjustment of conventional lms is the same as that of orthogonalized lms which in the stationary case is shown to perform essentially as an exact least squares algorithm

mean square convergence analysis of adaline training with minimum error entropy criterion recently the minimum error entropy mee criterion has been used as an information theoretic alternative to traditional mean square error criterion in supervised learning systems mee yields nonquadratic nonconvex performance surface even for adaptive linear neuron adaline training which complicates the theoretical analysis of the method in this paper we develop a unified approach for mean square convergence analysis for adaline training under mee criterion the weight update equation is formulated in the form of block data based on a block version of energy conservation relation and under several assumptions we carry out the mean square convergence analysis of this class of adaptation algorithm including mean square stability mean square evolution transient behavior and the mean square steady state performance simulation experimental results agree with the theoretical predictions very well

extended similarity trees proximity data can be represented by an extended tree which generalizes traditional trees by including marked segments that correspond to overlapping clusters an extended tree is a graphical representation of the distinctive features model a computer program extree that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data

estimation of co channel signals with linear complexity to increase wireless system capacity using co channel signals and multiple receiver antennas we develop the partitioned viterbi algorithm pva the pva estimation complexity increases linearly with each additional co channel signal rather than exponentially as it does with joint maximum likelihood sequence estimation mlse the estimation problem involves multiple signals simultaneously transmitted and observed through slow fading frequency selective channels although transmission is assumed to be in bursts according to a time division multiple access scheme more than one signal can occupy the same time and frequency slot these signals are referred to as co channel signals separation and estimation of the symbol bursts is accomplished by exploiting channel differences pva estimation consists of a set of viterbi detectors one per signal that operate in parallel with cross coupling to allow approximate interference cancellation by means of tentative decisions the forward filter of a decision feedback equalizer dfe is used to prefilter received signals prior to pva estimation prefiltering delays the energy of interfering signals so that tentative decisions become reliable enough to use simulation results show pva performance remains near optimal with respect to the performance of joint mlse

performance of lms based adaptive filters in tracking a time varying plant the article gives a general analysis of the lms based adaptive filters when used for tracking a class of time varying plants the algorithms covered are the conventional lms the transform domain normalized lms and the lms newton algorithm an important fact that we observe is that in comparing these algorithms better initial convergence does not necessarily mean better tracking a few special cases are presented that show the contrary

transform domain lms algorithm the concept of transform domain adaptive filtering is introduced in certain applications filtering in the transform domain results in great improvements in convergence rate over the conventional time domain adaptive filtering the relationship between several existing frequency domain adaptive filtering algorithms is established applications of the discrete fourier transform dft and the discrete cosine transform dct domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed

comparison of rls lms and sign algorithms for tracking randomly time varying channels the performance of adaptive fir filters governed by the recursive least squares rls algorithm the least mean square lms algorithm and the sign algorithm sa are compared when the optimal filtering vector is randomly time varying the comparison is done in terms of the steady state excess mean square estimation error spl xi and the steady state mean square weight deviation spl eta it is shown that spl xi does not depend on the spread of eigenvalues of the input covariance matrix r in the cases of the lms algorithm and the sa while it does in the case of the rls algorithm in the three algorithms spl eta is found to be increasing with the eigenvalue spread the value of the adaptation parameter that minimizes spl xi is different from the one that minimizes spl eta it is shown that the minimum values of spl xi and spl eta attained by the rls algorithm are equal to the ones attained by the lms algorithm in any one of the three following cases 1 if r has equal eigenvalues 2 if the fluctuations of the individual elements of the optimal vector are mutually uncorrelated and have the same mean square value or 3 if r is diagonal and the fluctuations of the individual elements of the optimal vector have the same mean square value conditions that make the values of spl xi and spl eta of the lms algorithm smaller or greater than the ones of the rls algorithm are derived for gaussian input data the minimum values of spl xi and spl eta attained by the sa are found to exceed the ones attained by the lms algorithm by 1 db independently of r and the mutual correlation between the elements of the optimal vector

steady state mean square performance analysis of a relaxed set membership nlms algorithm by the energy conservation argument this paper presents an analysis of the steady state mean square error mse of the set membership normalized least mean square sm nlms algorithm with relaxation and regularization parameters these parameters are introduced for the purpose of deriving in a unified way the steady state mse performances of the epsiv normalized least mean square epsiv nlms algorithm and a special case of the adaptive parallel subgradient projection psp algorithm the approach of the paper is to employ the energy conservation relation as a starting point of our analysis this relation enables us to avoid the transient analysis of the sm nlms algorithm which is in general hard due to the nonlinearity of the sm nlms algorithm as a result a few nonlinear equations whose solutions are theoretical steady state mses are derived where two types of reasonable assumptions are introduced to overcome the nonlinearity of the sm nlms algorithm our results are generalizations of well known results of the steady state mse of the epsiv nlms extensive simulations show the close agreement between our theories and experiments

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

autocovariance preserving estimator ape interpretation of the mlsd metric for rayleigh fading channels this paper describes a new interpretation of the maximum likelihood sequence detector metric for a linearly modulated signal and an unknown time varying dispersive rayleigh fading channel the metric which involves the channel and noise autocovariances is transformed into the intuitive mahalanobis distance squared euclidean distance in white noise between the observations and a reference estimated from them a novel estimator called the autocovariance preserving estimator is obtained that trades off increased estimation bias for reduced sequence error probability

transient analysis of adaptive filters with error nonlinearities the paper develops a unified approach to the transient analysis of adaptive filters with error nonlinearities in addition to deriving earlier results in a unified manner the approach also leads to new performance results without restricting the regression data to being gaussian or white the framework is based on energy conservation arguments and avoids the need for explicit recursions for the covariance matrix of the weight error vector

sparse principal component analysis and iterative thresholding principal component analysis pca is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix however it behaves poorly when the number of features p is comparable to or even much larger than the sample size n in this paper we propose a new iterative thresholding approach for estimating principal subspaces in the setting where the leading eigenvectors are sparse under a spiked covariance model we find that the new approach recovers the principal subspace and leading eigenvectors consistently and even optimally in a range of high dimensional sparse settings simulated examples also demonstrate its competitive performance

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

robust set membership affine projection adaptive filtering algorithm an improved set membership affine projection ap adaptive filtering algorithm is proposed the new algorithm uses two error bounds that are estimated during the learning phase and by this means significantly reduced steady state misalignment is achieved as compared to those in the conventional ap and set membership ap algorithms while achieving similar convergence speed and re adaptation capability in addition the proposed algorithm offers robust performance with respect to the error bound projection order impulsive noise interference and in tracking abrupt changes in the underlying system these features of the proposed algorithm are demonstrated through extensive simulation results in system identification and echo cancellation applications

an affine projection algorithm with update interval selection this paper presents a mean square deviation msd analysis of the periodic affine projection algorithm p apa and two update interval selection methods to achieve improved performance in terms of the convergence and the steady state error the msd analysis of the p apa considers the correlation between the weight error vector and the measurement noise vector using this analysis it is verified that the update interval governs the trade off between the convergence rate and the steady state errors in the p apa to overcome this drawback the proposed apas increase the update interval when the adaptive filter reaches the steady state consequently these algorithms can reduce the overall computational complexity the simulation results show that the proposed apas perform better than the previous algorithms

innovations based map detection for time varying frequency selective channels by using the innovations process this paper provides a unification and extension of the existing maximum a posteriori map detectors mapds the practically important topics of linear modulations time varying frequency selective channels differential phase detection and fractional sampling are accounted for the mapds are derived under different conditions of optimality and a priori knowledge as follows when the map criterion is applied to the constellation mapper s input bits or output symbols when all observations or only a fixed number of future observations i e fixed lag mapds from a transmission are available when the time varying channel impulse response is perfectly known and when only the gaussian distributed channel s mean and autocovariance and the noise variance are known as these quantities are actually unknown their estimation in the context of map detection is also discussed the mapds are characterized through simulation and a novel unified analysis although mapds are less suited to hardware implementation than the traditional maximum likelihood sequence detectors the mapds can accept nonuniform a priori bit or symbol probabilities and provide soft outputs in this way the mapds are well suited to iterative decoding and so they will become increasingly integral to high performance receiver designs

prediction in lms type adaptive algorithms for smoothly time varying environments the aim of this correspondence is to improve the performance of the least mean square lms and normalized lms nlms adaptive algorithms in tracking of time varying models a new procedure for estimation of weight increments for including in the lms type adaptive algorithms is proposed this procedure applies a simple smoothing on the increment of the estimated weights to estimate the speed of weights the estimated speeds are then used to predict the weights for the next iteration the efficiency of the algorithm is confirmed by simulation results the algorithm has a very low order of arithmetic complexity moreover this procedure could be combined with a wide class of adaptive filters e g rls gradient lattice algorithm etc to improve their behaviors the proposed algorithm is obtained by simplifying a kalman filter to this end a markov model of second order is considered for the weight vector this model shows that the estimation of parameter increments inferred from the predicted parameters improves the tracking performance

variable step size lms algorithm for fractal signals this paper presents a novel variable step size lms vslms algorithm for tracking signals from the gaussian 1 fbeta family of fractal signals that are inherently nonstationary the proposed algorithm differs from the existing vslms algorithms in the following ways 1 it deals with a specific class of nonstationary signals 2 it utilizes a nondiagonal step size matrix which is simultaneously diagonalizable with the auto covariance matrix of the input signal 3 in the decoupled weight vector space one of the step size parameters requires time varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step size parameters are time invariant and 4 it computes the step size matrix by estimating the hurst exponent required to characterize the statistical properties of the signal at the input of the adaptive filter the experimental setup of an adaptive channel equalizer is considered for equalization of fractal signals transmitted over stationary awgn channel the performance of the proposed fractal based variable step size least mean square fb vslms algorithm is compared with the unsigned vslms algorithm and is observed to be better for the class of nonstationary signals considered

a significance test for the lasso in the sparse linear regression setting we consider testing the significance of the predictor variable that enters the current lasso model in the sequence of models visited along the lasso solution path we propose a simple test statistic based on lasso fitted values called the covariance test statistic and show that when the true model is linear this statistic has an exp 1 asymptotic distribution under the null hypothesis the null being that all truly active variables are contained in the current lasso model our proof of this result for the special case of the first predictor to enter the model i e testing for a single significant predictor variable against the global null requires only weak assumptions on the predictor matrix x on the other hand our proof for a general step in the lasso path places further technical assumptions on x and the generative model but still allows for the important high dimensional case p n and does not necessarily require that the current lasso model achieves perfect recovery of the truly active variables of course for testing the significance of an additional variable between two nested linear models one typically uses the chi squared test comparing the drop in residual sum of squares rss to a formula see text distribution but when this additional variable is not fixed and has been chosen adaptively or greedily this test is no longer appropriate adaptivity makes the drop in rss stochastically much larger than formula see text under the null hypothesis our analysis explicitly accounts for adaptivity as it must since the lasso builds an adaptive sequence of linear models as the tuning parameter decreases in this analysis shrinkage plays a key role though additional variables are chosen adaptively the coefficients of lasso active variables are shrunken due to the formula see text penalty therefore the test statistic which is based on lasso fitted values is in a sense balanced by these two opposing properties adaptivity and shrinkage and its null distribution is tractable and asymptotically exp 1

sequential selection procedures and false discovery rate control summary we consider a multiple hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block of hypotheses a rejection rule in this setting amounts to a procedure for choosing the stopping point k this setting is inspired by the sequential nature of many model selection problems where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter we propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting we also show how the methods can be applied to model selection by using recent results on p values in sequential model selection settings

a time domain feedback analysis of filtered error adaptive gradient algorithms this paper provides a time domain feedback analysis of gradient based adaptive schemes a key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties along the lines of h sup spl infin theory and robust filtering the analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions it is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes the feedback structure is motivated via energy arguments and is shown to consist of two major blocks a time variant lossless i e energy preserving feedforward path and a time variant feedback path the configuration is further shown to lend itself to analysis via a so called small gain theorem thus leading to stability and robustness conditions that require the contractivity of certain operators choices for the step size parameter in order to guarantee faster rates of convergence are also derived and simulation results are included to demonstrate the theoretical findings in addition the time domain analysis provided in this paper is shown to extend the so called transfer function approach to a general time variant scenario without any approximations

quantized kernel least mean square algorithm in this paper we propose a quantization approach as an alternative of sparsification to curb the growth of the radial basis function structure in kernel adaptive filtering the basic idea behind this method is to quantize and hence compress the input or feature space different from sparsification the new approach uses the redundant data to update the coefficient of the closest center in particular a quantized kernel least mean square qklms algorithm is developed which is based on a simple online vector quantization method the analytical study of the mean square convergence has been carried out the energy conservation relation for qklms is established and on this basis we arrive at a sufficient condition for mean square convergence and a lower and upper bound on the theoretical value of the steady state excess mean square error static function estimation and short term chaotic time series prediction examples are presented to demonstrate the excellent performance

adaptive stepsize selection for tracking in a regime switching environment we consider the problem of using a stochastic approximation algorithm to perform online tracking in a non stationary environment characterised by abrupt regime changes the primary contribution of this paper is a new approach for adaptive stepsize selection that is suitable for this type of non stationarity our approach is pre emptive rather than reactive and is based on a strategy of maximising the rate of adaptation subject to a constraint on the probability that the iterates fall outside a pre determined range of acceptable error the basis for our approach is provided by the theory of weak convergence for stochastic approximation algorithms

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

statistical significance of clustering for high dimension low sample size data clustering methods provide a powerful tool for the exploratory analysis of high dimension low sample size hdlss data sets such as gene expression microarray data a fundamental statistical issue in clustering is which clusters are really there as opposed to being artifacts of the natural sampling variation we propose sigclust as a simple and natural approach to this fundamental statistical problem in particular we define a cluster as data coming from a single gaussian distribution and formulate the problem of assessing statistical significance of clustering as a testing procedure this gaussian null assumption allows direct formulation of p values that effectively quantify the significance of a given clustering hdlss covariance estimation for sigclust is achieved by a combination of invariance principles together with a factor analysis model the properties of sigclust are studied simulated examples as well as an application to a real cancer microarray data set show that the proposed method

multiresolution sequence detection in rapidly fading channels based on focused wavelet decompositions the problem of detecting a sequence using the maximum likelihood strategy when the time varying multipath channel is unknown can be in principle solved using the generalized likelihood detector gld the gld metric involves finding the orthogonal projection of the received signal onto the subspace of the transmitted signal distorted by the multipath channel the faded signal corresponding to one of the transmitted sequences is in fact known to lie in a subspace but its exact location is not known because the channel parameters are unknown this detector which in the case of a static channel collapses to the per survivor processing method is also called a matched subspace detector because its statistic is matched to the a priori known signal subspace unfortunately the computation of the perfectly matched orthogonal projection of the received signal onto the multipath faded signal subspace is in the general time varying case impossible we introduce in this work the idea of using new wavelet based subspaces that approximate the original signal subspace the nested sequence of linear vector spaces defined by a wavelet based multiresolution decomposition of the fading channel time variations provides a set of subspaces that at an increasingly high level of detail are efficient representations of the original signal subspace for each of these representations sequence detection at different levels of resolution can be performed

analytical performance of the lms algorithm on the estimation of wide sense stationary channels the performance of the least mean square lms algorithm on the estimation of time varying channels is analytically evaluated using the estimation error correlation matrix the mean square weight error mswe and the mean square estimation error mse as parameters expressions for those parameters are obtained from a set of hypotheses usually adopted in the communication systems context the channel is modeled as a wide sense stationary wss discrete time stochastic field with known autocorrelation the expressions for the steady state mswe and mse are particularized for the class of wss channel models and an original analysis of the optimum lms step size parameter for usual channel models is addressed for the sake of comparison with other works the analytical step size optimization for random walk models is also considered several estimates of mswe curves obtained by computer simulation are compared with analytical results for validation purposes a very good agreement between simulated and analytical results for both the mswe expressions and the optimum value of the lms step size parameter is shown

performance analysis of the linearly constrained constant modulus algorithm based multiuser detector this paper quantifies the adaptive performance of a blind adaptive multiuser detector mud based on the linearly constrained constant modulus algorithm lccma in both a stationary and nonstationary channel a framework is developed to apply the feedback analysis method to analyzing adaptive mud schemes a closed form expression for the excess mean square error emse of lccma blind adaptive mud in a cdma communications system is derived for both of the steady state and tracking cases the effects of additive noise and multiple access interference are considered a transient analysis is performed that predicts the learning curve of the adaptive filter computer simulation is used to verify the accuracy of the analysis

transient analysis of data normalized adaptive filters this paper develops an approach to the transient analysis of adaptive filters with data normalization among other results the derivation characterizes the transient behavior of such filters in terms of a linear time invariant state space model the stability of the model then translates into the mean square stability of the adaptive filters likewise the steady state operation of the model provides information about the mean square deviation and mean square error performance of the filters in addition to deriving earlier results in a unified manner the approach leads to stability and performance results without restricting the regression data to being gaussian or white the framework is based on energy conservation arguments and does not require an explicit recursion for the covariance matrix of the weight error vector

adaptive fuzzy filtering in a deterministic setting many real world applications involve the filtering and estimation of process variables this study considers the use of interpretable sugeno type fuzzy models for adaptive filtering our aim in this study is to provide different adaptive fuzzy filtering algorithms in a deterministic setting the algorithms are derived and studied in a unified way without making any assumptions on the nature of signals i e process variables the study extends in a common framework the adaptive filtering algorithms usually studied in signal processing literature and p norm algorithms usually studied in machine learning literature to semilinear fuzzy models a mathematical framework is provided that allows the development and an analysis of the adaptive fuzzy filtering algorithms we study a class of nonlinear lms like algorithms for the online estimation of fuzzy model parameters a generalization of the algorithms to the p norm is provided using bregman divergences a standard tool for online machine learning algorithms

controlling the false discoveries in lasso the lasso method estimates coefficients by minimizing the residual sum of squares plus a penalty term the regularization parameter in lasso controls the trade off between data fitting and sparsity we derive relationship between and the false discovery proportion fdp of lasso estimator and show how to select so as to achieve a desired fdp our estimation is based on the asymptotic distribution of lasso estimator in the limit of both sample size and dimension going to infinity with fixed ratio we use a factor analysis model to describe the dependence structure of the design matrix an efficient majorization minimization based algorithm is developed to estimate the fdp at fixed value of the analytic results are compared with those of numerical simulations on finite size systems and are confirmed to be correct an application to the high throughput genomic riboavin data set also demonstrates the usefulness of our method

application of orthonormal transforms to implementation of quasi lms newton algorithm an efficient implementation of the lms newton lmsn algorithm is proposed the scheme uses a quasi inverse of the correlation matrix of the input instead of its exact inverse the proposed algorithm which is an alternative formulation of a class of transform domain adaptive filters tdafs has some advantages over the tdaf a feature of the scheme that greatly simplifies its implementations is the possibility of coarse quantization of the stochastic gradient terms in the adjustment recursion to back this up an analysis of the lmsn algorithm which includes the effect of coarse quantization of the stochastic gradient terms is given for correlated gaussian data computer simulation results that support the developed theories are also presented

adaptive mlsde using the em algorithm the theory of adaptive sequence detection incorporating estimation of channel and related parameters is studied in the context of maximum likelihood ml principles in a general framework based on the expectation and maximization em algorithm a generalized ml sequence detection and estimation gmlsde criterion is derived based on the em approach and it is shown how the per survivor processing and per branch processing methods emerge naturally from gmlsde gmlsde is developed into a real time detection estimation algorithm using the online em algorithm with coupling between estimation and detection by utilizing titterington s 1984 stochastic approximation approach different adaptive ml sequence detection and estimation mlsde algorithms are formulated in a unified manner for different channel models and for different amounts of channel knowledge available at the receiver computer simulation results are presented for differentially encoded quadrature phase shift keying in frequency flat and selective fading channels and comparisons are made among the performances of the various adaptive mlsde algorithms derived earlier

optimum step size of sign algorithm for nonstationary adaptive filtering the adaptive filtering sign algorithm is analyzed in the case of nonstationary and correlated data the excess time average absolute estimation error eaae is used as a performance index of the algorithm it is proved that the eaae is the sum of two terms one proportional to the algorithm step size mu and the other proportional to 1 mu the optimum step size that minimizes the eaae is found equal to square root q p with q being the power of fluctuations of the optimal filter weights and p being the power of filter input this formula is derived under the assumption that increments of optimal filter weights are white computer simulations are used to examine the validity of the formula for other models of variation of the optimal filter simulation results show a good fit with the obtained optimum step size formula

a fast quasi newton adaptive filtering algorithm the convergence rate of an adaptive system is closely related to its ability to track a time varying optimum basic adaptive filtering algorithms give poor convergence performance when the input to the adaptive system is colored more sophisticated algorithms which converge very rapidly regardless of the input spectrum algorithms typically require o n sup 2 computation where n is the order of the adaptive filter a significant disadvantage for real time applications also many of these algorithms behave poorly in finite precision implementation an adaptive filtering algorithm is introduced which employs a quasi newton approach to give rapid convergence even with colored inputs the algorithm achieves an overall computational requirement of o n and appears to be quite robust in finite precision implementations