performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

a novel kurtosis driven variable step size adaptive algorithm a new variable step size lms filter is introduced the time varying step size sequence is adjusted utilizing the kurtosis of the estimation error therefore reducing performance degradation due to the existence of strong noise the convergence properties of the algorithm are analyzed and an adaptive kurtosis estimator that takes into account noise statistics and optimally adapts itself is also presented simulation results confirm the algorithm s improved performance and flexibility

on the optimum gain parameter in lms adaptation in this correspondence the optimum selection of the adaptation parameter in lms adaptive estimation is discussed for a white data covarianee matrix it is shown via analysis and numerical evaluation that the optimum selection of is a complicated function of the number of filter taps the initial weight setting the wiener weights and the number of learning samples is not chosen in general to yield the most rapid transient response for most cases of interest a smaller value of will be selected for slower adaptation and smaller misadjustment error at the end of the learning phase

optimal regularization parameter of the multichannel filtered x affine projection algorithm we discuss the optimal regularization parameter of the filtered affine projection fx ap algorithm suitable for feedforward active noise control while the original fx ap algorithm always provides a biased estimate of the minimum mean square solution we show that the optimal regularized fx ap algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual mse of the algorithm we derive some expressions for the optimal regularization parameter and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions

fuzzy based learning rate determination for blind source separation many independent component analysis ica algorithms have been proposed for blind source separation these algorithms belong to the lms type algorithm in natural hence the choice of the step size reflects a tradeoff between misadjustment and the speed of convergence based on the separation state of outputs of the neural network for ica the paper develops a fuzzy inference based step size selection algorithm the fuzzy inference system consists of two inputs the second and higher order correlation coefficients of output components and one output the fuzzy learning rate in this way the ica algorithms become more efficient which is verified by simulation results

low complexity stochastic gradient pursuit algorithm and architecture for robust compressive sensing reconstruction compressive sensing cs is able to measure sparse signals with fewer measurements than nyquist rate the reconstruction of sparse signals in cs is an underdetermined problem for realistic applications the sparsity information may not be available the measurements are used to be disturbed by noise and efficient hardware realization is important existing cs reconstruction algorithms are tradeoff between noise tolerance and low complexity in this paper we propose a novel reconstruction algorithm called stochastic gradient pursuit sgp the stochastic gradient approach is applied to replace least square process of well known orthogonal matching pursuit omp algorithm since stochastic gradient approach iterates toward a minimum mean square error solution proposed algorithm shows robustness against noise furthermore proposed algorithm inherits the low complexity property of omp and shows feasibility of hardware implementation the sgp algorithm can achieve 36 higher success rate as well as 27 less complexity than omp when snr is 20 db finally we implement the algorithm with designed hardware sharing architecture in tsmc 90 nm technology the postlayout result shows that the core size is only 1 08 mm 2 at 150 mhz operation frequency compared with state of the art asic designs the proposed engine achieves 29 higher throughput to area ratio

applications of a variable step size algorithm to qcee adaptive iir filters the quadratic constraint equation error qcee method was proposed by ho and chan see ibid vol 43 no 1 p 51 62 1995 to achieve bias removal for the equation error adaptive iir filters however this approach is limited to slow convergence in estimation when a small step size is used large step sizes lead to significant misadjustment this article presents a variable step size vss technique to greatly improve the qcee under its quadratic constraint to achieve both fast convergence and reduced misadjustment for adaptive iir filters

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

consistent normalized least mean square filtering with noisy data matrix when the ordinary least squares method is applied to the parameter estimation problem with noisy data matrix it is well known that the estimates turn out to be biased while this bias term can be somewhat reduced by the use of models of higher order or by requiring a high signal to noise ratio snr it can never be completely removed consistent estimates can be obtained by means of the instrumental variable method ivm or the total data least squares method tls dls in the adaptive setting for the such problem a variety of least mean squares lms type algorithms have been researched rather than their recursive versions of ivm or tls dls that cost considerable computations motivated by these observations we propose a consistent lms type algorithm for the data least square estimation problem this novel approach is based on the geometry of the mean squared error mse function rendering the step size normalization and the heuristic filtered estimation of the noise variance respectively for fast convergence and robustness to stochastic noise monte carlo simulations of a zero forcing adaptive finite impulse response fir channel equalizer demonstrate the efficacy of our algorithm

reduced complexity self tuning adaptive algorithms in application to channel estimation in this letter reduced complexity self tuning algorithms are proposed using simplified parameter updating procedures convergence analysis based on the independence assumption and the ordinary differential equation ode method shows that the tuning parameter of the proposed algorithm attains the same limit as the conventional self tuning adaptive algorithm simulations are carried out for channel estimation to support the analysis and performance of the proposed algorithms

an online auc formulation for binary classification the area under the roc curve auc provides a good scalar measure of ranking performance without requiring a specific threshold for performance comparison among classifiers auc is useful for imprecise environments since it operates independently with respect to class distributions and misclassification costs a direct optimization of this auc criterion thus becomes a natural choice for binary classifier design however a direct formulation based on the auc criterion would require a high computational cost due to the drastically increasing input pair features in this paper we propose an online learning algorithm to circumvent this computational problem for binary classification different from those conventional recursive formulations the proposed formulation involves a pairwise cost function which pairs up a newly arrived data point with those of opposite class in stored data moreover with incorporation of a sparse learning into the online formulation the computational effort can be significantly reduced our empirical results on three different scales of public databases show promising potential in terms of classification auc accuracy and computational efficiency

an affine combination of two lms adaptive filters transient mean square analysis this paper studies the statistical behavior of an affine combination of the outputs of two least mean square lms adaptive filters that simultaneously adapt using the same white gaussian inputs the purpose of the combination is to obtain an lms adaptive filter with fast convergence and small steady state mean square deviation msd the linear combination studied is a generalization of the convex combination in which the combination factor lambda n is restricted to the interval 0 1 the viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel thus there exists a sequence of optimal affine combining coefficients which minimizes the mean square error mse first the optimal unrealizable affine combiner is studied and provides the best possible performance for this class then two new schemes are proposed for practical applications the mean square performances are analyzed and validated by monte carlo simulations with proper design the two practical schemes yield an overall msd that is usually less than the msds of either filter

low complexity variable step size mechanisms for stochastic gradient algorithms in minimum variance cdma receivers in this paper the performance of blind adaptive receivers for direct sequence code division multiple access ds cdma systems that employ stochastic gradient sg algorithms with variable step size mechanisms is investigated two low complexity variable step size mechanisms are proposed for estimating the parameters of linear cdma receivers that operate with sg algorithms for multipath channels the novel adaptation mechanisms are also incorporated in the channel estimation algorithms whereas for the single path case the novel techniques are restricted to the linear receiver parameter vector estimation analytical expressions for the excess mean squared error mse are derived and a convergence analysis of the proposed adaptation techniques is carried out for both frequency selective and flat scenarios finally numerical experiments are presented for nonstationary environments showing that the new mechanisms achieve superior performance to previously reported methods at a reduced complexity

on minimum wer performance of a class of ldpc codes for the bsc e under extended bounded distance decoding we study the word error rate wer performance and the wer minimizing decision thresholds plusmnt for the class of row column diagonal rcd array codes and their generalizations on the binary symmetric channel with erasures bsc e where decoding is via an extended bounded distance decoder e bdd this model applies to very high data rate systems where soft decision iterative decoding is impractical we demonstrate that substantial wer performance gain can be obtained especially at higher channel signal to noise ratio csnr csnr delta 10 log10 1 2sigma2 values by employing two optimal thresholds plusmnt chosen to minimize wer we study the wer improvement and signal to noise ratio snr performance gain as a function of code length n for fixed minimum distance dmin and as a function of dmin for fixed n a distinct difference in the behavior of wer versus the threshold t and the optimal threshold t versus snr is observed between codes with odd and even dmin with the even dmin codes exhibiting larger performance improvements when employing a bsc e instead of a bsc

stochastic adaptive control for exponentially convergent time varying systems this paper shows that the standard stochastic adaptive control algorithms for time invariant systems have an inherent robustness property which renders them applicable without modification to time varying systems whose parameters converge exponentially one class of systems satisfying this requirement is those having non steady state kalman filter or innovations representations this allows the usual assumption of a stationary armax representation to be replaced by a more general state space model

on the probability density function of the lms adaptive filter weights the joint probability density function of the weight vector in least mean square lms adaptation is studied for gaussian data models an exact expression is derived for the characteristic function of the weight vector at time n 1 conditioned on the weight vector at time n the conditional characteristic function is expanded in a taylor series and averaged over the unknown weight density to yield a first order partial differential difference equation in the unconditioned characteristic function of the weight vector the equation is approximately solved for small values of the adaption parameter and the weights are shown to be jointly gaussian with time varying mean vector and covariance matrix given as the solution to well known difference equations for the weight vector mean and covariance matrix the theoretical results are applied to analyzing the use of the weights in detection and time delay estimation simulations that support the theoretical results are also presented

uncoded and coded performance of mfsk and dpsk in nakagami fading channels the author presents uncoded and coded performance results for noncoherent m ary frequency shift keying mfsk and differentially coherent binary phase shift keying dpsk in a slow nonselective nakagami m 1960 fading channel he gives simple expressions for the asymptotic slopes of probability of bit error for large signal to noise ratio and shows that the effective order of diversity compared to an uncoded rayleigh channel is the product of two parameters one for the channel and one for the code he also compares the uncoded nakagami m results to those of the rician channel in order to show performance differences between these two generalized fading channel models

new analytical probability of error expressions for classes of orthogonal signals in rayleigh fading new exact expressions for the symbol error rate and bit error rate of coherent 3 ary and 4 ary orthogonal and transorthogonal signaling in slowly fading rayleigh channels are derived new exact error probability expressions for coherent 6 ary and 8 ary biorthogonal signaling in slow rayleigh fading are also presented the use of these exact expressions as accurate approximations for the error rates of m ary orthogonal biorthogonal and transorthogonal signaling with arbitrary m is illustrated

on the symbol error probability of maximum selection diversity reception schemes over a rayleigh fading channel the symbol error probability of two selection schemes namely maximum signal to noise ratio m gamma selection and maximum output mo selection for m ary multidiversity reception over a rayleigh fading channel are discussed the symbol error probability of the mo scheme is lower than that of the m gamma scheme the more diversity receptions that are used the larger is the difference a simple expression of crossover average signal to noise ratio per bit is presented as a guideline for increasing the number of diversity receptions

a variable step size lms algorithm a least mean square lms adaptive filter with a variable step size is introduced the step size increases or decreases as the mean square error increases or decreases allowing the adaptive filter to track changes in the system as well as produce a small steady state error the convergence and steady state behavior of the algorithm are analyzed the results reduce to well known results when specialized to the constant step size case simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual lms algorithm and another variable step size algorithm they show that its performance compares favorably with these existing algorithms

an mgf based performance analysis of generalized selection combining over rayleigh fading channels using the notion of the spacing between ordered exponential random variables a performance analysis of the generalized selection combining gsc diversity scheme over rayleigh fading channels is presented and compared with that of the conventional maximal ratio combining and selection combining schemes starting with the moment generating function mgf of the gsc output signal to noise ratio snr we derive closed form expressions for the average combined snr outage probability and average error probability of a wide variety of modulation schemes operating over independently identically distributed i i d diversity paths because of their simple form these expressions readily allow numerical evaluation for cases of practical interest the results are also extended to the case of non i i d diversity paths

a variable step vs adaptive filter algorithm in recent work a new version of an lms algorithm has been developed which implements a variable feedback constant for each weight of an adaptive transversal filter this technique has been called the vs variable step algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents the method may be implemented in hardware with only modest increases in complexity approx 15 percent over the lms widrow hoff algorithm it is shown that an upper bound for the convergence time is the classical mean square error time constant and examples are given to demonstrate that for broad signal classes both narrow band and broad band the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters finally the vs algorithm is applied to an iir filter and simulations are presented for applications of the vs fir and iir adaptive filters

low complexity variable forgetting factor mechanism for blind adaptive constrained constant modulus algorithms in this paper we propose a novel low complexity variable forgetting factor vff mechanism for blind adaptive constrained constant modulus ccm recursive least squares rls algorithms applied to linear interference suppression in direct sequence code division multiple access ds cdma systems the proposed variable forgetting factor mechanism employs an updated component related to the time average of the constant modulus cm cost function to automatically adjust the forgetting factor in order to ensure good tracking of the interference and the channel convergence and tracking analyses are carried out analytical expressions for predicting the mean squared error of the proposed adaptation technique are obtained simulation results are presented for nonstationary environments and show that the proposed variable forgetting factor mechanism achieves superior performance to previously reported methods at a reduced complexity

mean square performance of a convex combination of two adaptive filters combination approaches provide an interesting way to improve adaptive filter performance in this paper we study the mean square performance of a convex combination of two transversal filters the individual filters are independently adapted using their own error signals while the combination is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure general expressions are derived that show that the method is universal with respect to the component filters i e in steady state it performs at least as well as the best component filter furthermore when the correlation between the a priori errors of the components is low enough their combination is able to outperform both of them using energy conservation relations we specialize the results to a combination of least mean square filters operating both in stationary and in nonstationary scenarios we also show how the universality of the scheme can be exploited to design filters with improved tracking performance

the stability of variable step size lms algorithms variable step site lms vslms algorithms are a popular approach to adaptive filtering which can provide improved performance while maintaining the simplicity and robustness of conventional fixed step size lms here we examine the stability of vslms with uncorrelated stationary gaussian data most vslms described in the literature use a data dependent step size where the step size either depends on the data before the current time prior step size rule or through the current time posterior step size rule it has often been assumed that vslms algorithms are stable in the sense of mean square bounded weights provided that the step size is constrained to lie within the corresponding stability region for the lms algorithm for a single tap fitter we find exact expressions for the stability region of vslms over the classes of prior and posterior step sizes and show that the stability region for prior step size coincides with that of fixed step size but the region for posterior step size is strictly smaller than for fixed step size for the multiple tap case we obtain bounds on the stability regions with similar properties the approach taken here is a generalization of the classical method of analyzing the exponential stability of the weight covariance equation for lms although it is not possible to derive a weight covariance equation for general data dependent vslms the weight variances can be upper bounded by the solution of a linear time invariant difference equation after appropriately dealing with certain nonlinear terms for prior step size like fixed step size the state matrix is symmetric whereas for posterior step size the symmetry is lost requiring a more detailed analysis the results are verified by computer simulations

asymptotic performance of m ary orthogonal signals in worst case partial band interference and rayleigh fading it is shown that for worst case partial band jamming the error probability performance for fixed e sub b n sub i becomes worse with increasing m for m 16 the asymptotic probability of error is not zero for any e sub b n sub i ln 2 but decreases inverse linearly with respect to it in the fading case the error probability performance for fixed e sub b n sub 0 improves with m for noncoherent detection but worsens with m for coherent detection for large e sub b n sub 0 the performance of the rayleigh fading channel asymptotically approaches the same limit as the worst case partial band jammed channel however for values of m at least up to 4096 the partial band jammed channel does better while it is unlikely that an m ary orthogonal signal set with m 1024 will be used in a practical situation these results suggest an important theoretical problem namely what signal set achieves reliable communication

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

on some generalizations of the thue morse morphism in 1912 the norwegian mathematician axel thue was the first to describe an overlap free binary infinite word this word was generated by a morphism which is called since the works of morse the thue morse morphism here we present two generalizations of the thue morse morphism in the case of alphabets with more than two letters the extension of the characteristic properties of the word of thue to the words generated by these morphisms is considered one of these generalizations corresponds to the construction of prouhet and a link with the arshon words is given in particular we prove that if n is an even number then the n letter arshon word is generated by morphism

comparison of diversity combining techniques for rayleigh fading channels several methods of diversity combining for a rayleigh faded channel are evaluated and compared the methods considered are for coherent reception maximal ratio combining mrc selection combining sc and a generalization of sc whereby the two three signals with the two three largest amplitudes are coherently combined we will call this method second third order sc and denote it sc2 sc3 similar techniques are also investigated for noncoherent reception with equal gain combining egc replacing mrc and noncoherent versions of sc2 and sc3 numerical results indicate that sc2 and sc3 significantly enhances the bit error rate ber performance relative to that achievable with sc and under certain conditions approaches the performance achieved by mrc or egg the performance enhancement of sc2 and sc3 is especially noticable for noncoherent reception where egc is seen to provide the best performance only for low ber values in fact when the ber is 10 sup 3 or greater sc2 and sc3 performed comparably to egg and in some cases performed better than egc

some combinatorial properties of the thue morse sequence and a problem in semigroups abstract some combinatorial properties of the special factors of the thue morse sequence in a two letter alphabet are considered an application of this analysis to a problem in semigroups is given

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

coding for frequency hopped spread spectrum communication with partial band interference part i capacity and cutoff rate the performance of optimal codes on frequency hopped channels with partial band interference is investigated the performance measures considered are channel capacity and cutoff rate worst case partial band gaussian noise interference is assumed with the interference independent of the transmitted signal the capacity and cutoff rate are calculated as a function of the signal to noise ratio we consider soft decision receivers and hard decision receivers with and without side information optimal code rates are found for each of the above cases the required signal to noise ratio for reliable communication when codes are used is determined as a function of the code rate

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

recursive nonlinear system identification by a stochastic gradient algorithm stability performance and model nonlinearity considerations a parameter estimation problem in a class of nonlinear systems is considered where the input output relation of a nonlinear system is approximated by a polynomial model e g a volterra series a least mean squares lms type algorithm is utilized for the recursive estimation of the polynomial coefficients and its resulting mean square error mse convergence properties are investigated conditions for the algorithm stability in the mean square sense are established steady state mse bounds are obtained and the convergence rate is discussed in addition modeling accuracy versus steady state performance is examined it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance that is yielding a larger steady state mse linear system identification is studied as a special case

on the subword complexity of thue morse polynomial extractions let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m is the number of distinct blocks of length m in u let t t n n 0 denote the thue morse sequence in this paper we study the complexity of the sequences t h t h n n 0 when h n q n is a polynomial with h n n in particular we solve an open problem of allouche and shallit regarding t n 2 n 0 we also study the vector space over z 2z spanned by the sequences t h

on the irrationality exponent of the regular paperfolding numbers abstract in this paper improving the method of allouche et al we calculate the hankel determinant of the regular paperfolding sequence and prove that the hankel determinant sequence modulo 2 is periodic with period 10 which answers coon s conjecture then we extend bugeaud s method to obatin the exact value of the irrationality exponent for some general transcendental numbers using the results above we prove that the irrationality exponents of the regular paperfolding numbers are exactly 2

blind adaptive constrained reduced rank parameter estimation based on constant modulus design for cdma interference suppression this paper proposes a multistage decomposition for blind adaptive parameter estimation in the krylov subspace with the code constrained constant modulus ccm design criterion based on constrained optimization of the constant modulus cost function and utilizing the lanczos algorithm and arnoldi like iterations a multistage decomposition is developed for blind parameter estimation a family of computationally efficient blind adaptive reduced rank stochastic gradient sg and recursive least squares rls type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods an analysis of the convergence properties of the method is carried out and convergence conditions for the reduced rank adaptive algorithms are established simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in ds cdma systems

performance limits of m fsk with reed solomon coding and diversity combining this paper examines the asymptotic m spl rarr spl infin performance of m ary frequency shift keying m fsk in multi channels or multiple frequency nonselective slowly fading channels with coding side information and diversity reception in particular reed solomon rs coding is considered in conjunction with the ratio threshold test rtt which generates side information regarding the reliability of received symbols the asymptotic performance of orthogonal signaling in multichannels with maximal ratio combining mrc postdetection equal gain combining egc hybrid selection combining h sc and selection combining sc is derived for an arbitrary statistical fading model and diversity order the derivations reveal that coherent and noncoherent implementations of diversity combining schemes yield the same performance asymptotically in addition the asymptotic results are evaluated assuming a nakagami m fading model and the effect of fading severity diversity order code rate and side information upon the performance of the various diversity combiners is investigated the minimum signal to noise ratio snr required to achieve arbitrarily reliable or error free communication as well as the associated optimal rs code rate are determined for various cases

krylov proportionate adaptive filtering techniques not limited to sparse systems this paper proposes a novel adaptive filtering scheme named the krylov proportionate normalized least mean square kpnlms algorithm kpnlms exploits the benefits i e fast convergence for sparse unknown systems of the proportionate nlms algorithm but its applications are not limited to sparse unknown systems a set of orthonormal basis vectors is generated from a certain krylov sequence it is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data different adaptation gain is allocated to a coefficient of each basis vector and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate kpnlms enjoys i fast convergence ii linear complexity per iteration and iii no use of any a priori information numerical examples demonstrate significant advantages of the proposed scheme over the reduced rank method based on the multistage wiener filter mwf and the transform domain adaptive filter tdaf both in noisy and silent situations

a variable step size diffusion lms algorithm for distributed estimation we propose a new variable step size diffusion least mean square algorithm for distributed estimation that adaptively adjusts the step size in every iteration for a network application the proposed method determines a suboptimal step size at each node to minimize the mean square deviation for the intermediate estimate the algorithm thus adapts the different node environments and profiles across the networks and requires relatively less user interaction than existing algorithms in experiments the algorithm achieves both fast convergence speed and low misadjustment by remarkable improvement in an adaptation stage we analyze the mean square performance of the proposed algorithm also the proposed algorithm works well even in non stationary environments

adaptive orthogonal signaling with diversity in a frequency nonselective rayleigh fading channel power and rate adaptations with diversity are considered for m ary orthogonal signals in a frequency nonselective rayleigh fading channel we derived the minimum required e sub b n sub 0 for a given probability of error the maximum average data rate and the outage probability when maximal ratio combining is performed with an imperfect channel estimation we analyzed the effects of channel estimation errors on the required e sub b n sub 0 and outage probability as a function of diversity order and adaptation methods the relative benefits of rate and power control techniques are further presented in terms of channel estimation error diversity order and outage probability the minimum required e sub b n sub 0 with reed solomon codes is also presented for comparison purposes

a new variable step size nlms algorithm and its performance analysis numerous variable step size normalized least mean square vss nlms algorithms have been derived to solve the dilemma of fast convergence rate or low excess mean square error in the past two decades this paper proposes a new easy to implement nonparametric vss nlms algorithm that employs the mean square error and the estimated system noise power to control the step size update theoretical analysis of its steady state behavior shows that when the input is zero mean gaussian distributed the misadjustment depends only on a parameter controlling the update of step size simulation experiments show that the proposed algorithm performs very well furthermore the theoretical steady state behavior is in very good agreement with the experimental results

increasing the speed of convergence of the constant modulus algorithm for blind channel equalization the constant modulus algorithm cma is an excellent technique for blind channel equalization a signed error version of cma se cma and dithered signed error version dse cma have been proposed which afford overall computational efficiency we propose three different error functions for faster convergence this would be essential for communication systems which cannot afford a high startup delay or for systems where the channel s impulse response is rapidly fluctuating one of these algorithms relies on the idea of a variable step size which increases the rate of convergence

a set of algorithms linking nlms and block rls algorithms this paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares nlms and the block recursive least squares brls algorithms all these algorithms use small block lengths thus allowing easy implementation and small input output delay it is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares lms algorithm while converging much faster a precise evaluation of the arithmetic complexity is provided and the adaptive behavior of the algorithm is analyzed simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the nlms algorithm the conclusions of the theoretical analysis are checked by simulations illustrating that even in the case where noise is added to the reference signal the proposed algorithm allows altogether a faster convergence and a lower residual error than the nlms algorithm finally a sample by sample version of this algorithm is outlined which is the link between the nlms and recursive least squares rls algorithms

a robust variable step size lms type algorithm analysis and simulations a number of time varying step size algorithms have been proposed to enhance the performance of the conventional lms algorithm experimentation with these algorithms indicates that their performance is highly sensitive to the noise disturbance this paper presents a robust variable step size lms type algorithm providing fast convergence at early stages of adaptation while ensuring small final misadjustment the performance of the algorithm is not affected by existing uncorrelated noise disturbances an approximate analysis of convergence and steady state performance for zero mean stationary gaussian inputs and for nonstationary optimal weight vector is provided simulation results comparing the proposed algorithm to current variable step size algorithms clearly indicate its superior performance for cases of stationary environments for nonstationary environments our algorithm performs as well as other variable step size algorithms in providing performance equivalent to that of the regular lms algorithm

performance limits of reed solomon coded cdma with orthogonal signaling in a rayleigh fading channel the asymptotic performance of reed solomon rs coded m ary orthogonal signaling with ratio threshold test rtt type demodulation in a rayleigh fading channel is considered we show that the minimum e sub b n sub 0 needed for error free communication is eln2 2 75 db with rtt and 4 79 6 8 db with hard decisions the optimum code rate that minimizes the required e sub b n sub 0 is e sup 1 with rtt and 0 46 with hard decision and the optimum ratio threshold approaches 1 for large m next we investigate the fundamental limit in a direct sequence spread spectrum multiple access ds ssma system employing an m ary orthogonal code of length n mm which is obtained by spreading every row of an m spl times m hadamard matrix with a user specific random sequence of length n we derive the minimum e sub b n sub 0 for error free communication as a function of the number of users the optimum code rate that minimizes e sub b n sub 0 and the maximum limit on the total information transmission rate then we consider a multirate ds ssma system where a population of users simultaneously transmit at different power levels a variety of traffic types of different information rates we derive the minimum required e sub b n sub 0 and the optimum code rate for each traffic type

noise constrained least mean squares algorithm we consider the design of an adaptive algorithm for finite impulse response channel estimation which incorporates partial knowledge of the channel specifically the additive noise variance although the noise variance is not required for the offline wiener solution there are potential benefits and limitations for the learning behavior of an adaptive solution in our approach a robbins monro algorithm is used to minimize the conventional mean square error criterion subject to a noise variance constraint and a penalty term necessary to guarantee uniqueness of the combined weight multiplier solution the resulting noise constrained lms nclms algorithm is a type of variable step size lms algorithm where the step size rule arises naturally from the constraints a convergence and performance analysis is carried out and extensive simulations are conducted that compare nclms with several adaptive algorithms this work also provides an appropriate framework for the derivation and analysis of other adaptive algorithms that incorporate partial knowledge of the channel

a class of adaptive step size control algorithms for adaptive filters a class of new adaptive step size control algorithms which is applicable to most of the lms derived tap weight adaptation algorithms is proposed analysis yields a set of difference equations for theoretically calculating the transient behavior of the filter convergence and derives an explicit formula for the steady state excess mean square error emse experiments for some examples prove that the proposed algorithm is highly effective in improving the convergence rate in both transient and tracking phases the theoretically calculated convergence is shown to be in good agreement with that obtained through simulations alternative formulae of the step size adaptation for specific tap weight adaptation algorithms are also proposed

on t extensions of the hankel determinants of certain automatic sequences in 1998 allouche peyriere wen and wen considered the thue morse sequence and proved that all the hankel determinants of the period doubling sequence are odd integers we speak of t extension when the entries along the diagonal in the hankel determinant are all multiplied by t we prove that the t extension of each hankel determinant of the period doubling sequence is a polynomial in t whose leading coefficient is the only one to be an odd integer our proof makes use of the combinatorial set up developed by bugeaud and han which appears to be very suitable for this study as the parameter t counts the number of fixed points of a permutation finally we prove that all the t extensions of the hankel determinants of the regular paperfolding sequence are polynomials in t of degree less than or equal to 3

low density parity check codes based on finite geometries a rediscovery and new results this paper presents a geometric approach to the construction of low density parity check ldpc codes four classes of ldpc codes are constructed based on the lines and points of euclidean and projective geometries over finite fields codes of these four classes have good minimum distances and their tanner 1981 graphs have girth 6 finite geometry ldpc codes can be decoded in various ways ranging from low to high decoding complexity and from reasonably good to very good performance they perform very well with iterative decoding furthermore they can be put in either cyclic or quasi cyclic form consequently their encoding can be achieved in linear time and implemented with simple feedback shift registers this advantage is not shared by other ldpc codes in general and is important in practice finite geometry ldpc codes can be extended and shortened in various ways to obtain other good ldpc codes several techniques of extension and shortening are presented long extended finite geometry ldpc codes have been constructed and they achieve a performance only a few tenths of a decibel away from the shannon theoretical limit with iterative decoding

asymptotic performance of m ary orthogonal modulation in generalized fading channels the asymptotic m to infinity probability of symbol error p sub e sub m for m ary orthogonal modulation in a nakagami m fading channel is given by the incomplete gamma function p m mx where x in 2 e sub b n sub 0 and e sub b is the average energy per bit for large signal to noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of e sub b n sub 0 these channels exist for all m or 1 2 the special case of m 1 corresponds to rayleigh fading an inverse linear channel