an eigenanalysis interference canceler eigenanalysis methods are applied to interference cancellation problems while with common array processing methods the cancellation is effected by global optimization procedures that include the interferences and the background noise the proposed technique focuses on the interferences only resulting in superior cancellation performance furthermore the method achieves full effectiveness even for short observation times when the number of samples used for processing is of the the order of the number of interferences adaptive implementation is obtained with a simple fast converging algorithm

entropy sensitivity of languages defined by infinite automata via markov chains with forbidden transitions a language l over a finite alphabet is growth sensitive or entropy sensitive if forbidding any finite set of factors f of l yields a sublanguage lf whose exponential growth rate entropy is smaller than that of l let x e be an infinite oriented edge labelled graph with label alphabet considering the graph as an infinite automaton we associate with any pair of vertices x y x the language lx y consisting of all words that can be read as labels along some path from x to y under suitable general assumptions we prove that these languages are growth sensitive this is based on using markov chains with forbidden transitions

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a multistage representation of the wiener filter based on orthogonal projections the wiener filter is analyzed for stationary complex gaussian signals from an information theoretic point of view a dual port analysis of the wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the wiener filter using a nested chain of scalar wiener filters this new representation of the wiener filter provides the capability to perform an information theoretic analysis of previous basis dependent reduced rank wiener filters this analysis demonstrates that the cross spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes a new reduced rank wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal lower dimensional subspaces the performance is evaluated using a comparative computer analysis model and it is demonstrated that the low complexity multistage reduced rank wiener filter is capable of outperforming the more complex eigendecomposition based methods

shrinkage of covariance matrices for linear signal estimation using cross validation linear estimation of signals is often based on covariance matrices estimated from training which can perform poorly if the training data are limited and the estimated covariance matrices are ill conditioned shrinking the covariance matrix toward a scaled identity matrix can improve the robustness against the model uncertainty provided the shrinkage factor is appropriately chosen this paper introduces several cross validation schemes for choosing the shrinkage factors in applications where the covariance matrices are replaced with sample covariance matrices or constructed from least squares estimates of the linear model parameters for cases where the training and out of training data are identically distributed we derive leave one out cross validation loocv schemes that repeatedly split the training data with respect to time to determine the optimal shrinkage factors for either model fitting or signal estimation for cases where they are distributed differently we develop alternative loocv schemes that repeatedly split the out of training observations with respect to space we derive computationally efficient implementations of those schemes and provide examples to demonstrate their performance

adaptive reduced rank constrained constant modulus algorithms based on joint iterative optimization of filters for beamforming this paper proposes a robust reduced rank scheme for adaptive beamforming based on joint iterative optimization jio of adaptive filters the novel scheme is designed according to the constant modulus cm criterion subject to different constraints the proposed scheme consists of a bank of full rank adaptive filters that forms the transformation matrix and an adaptive reduced rank filter that operates at the output of the bank of filters to estimate the desired signal we describe the proposed scheme for both the direct form processor dfp and the generalized sidelobe canceller gsc structures for each structure we derive stochastic gradient sg and recursive least squares rls algorithms for its adaptive implementation the gram schmidt gs technique is applied to the adaptive algorithms for reformulating the transformation matrix and improving the performance an automatic rank selection technique is developed and employed to determine the most adequate rank for the derived algorithms a detailed complexity study and a convexity analysis are carried out simulation results show that the proposed algorithms outperform the existing full rank and reduced rank methods in convergence and tracking performance

optimal transform formed by a combination of nonlinear operators the case of data dimensionality reduction in this paper a new approach to constructing optimal nonlinear transforms of random vectors is proposed and justified the proposed transform t sub p is presented in the form of a sum with p terms where each term is interpreted as a particular rank reduced transform moreover terms in t sub p are represented as a combination of three operations f sub k q sub k and spl psi sub k with k 1 p the prime idea is to determine f sub k separately for each k 1 p from an associated rank constrained minimization problem similar to that used in the karhunen loe spl grave ve transform klt the operations q sub k and spl psi sub k are auxiliary for finding f sub k the contribution of each term in t sub p improves the entire transform performance a rigorous analysis of errors associated with the proposed transforms is given it is shown that the proposed transform improves such characteristics of rank reduced transforms as compression ratio and the accuracy of decompression and reduces required computational work the fourier series in hilbert space the wiener filter the klt and the transforms presented in earlier author papers in the field are particular cases of the proposed method theoretical results are illustrated with numerical simulations

a subspace method for signature waveform estimation in synchronous cdma systems synchronous code division multiple access cdma techniques possess intrinsic protection against co channel interference due to orthogonal codes employed and thus offers higher capacity than existing frequency division multiple access fdma or time division multiple access tdma systems in the presence of multipath however each signal is subject to frequency selective fading and the orthogonality condition does not necessarily hold leading to increased cross correlation in these scenarios multiuser detection need to be performed to suppress interference and recover the message symbols to implement such a technique explicit knowledge of the nonorthogonal signature waveforms of all users is required we propose a blind estimation scheme that provides closed form estimates of the signature waveforms by exploiting the structure information of the data output in particular we show that the subspace of the data matrix contains sufficient information for unique determination of the signature waveforms based on this observation a multiple signal classification music like algorithm is derived performance analysis of the new approach is also presented

canonical space time processing for wireless communications a canonical space time characterization of mobile wireless channels is introduced in terms of a fixed basis that is independent of the true channel parameters the basis captures the essential degrees of freedom in the received signal using discrete multipath delays doppler shifts and directions of arrival doa the canonical representation provides a robust representation of the propagation dynamics and eliminates the need for estimating delay doppler and doa parameters of different multipaths furthermore it furnishes a natural framework for designing low complexity space time receivers single user receivers based on the canonical channel representation are developed and analyzed it is demonstrated that the resulting canonical space time receivers deliver near optimal performance at substantially reduced complexity compared to existing designs

generalized consistent estimation on low rank krylov subspaces of arbitrarily high dimension the problem of krylov subspace estimation based on the sample covariance matrix is addressed the focus is on signal processing applications where the krylov subspace is defined by the unknown second order statistics of the observed samples and the signature vector associated with the desired parameter in particular the consistency of traditionally optimal sample estimators is revised and analytically characterized under a practically more relevant asymptotic regime according to which not only the number of samples but also the observation dimension grow without bound at the same rate furthermore an improved construction of a class of krylov subspace estimators is proposed based on the generalized consistent estimation of a set of vector valued power functions of the observation covariance matrix to that effect an extension of some known results from random matrix theory on the estimation of certain spectral functions of the covariance matrix to the convergence of not only the covariance eigenspectrum but also the associated eigensubspaces is provided a new family of estimators is derived that generalizes conventional implementations by proving to be consistent for observations of arbitrarily high dimension the proposed estimators are shown to outperform traditional constructions via the numerical evaluation of the solution to two fundamental problems in sensor array signal processing namely the problem of estimating the power of an intended source and the estimation of the principal eigenspace and dominant eigenmodes of a structured covariance matrix

the root number class and chinburg s second invariant let n k be a finite normal extension of number fields with g gal n k by e noether s theorem the ring of integers on of n is a projective z g module if and only if n k is at most tamely ramified thus for such n k 0 defines a class q n k on k q z g in the class group cl z g the finite torsion subgroup of the grothendieck group k z g of finitely generated g modules of finite projective dimension in 14 m taylor proved that in this case q n k is equal to the root number class wnik which was defined by ph cassou nogds and friihlich by means of the artin root numbers of the irreducible symplectic representations of g cf s chap 1 or 3 p 183 in 4 t chinburg defined galois invariants q n k i i 1 2 3 of n k in cl z g and proved q n k 2 qjn k for arbitrary n k which are at most tamely ramified since both classes q n k 2 and w are defined for all n k including those which are wildly ramified one may be led to the following conjecture

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

a linear receiver for direct sequence spread spectrum multiple access systems with antenna arrays and blind adaptation a linear receiver for direct sequence spread spectrum multiple access communication systems under the aperiodic random sequence model is considered the receiver consists of the conventional matched filter followed by a tapped delay line with the provision of incorporating the use of antenna arrays it has the ability of suppressing multiple access interference mai and narrowband interference in some weighted proportions as well as combining multipath components without explicit estimation of any channel conditions under some specific simplified channel models the receiver reduces to the minimum variance distortionless response beamformer the rake receiver a notch filter or an mai suppressor the interference rejection capability is made possible through a suitable choice of weights in the tapped delay line the optimal weights can be obtained by straightforward but computationally complex eigenanalysis in order to reduce the computational complexity a simple blind adaptive algorithm is also developed

on the equivalence of three reduced rank linear estimators with applications to ds cdma this correspondence shows the equivalence of three previously proposed reduced rank detection schemes for direct sequence code division multiple access ds cdma communication systems the auxiliary vector filtering avf algorithm is simplified through a key observation on the construction of the auxiliary vectors after simplification it is shown that the avf algorithm is equivalent to the multistage wiener filtering mwf algorithm of honig and goldstein 2002 furthermore these schemes can be shown to be equivalent to the multistage linear receiver scheme based on the cayley hamilton ch theorem when the minimum mean square error mmse criterion is applied to the reduced dimensional space of the received signal

on galois structure invariants associated to tate motives we establish the equivalence of two definitions of invariants measuring the galois module structure of k groups of rings of integers in number fields due to chinburg et al on the one hand and the authors on the other we also make some remarks concerning the possibility of yet another such definition via lichtenbaum complexes

performance of reduced rank linear interference suppression the performance of reduced rank linear filtering is studied for the suppression of multiple access interference a reduced rank filter resides in a lower dimensional space relative to the full rank filter which enables faster convergence and tracking we evaluate the large system output signal to interference plus noise ratio sinr as a function of filter rank d for the multistage wiener filter mswf presented by goldstein and reed the large system limit is defined by letting the number of users k and the number of dimensions n tend to infinity with k n fixed for the case where all users are received with the same power the reduced rank sinr converges to the full rank sinr as a continued fraction an important conclusion from this analysis is that the rank d needed to achieve a desired output sinr does not scale with system size numerical results show that d 8 is sufficient to achieve near full rank performance even under heavy loads k n 1 we also evaluate the large system output sinr for other reduced rank methods namely principal components and cross spectral which are based on an eigendecomposition of the input covariance matrix and partial despreading for those methods the large system limit lets d spl rarr spl infin with d n fixed our results show that for large systems the mswf allows a dramatic reduction in rank relative to the other techniques considered

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

on equivariant global epsilon constants for certain dihedral extensions we consider a conjecture of bley and burns which relates the epsilon constant of the equivariant artin l function of a galois extension of number fields to certain natural algebraic invariants for an odd prime number p we describe an algorithm which either proves the conjecture for all degree 2p dihedral extensions of the rational numbers or finds a counterexample we apply this to show the conjecture for all degree 6 dihedral extensions of q the correctness of the algorithm follows from a finiteness property of the conjecture which we prove in full generality

multi access interference suppression in canonical space time coordinates a decentralized approach we propose a decentralized space time multiuser detection scheme based on the notion of canonical space time coordinates cstcs for representing the received signal the cstc representation provides a natural framework for decentralized multi access interference mai suppression in lower dimensional subspaces that results in complexity reduction relative to existing chip rate filtering schemes the framework is based on a partitioning of the signal space into active and inactive cstcs the active cstcs contain the signal of the desired user facilitate maximal diversity exploitation and minimal complexity interference suppression the inactive cstcs only contain mai and can be included progressively to attain a desired level of mai suppression at the cost of increased complexity we develop cstc based linear coherent multiuser detectors using the linearly constrained minimum variance lcmv criterion we characterize the set of inactive coordinates and analyze the performance of the lcmv receiver as a function of the number of inactive cstcs channel estimation and detector sensitivity to channel estimation errors are discussed we demonstrate that the low complexity adaptive receivers designed via the cstc framework are more robust to channel estimation errors than existing chip domain filtering schemes

minimum variance beamforming with soft response constraints soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming a quadratic constraint on the beamformer weights is used to control the mean squared error between a desired response and the actual response in the signal direction the constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation under the assumptions of known signal direction and spectral shape the signal to noise ratio is shown to be a nondecreasing function of the mean square distortion the distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired properties of this beamforming method and its relationship to linear constrained beamforming are discussed simulations verify analytic results and illustrate the utility of the soft constrained approach

on the entropy of regular languages let l be an irreducible regular language let w be a non empty set of words or sub words of l and denote by lw v l w v w w the language obtained from l by forbidding all the words w in w then the entropy decreases strictly ent lw ent l in this note we present a new proof of this fact based on a method of gromov which avoids the perron frobenius theory this result applies to the regular languages of finitely generated free groups and an additional application is presented

rank reduction for modeling stationary signals rank reduction is developed as a general principle for trading off model bias and model variance in the analysis and synthesis of signals the principle is applied to three basic problems stationary time series modeling stationary time series whitening and vector quantization each problem brings its own surprises and insights

an iterative algorithm for the computation of the mvdr filter statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter or constraint vector and generates a sequence of filters that converges to the minimum variance distortionless response mvdr solution for any positive definite input autocorrelation matrix computationally the algorithm is a simple noninvasive recursive procedure that avoids any form of explicit autocorrelation matrix inversion decomposition or diagonalization theoretical analysis reveals basic properties of the algorithm and establishes formal convergence when the input autocorrelation matrix is replaced by a conventional sample average positive definite estimate the algorithm effectively generates a sequence of mvdr filter estimators the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample matrix inversion smi estimator in fact formal convergence of the estimator sequence to the smi estimate is established however for short data records it is the early nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean square estimation error constraint lms rls type orthogonal multistage decomposition as well as plain and diagonally loaded smi estimates an illustrative interference suppression example is followed throughout this presentation

performance of linear reduced rank multistage receivers for ds cdma in frequency selective fading channels the performance of a set of linear reduced rank multistage filter banks is studied in the context of multiuser detection for direct sequence ds code division multiple access cdma systems the set of filter banks under consideration is comprised of the minimum mean square error mmse the minimum output energy moe the best linear unbiased estimator blue and the maximum likelihood ml detector based on a common framework for the multistage implementations of the aforementioned filter banks the signal to interference plus noise ratios sinrs and bit error rates bers of these reduced rank filter banks are studied for multipath rayleigh fading channels a generic ber formula is provided for coherent detection and noncoherent differential detection schemes constructed under this common framework analysis shows that all of these performance measures are characterized by a kernel matrix k sub mmse whose trace forms the output sinr of the mmse filter bank through investigating the recursive structure of k sub mmse the output sinrs are proven to be monotonically increasing with the number of stages and upper bounded by a number equal to the paths of the desired user s channel the condition for asymptotically achieving this upper bound is also provided which leads to the notion of effective user capacity of linear reduced rank multiuser detection as well as serves as a test for the existence of a ber floor for coherent detection in addition the channel mismatch due to differential detection is also shown to yield a ber floor for noncoherent detection based on this analysis a simple yet effective rule for choosing the number of stages is provided for both coherent and noncoherent linear multistage multiuser detection

growth sensitivity of context free languages a language l over a finite alphabet is called growth sensitive if forbidding any set of subwords f yields a sub language lf whose exponential growth rate is smaller than that of l it is shown that every essentially ergodic non linear context free language of convergent type is growth sensitive ergodic means that the dependency di graph of the generating context free grammar is strongly connected and essentially ergodic means that there is only one nonregular strong component in that graph the methods combine 1 an algorithm for constructing from a given grammar one that generates the associated 2 block language and 2 a generating function technique regarding systems of algebraic equations furthermore the algorithm of 1 preserves unambiguity as well as the number of non regular strong components of the dependency di graph

reduced rank adaptive filtering a novel rank reduction scheme is introduced for adaptive filtering problems this rank reduction method uses a cross spectral metric to select the optimal lower dimensional subspace for reduced rank adaptive filtering as a function of the basis vectors of the full rank space

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

normalized adaptive channel equalizer based on minimal symbol error rate existing minimum symbol error rate equalizers were derived based on the symbol error rate objective function due to the complexity of the objective function the derivation is not straightforward in this paper we present a new approach to derive the minimum symbol error rate adaptive equalizers the problem is formulated as minimizing the norm between two subsequent parameter vectors under the constraint of symbol error rate minimization the constrained optimization problem then is solved with the lagrange multiplier method which results in an adaptive algorithm with normalization simulation results show that the proposed algorithm outperforms the existing adaptive minimum symbol error rate equalizer in convergence speed and steady state performance

on the algorithmic solvability of spectral factorization and applications spectral factorization is an operation which appears in many different engineering applications this paper studies whether spectral factorization can be algorithmically computed on an abstract machine a turing machine it is shown that there exist computable spectral densities with very good analytic properties i e smooth with finite energy such that the corresponding spectral factor cannot be determined on a turing machine further it will be proved that it is impossible to decide algorithmically whether or not a given computable density possesses a computable spectral factor this negative result has consequences for applications of spectral factorization in computer aided design because there it is necessary that this problem be decidable conversely this paper will show that if the logarithm of a computable spectral density belongs to certain sobolev space of sufficiently smooth functions then the spectral factor is always computable as an application the paper discusses the possibility of calculating the optimal causal wiener filter on an abstract machine

adaptive reduced rank processing based on joint and iterative interpolation decimation and filtering we present an adaptive reduced rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems the proposed method is based on the concept of joint and iterative interpolation decimation and filtering we describe an iterative least squares ls procedure to jointly optimize the interpolation decimation and filtering tasks for reduced rank adaptive filtering in order to design the decimation unit we present the optimal decimation scheme and also propose low complexity decimation structures we then develop low complexity least mean squares lms and recursive least squares rls algorithms for the proposed scheme along with automatic rank and branch adaptation techniques an analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed we consider the application of the proposed algorithms to interference suppression in code division multiple access cdma systems simulations results show that the proposed algorithms outperform the best known reduced rank schemes with lower complexity

adaptive reduced rank interference suppression based on the multistage wiener filter a class of adaptive reduced rank interference suppression algorithms is presented based on the multistage wiener filter mswf the performance is examined in the context of direct sequence ds code division multiple access cdma unlike the principal components method for reduced rank filtering the algorithms presented can achieve near full rank performance with a filter rank much less than the dimension of the signal subspace we present batch and recursive algorithms for estimating the filter parameters which do not require an eigen decomposition the algorithm performance in a heavily loaded ds cdma system is characterized via computer simulation the results show that the reduced rank algorithms require significantly fewer training samples than other reduced and full rank algorithms

noniterative subspace tracking a rank one spherical subspace update that is appropriate for subspace based methods like music and minimum norm is introduced this noniterative highly parallel numerically stabilized subspace update is closely related to rank one eigenstructure updating however a rank one subspace update involves less computation than simple rank one correlation accumulation moreover the frequency tracking capabilities of the noniterative subspace update are virtually identical to and in some case more robust than the more computationally expensive eigen based methods

consistent reduced rank lmmse estimation with a limited number of samples per observation dimension an improved construction of the optimal reduced rank linear minimum mean square error mmse estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree of freedom the new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate and being consistent when all dimensions in the model but the number of samples remain bounded our solution not only generalizes the conventional estimator but also turns out to appropriately characterize model mismatch constraints due to finite sample size limitations of fundamental importance in practical situations the proposed implementation results from a generalized consistent estimation of the set of mmse filter subspace coefficients on the reduced dimensional subspace results are based on the theory of the spectral analysis of large dimensional random matrices in particular we build on the analytical description of the asymptotic spectrum of sample covariance type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate as a result the proposed mmse signal waveform estimator is shown to present a superior mean square error performance under a finite sample size by avoiding the breakdown experienced as the selected rank increases

blind adaptive constrained constant modulus reduced rank interference suppression algorithms based on interpolation and switched decimation this work proposes a blind adaptive reduced rank scheme and constrained constant modulus ccm adaptive algorithms for interference suppression in wireless communications systems the proposed scheme and algorithms are based on a two stage processing framework that consists of a transformation matrix that performs dimensionality reduction followed by a reduced rank estimator the complex structure of the transformation matrix of existing methods motivates the development of a blind adaptive reduced rank constrained barc scheme along with a low complexity reduced rank decomposition the proposed barc scheme and a reduced rank decomposition based on the concept of joint interpolation switched decimation and reduced rank estimation subject to a set of constraints are then detailed the proposed set of constraints ensures that the multipath components of the channel are combined prior to dimensionality reduction we develop low complexity joint interpolation and decimation techniques stochastic gradient and recursive least squares reduced rank estimation algorithms a model order selection algorithm for adjusting the length of the estimators is devised along with techniques for determining the required number of switching branches to attain a predefined performance an analysis of the convergence properties and issues of the proposed optimization and algorithms is carried out and the key features of the optimization problem are discussed we consider the application of the proposed algorithms to interference suppression in ds cdma systems the results show that the proposed algorithms outperform the best known reduced rank schemes while requiring lower complexity

adaptive widely linear reduced rank interference suppression based on the multistage wiener filter we propose a widely linear multistage wiener filter wl mswf receiver to suppress inter intra symbol interference multiuser interference and narrowband interference in a high data rate direct sequence ultra wideband ds uwb system the proposed wl receiver fully exploits the second order statistics of the received signal yielding a smaller minimum mean square error mmse than the linear receiver the wl mswf receiver mainly consists of a low rank transformation and an adaptive reduced rank after the rank reduction is achieved via a transformation matrix based on the linear mswf concept two constructions of this rank reduction matrix namely total wl twl and quasi wl qwl are proposed we develop stochastic gradient sg and recursive least squares rls adaptive versions of the proposed twl qwl mswf and theoretically analyze their convergence behavior the comparison of the proposed twl qwl mswf and the existing algorithms is carried out in terms of the computational complexity and the resulting mmse performance extensive simulation results show that the proposed twl qwl mswf schemes outperform the existing schemes in both convergence and steady state performance under various conditions

robust adaptive beamforming based on low rank and cross correlation techniques this paper presents cost effective low rank techniques for designing robust adaptive beamforming rab algorithms the proposed algorithms are based on the exploitation of the cross correlation between the array observation data and the output of the beamformer first we construct a general linear equation considered in large dimensions whose solution yields the steering vector mismatch then we employ the idea of the full orthogonalization method fom an orthogonal krylov subspace based method to iteratively estimate the steering vector mismatch in a reduced dimensional subspace resulting in the proposed orthogonal krylov subspace projection mismatch estimation okspme method we also devise adaptive algorithms based on stochastic gradient sg and conjugate gradient cg techniques to update the beamforming weights with low complexity and avoid any costly matrix inversion the main advantages of the proposed low rank and mismatch estimation techniques are their cost effectiveness when dealing with high dimension subspaces or large sensor arrays simulations results show excellent performance in terms of the output signal to interference plus noise ratio sinr of the beamformer among all the compared rab methods

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

fast and accurate rank selection methods for multistage wiener filter reduced rank adaptive processing rrap has received considerable attention in recent years one of the key problems with this technique is how to determine an appropriate dimension for the reduced rank subspace in this paper we study in detail four types of rank selection methods for the widely used rrap approach multistage wiener filter mwf all of these methods have a computational complexity of order o 1 compared with other existing methods with an order of o i or even o i 2 at the ith stage of the mwf the main idea underlying these methods is to find a recursive algorithm to calculate the stopping criterion the first two algorithms based on the generalized discrepancy principle gdp and error estimation ee respectively are fast versions of existing approaches the last two algorithms based on fast ritz values estimation rve and new information ni respectively are new and proposed in this paper in addition to requiring less computation simulation results show that the proposed algorithms have a higher accuracy in adaptive beamforming applications for both narrowband and broadband signals

successive interference cancellation via rank reduced maximum a posteriori detection this paper proposes a codeword based iterative detection and decoding idd algorithm for multiple input multiple output mimo systems in the proposed algorithm multiple streams in a codeword are jointly detected at the rank reduced rr maximum a posteriori map receiver and inter stream interference is mitigated with successive interference cancelation sic thus the algorithm is abbreviated to rr map sic recent wireless standards such as long term evolution require the system to encode data bits per codeword not per stream as a result conventional sic algorithms could lose joint information among streams in a codeword because different streams of the same codeword are treated as interference instead the proposed rr map sic minimizes the loss of joint information by using the rank reduced map detector in addition this paper compares the detector complexity of rr map sic and investigates how the probability of symbol error is changed in terms of the covariance of the residual interference as the number of iterations increases the covariance is reduced so that the error events also decrease lastly the extrinsic information transfer exit chart is used to analyze the performance of rr map sic simulation results demonstrate the superiority of rr map sic over the conventional algorithm and numerically verify the exit chart analysis

robust reduced rank adaptive algorithm based on parallel subgradient projection and krylov subspace in this paper we propose a novel reduced rank adaptive filtering algorithm exploiting the krylov subspace associated with estimates of certain statistics of input and output signals we point out that when the estimated statistics are erroneous e g due to sudden changes of environments the existing krylov subspace based reduced rank methods compute the point that minimizes a ldquowrongrdquo mean square error mse in the subspace the proposed algorithm exploits the set theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the ldquotruerdquo mse in the subspace therefore compared with the existing methods the proposed algorithm is more suited to adaptive filtering applications a convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method apsm numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems

the theory of ends pushdown automata and second order logic abstract a class of edge labeled graphs called context free are defined according to their behavior at infinity such graphs are generalizations of cayley graphs of context free groups they are also shown to be definable in a very natural way in terms of push down automata using rabin s theorem on the monadic second order theory of the finite binary tree these graphs are also shown to have a decidable monadic second order theory questions about tiling systems and cellular automata operating on these graphs are decidable even when the analogous questions are not when the systems operate on a two dimensional grid

growth and ergodicity of context free languages a language l over a finite alphabet e is called growth sensitive if forbidding any set of subwords f yields a sublanguage l f whose exponential growth rate is smaller than that of l it is shown that every ergodic unambiguous nonlinear context free language is growth sensitive ergodic means for a context free grammar and language that its dependency di graph is strongly connected the same result as above holds for the larger class of essentially ergodic context free languages and if growth is considered with respect to the ambiguity degrees then the assumption of unambiguity may be dropped the methods combine a construction of grammars for 2 block languages with a generating function technique regarding systems of algebraic equations

generic weighted filtering of stochastic signals in this paper a new theory of optimal weighted nonlinear filtering is presented two filter models are considered the first model is based on a representation of the filter in the polynomial like form with q terms where each term consists of weighted matrices and the matrix determined from the error minimization problem the second model extends the first one to the case of the filter concatenation the filter models are given in terms of pseudo inverse matrices i e the requirement of invertibility for covariance matrices is omitted thus our filters always exist we develop methods which allow us to exploit advantages associated with the proposed nonlinear filter models the methods consist of the orthogonalization procedure and the reduction of the original problem to q individual minimization problems for smaller matrices this leads to a considerable reduction in the required computational work the error associated with the first filter model decreases when the number q of terms of filter increases its compression ratio can be adjusted by varying a particular value of ranks in each of its q terms this means that the proposed filer structure provides the two degrees of freedom the second filter model provides another degree of freedom a number k of filters in the concatenation variations of the degrees of freedom improve the performance of the proposed filters in particular the error associated with the filter concatenation decreases as the filter number k in the concatenation increases

orthogonal multiple access over time and frequency selective channels suppression of multiuser interference mui and mitigation of time and frequency selective doubly selective channel effects constitute major challenges in the design of third generation wireless mobile systems relying on a basis expansion model bem for doubly selective channels we develop a channel independent block spreading scheme that preserves mutual orthogonality among single cell users at the receiver this alleviates the need for complex multiuser detection and enables separation of the desired user by a simple code matched channel independent block despreading scheme that is maximum likelihood ml optimal under the bem plus white gaussian noise assumption on the channel in addition each user achieves the maximum delay doppler diversity for gaussian distributed bem coefficients issues like links with existing multiuser transceivers existence user efficiency special cases backward compatibility with direct sequence code division multiple access ds cdma and error control coding are briefly discussed

reduced rank multistage receivers for ds cdma in frequency selective fading channels multistage ms implementation of the minimum mean square error mmse minimum output energy moe best linear unbiased estimation blue and maximum likelihood ml filter banks fbs is developed based on the concept of the ms wiener filtering mswf introduced by goldstein et al these fbs are shown to share a common ms structure for interference suppression modulo a distinctive scaling matrix at each filter s output based on this finding a framework is proposed for joint channel estimation and multiuser detection mud in frequency selective fading channels adaptive reduced rank equal gain combining egc schemes for this family of fbs mmse moe blue and ml are proposed for noncoherent blind mud of direct sequence code division multiple access systems and contrasted with the maximal ratio combining counterparts that are also formed with the proposed common structure under the assumption of known channel state information the bit error rate steady state output signal to interference plus noise ratio sinr and convergence of the output sinrs are investigated via computer simulation simulation results indicate that the output sinrs attain full rank performance with much lower rank for a highly loaded system and that the adaptive reduced rank egc blue ml fbs outperform the egc mmse moe fbs due to the unbiased nature of the implicit blue channel estimators employed in the egc blue ml schemes

adaptive reduced rank receive processing based on minimum symbol error rate criterion for large scale multiple antenna systems in this work we propose a novel adaptive reduced rank receive processing strategy based on joint preprocessing decimation and filtering jpdf for large scale multiple antenna systems in this scheme a reduced rank framework is employed for linear receive processing and multiuser interference suppression based on the minimization of the symbol error rate ser cost function we present a structure with multiple processing branches that performs a dimensionality reduction where each branch contains a group of jointly optimized preprocessing and decimation units followed by a linear receive filter we then develop stochastic gradient sg algorithms to compute the parameters of the preprocessing and receive filters along with a low complexity decimation technique for both binary phase shift keying bpsk and m ary quadrature amplitude modulation qam symbols in addition an automatic parameter selection scheme is proposed to further improve the convergence performance of the proposed reduced rank algorithms simulation results are presented for time varying wireless environments and show that the proposed jpdf minimum ser receive processing strategy and algorithms achieve a superior performance than existing methods with a reduced computational complexity

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

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

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

on updating signal subspaces the authors develop an algorithm for adaptively estimating the noise subspace of a data matrix as is required in signal processing applications employing the signal subspace approach the noise subspace is estimated using a rank revealing qr factorization instead of the more expensive singular value or eigenvalue decompositions using incremental condition estimation to monitor the smallest singular values of triangular matrices the authors can update the rank revealing triangular factorization inexpensively when new rows are added and old rows are deleted experiments demonstrate that the new approach usually requires o n sup 2 work to update an n n matrix and that it accurately tracks the noise subspace

large system transient analysis of adaptive least squares filtering the performance of adaptive least squares ls filtering is analyzed for the suppression of multiple access interference both full rank ls filters and reduced rank ls filters which reside in a lower dimensional krylov space are considered with training and without training but with known signature for the desired user we compute the large system limit of output signal to interference plus noise ratio sinr as a function of normalized observations load and noise level specifically the number of users k the degrees of freedom n and the number of training symbols or observations i all tend to infinity with fixed ratios k n and i n our results account for an arbitrary power distribution over the users data windowing e g recursive ls rls with exponential windowing and initial diagonal loading of the covariance matrix to prevent ill conditioning numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom typically n 32 given a fixed short training length the relative performance of full and reduced rank filters depends on the selected rank and diagonal loading with an optimized diagonal loading factor the performance of full and reduced rank filters are similar however full rank performance is generally much more sensitive to the choice of diagonal loading factor than reduced rank performance

growth and ergodicity of context free languages ii the linear case a language l over a finite alphabet e is called growth sensitive if forbidding any non empty set f of subwords yields a sub language l f whose exponential growth rate is smaller than that of l say that a context free grammar and associated language is ergodic if its dependency di graph is strongly connected it is known that regular and unambiguous non linear context free languages which are ergodic are growth sensitive in this note it is shown that ergodic unambiguous linear languags are growth sensitive closing the gap that remained open

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors

adaptive constrained constant modulus algorithm based on auxiliary vector filtering for beamforming a constrained constant modulus ccm algorithm with the auxiliary vector filtering avf technique is introduced for robust adaptive beamforming the proposed scheme decomposes the adaptive filter into constrained reference vector filters and unconstrained auxiliary vector filters components the weight vector is iterated by subtracting the scaling auxiliary vector from the reference vector which are computed according to the ccm criterion the proposed algorithm provides an iterative exchange of information between the scalar factor and the auxiliary vector resulting in a faster convergence and an improved steady state performance as compared with existing techniques with large filters the convergence properties of the proposed algorithm are analyzed simulation results show that the proposed beamforming algorithm outperforms existing techniques and is robust against signature mismatch problems

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed