k homology asymptotic representations and unsuspended e theory connes and higson defined a bivariant homology theory e a b for separable c algebras the elements of e a b are taken to be homotopy classes of asymptotic momorphisms from sa k to sb k in symbols e a b sa sb k if a is k nuclear then e theory agrees with kasparov s bivariant k theory we show that in many cases one need not take suspensions to calculate the e theory group e a b for many a we show e a b a b k for all b among the a for which this is true are c0 x pt for x with the homotopy type of a finite connected cw complex this gives a concrete realization of k homology related to the brown douglas fillmore description for example k0 x arises as asymptotic representations k0 x c0 x k other a for which our isomorphic holds include the nonunital dimension drop intervals in this case there is no distinction between homomorphisms and asymptotic morphisms so we have succeeded in classifying all homomorphisms from a dimension drop interval to a stable c algebra this was subsequently used by elliott j reine angew math 443 1993 179 219 in the classification of certain c algebras the dimension drop interval may also be used to describe k x z n in terms of paths of asymptotic representations of c0 x

time variant channel estimation using discrete prolate spheroidal sequences we propose and analyze a low complexity channel estimator for a multiuser multicarrier code division multiple access mc cdma downlink in a time variant frequency selective channel mc cdma is based on orthogonal frequency division multiplexing ofdm the time variant channel is estimated individually for every flat fading subcarrier assuming small intercarrier interference the temporal variation of every subcarrier over the duration of a data block is upper bounded by the doppler bandwidth determined by the maximum velocity of the users slepian showed that time limited snapshots of bandlimited sequences span a low dimensional subspace this subspace is also spanned by discrete prolate spheroidal dps sequences we expand the time variant subcarrier coefficients in terms of orthogonal dps sequences we call slepian basis expansion this enables a time variant channel description that avoids the frequency leakage effect of the fourier basis expansion the square bias of the slepian basis expansion per subcarrier is three magnitudes smaller than the square bias of the fourier basis expansion we show simulation results for a fully loaded mc cdma downlink with classic linear minimum mean square error multiuser detection the users are moving with 19 4 m s using the slepian basis expansion channel estimator and a pilot ratio of only 2 we achieve a bit error rate performance as with perfect channel knowledge

towards a theory of classification abstract the well known difficulties arising in a classification which is not set theoretically trivial involving what is sometimes called a non smooth quotient have been overcome in a striking way in the theory of operator algebras by the use of what might be called a classification functor the very existence of which is already a surprise here the notion of such a functor is developed abstractly and a number of examples are considered including those which have arisen for various classes of operator algebras

classifying c algebras via ordered mod p k theory we introduce an order structure on k 0 9 k0 z p this group may also be thought of as ko 7z z p we exhibit new examples of real rank zero c algebras that are inductive limits of finite dimensional and dimension drop algebras have the same ordered graded k theory with order unit and yet are not isomorphic in fact they are not even stably shape equivalent the order structure on k0 z 3 z p naturally distinguishes these algebras the same invariant is used to give an isomorphism theorem for such realrank zero inductive limits as a corollary we obtain an isomorphism theorem for all real rank zero approximately homogeneous c algebras that arise from systems of bounded dimension growth and torsion free k0 group at the 1980 kingston conference effros posed the problem of finding suitable invariants for use in studying c algebras that are limits of sequences of homogeneous c algebras these are now called almost homogeneous ah c algebras the classification of ah algebras is a rapidly developing field and we will not attempt to summarize all this activity instead we will focus on the growth of the invariants used specifically we consider an ah algebra a that is the direct limit o f a system of the form

morphisms of extensions of c algebras pushing forward the busby invariant abstract we study completions of diagrams of extensions of c algebras in which all three c algebras in one of the rows and either the ideal or the quotient in the other are given along with the three morphisms between them we find universal solutions to all four of these problems under restrictions of varying severity on the given vertical maps and describe the solutions in terms of push outs and pull backs of certain diagrams our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products this leads to new results about the k theory of amalgamated free products verifying the cuntz conjecture in certain cases we also obtain new results about extensions of matricial field c algebras verifying partially a conjecture of blackadar and kirchberg finally we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes

block transmission over dispersive channels transmit filter optimization and realization and mmse dfe receiver performance optimal transmit filters for packet based data transmission on dispersive gaussian noise linear time invariant channels are derived by maximizing the mutual information subject to a fixed input power budget a quasi stationary approximation to the optimal nonstationary input covariance process is derived and shown to exhibit negligible mutual information loss from the optimal case for situations of most practical interest moreover this quasi stationary approximation results in efficiently computed lattice or pole zero implementations of the transmit filter by considering the popular finite impulse response minimum mean square error decision feedback equalizer fir mmse dfe as a receiver structure we show that transmitter optimization results in an appreciable improvement in the decision point signal to noise ratio finally we show that as the output blocklength becomes infinite the optimum finite dimensional nonstationary input covariance process converges to a stationary process whose power spectrum obeys the well known water pouring distribution

symmetries of the car algebra a automorphism of period two of the uhf c algebra of type 2 is constructed for which the fixed point algebra is not approximately finite dimensional the construction also yields a diagonal maximal commutative c subalgebra whose spectrum is not totally disconnected variations and consequences of the construction are discussed

on channel estimation and detection for multicarrier signals in fast and selective rayleigh fading channels time domain channel estimation and detection techniques are presented for multicarrier signals in a fast and frequency selective rayleigh fading channel as a consequence of the time varying channel the orthogonality between subcarriers is destroyed in conventional frequency domain approaches resulting in interchannel interference which increases an irreducible error floor in proportion to the normalized doppler frequency an important feature of the proposed technique is the ability to exploit the time selective channel as a provider of time diversity this enables us to achieve performance superior to any other structure without increasing bandwidth or incorporating redundancy in order to reduce the complexity of the estimator we apply the theory of optimal low rank approximation to a minimum mean squared error channel estimator and present a theoretical calculation of mean squared error and simulations to confirm that the estimator is robust to changes in channel characteristics

adaptive noncoherent dfe for mdpsk signals transmitted over isi channels a novel noncoherent decision feedback equalization ndfe scheme for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented a suboptimum version with lower computational complexity and a noncoherent linear equalizer nle are derived from the original ndfe scheme furthermore the relation of the novel nle to a previously proposed nle is investigated in contrast to known ndfe schemes the novel scheme can approach the performance of coherent minimum mean squared error decision feedback equalization for adaptation of the feedforward and feedback filters efficient novel modified least mean square and recursive least squares algorithms are presented finally it is shown that the proposed adaptive ndfe scheme is robust against frequency offset

error rate evaluation of linear equalization and decision feedback equalization with error propagation we propose applying an approximate fourier series to evaluate efficiently the bit error rate ber performance of finite length linear equalization le and decision feedback equalization dfe by extending the fourier series we enable ber calculations for quadrature phase shift keying qpsk transmission on complex channels with in phase and crosstalk intersymbol interference isi the ber calculation is based on determining the residual isi samples and background gaussian noise variance at the equalizer output for static channels or for realizations of quasi static fading channels a simple bound on the series error magnitude in terms of the fourier series parameters ensures the required accuracy and precision improved state transition probability estimates are derived and verified by simulation for an approximate markov model of the dfe error propagation for the case in which residual isi exists even when the previous decisions stored in the feedback filter fbf are correct we demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs our analysis includes symbol spaced and fractionally spaced minimum mean square error mmse le zero forcing zf le and mmse dfe with and without error propagation on static isi channels and multipath channels with quasi static rayleigh fading a comparison between suboptimum and optimum receiver filtering in conjunction with equalization and an assessment of the accuracy of some widely used equalization ber approximations and bounds

linear prediction error method for blind identification of periodically time varying channels blind channel estimation for single input multiple output simo periodically time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the linear prediction error method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for identifiability are investigated the cyclostationary nature of the received signal is exploited to consistently estimate the time varying correlation function of the data from a single observation record the proposed method requires the knowledge of the active basis functions but not the channel length an upper bound suffices several existing methods require precise knowledge of the channel length equalization of the time varying channel given the estimated channel is investigated computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches

analytical inversion of general periodic tridiagonal matrices in this paper we present an analytical forms for the inversion of general periodic tridiagonal matrices and provide some very simple analytical forms which immediately lead to closed formulae for some special cases such as symmetric or perturbed toeplitz for both periodic and non periodic tridiagonal matrices an efficient computational algorithm for finding the inverse of any general periodic tridiagonal matrices from the analytical form is given it is suited for implementation using computer algebra systems such as maple matlab macsyma and mathematica an example is also given to illustrate the algorithm

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

a semi infinite random walk associated with the game of roulette this paper is concerned with a discrete time random walk on the integers 0 1 2 which arises in the game of roulette at each step either a unit displacement to the left with probability 1 p or a fixed multiple displacement to the right with probability p can occur there is a partially absorbing barrier at the origin the probabilities of reflection and absorption at 0 are and 1 respectively using generating functions and lagrange s theorem for the expansion of a function as a power series explicit expression for the probabilities of the player s capital at the nth step are deduced as well as the probabilities of ultimate absorption at the origin

interior point least squares estimation transient convergence analysis and application to mmse decision feedback equalization in many communication systems training sequences are used to help the receiver identify and or equalize the channel the amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization in this paper we propose the use of a new adaptive filtering method called interior point least squares ipls for adaptive equalization first we show that ipls converges exponentially fast in the transient phase then we use the ipls algorithm to update the weight vector for a minimum mean square error decision feedback equalizer mmse dfe in a cdma downlink scenario numerical simulations show that when training sequences are short ipls consistently outperforms rls in terms of system bit error rate and packet error rate as the training sequence gets longer ipls matches the performance of the rls algorithm

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

robust design of adaptive equalizers although equalizers promise to improve the signal to noise energy ratio zero forcing equalizers are derived classically in a deterministic setting minimizing intersymbol interference while minimum mean square error mmse equalizer solutions are derived in a stochastic context based on quadratic wiener cost functions in this paper we show that it is possible and in our opinion even simpler to derive the classical results in a purely deterministic setup interpreting both equalizer types as least squares solutions this in turn allows the introduction of a simple linear reference model for equalizers which supports the exact derivation of a family of iterative and recursive algorithms with robust behavior the framework applies equally to multiuser transmissions and multiple input multiple output mimo channels a major contribution is that due to the reference approach the adaptive equalizer problem can equivalently be treated as an adaptive system identification problem for which very precise statements are possible with respect to convergence robustness and l2 stability robust adaptive equalizers are much more desirable as they guarantee a much stronger form of stability than conventional in the mean square sense convergence even some blind channel estimation schemes can now be included in the form of recursive algorithms and treated under this general framework

boundedness behavior of the spectral factorization for polynomial data in the wiener algebra spectral factorization is of fundamental importance in many areas of signal processing this paper investigates the boundedness behavior of the spectral factorization mapping in the wiener algebra thereby the focus lies on the factorization of polynomial spectral densities with a finite degree n since such spectra are especially important for practical applications the paper presents a lower and an upper bound on the boundedness behavior which will show that the boundedness constant of the spectral factorization mapping gets worse as the degree n of the spectra increases therewith one obtains independently the known result that the spectral factorization mapping is unbounded on the wiener algebra

rate of convergence in approximating the spectral factor of regular stochastic sequences common methods for the calculation of the spectral factorization rely on an approximation of the given spectral density by a polynomial and a subsequent factorization of this polynomial it is known that the regularity of the stochastic sequence determines the achievable approximation rate of its spectrum however since the approximative polynomial should be factorized it has to be positive it is shown that this restriction on the approximation polynomial implies a limitation on the approximation rate for linear methods whereas for nonlinear methods the optimal approximation rate can still be achieved this has also consequences for the rate of convergence of the spectral factor which is investigated in the second part there a lower and an upper bound for the error in the spectral factor is derived which shows the dependency on the approximation degree and on the regularity of the stochastic sequence finally if the spectral density is given only on a finite set of sampling points no linear approximation method exists such that the error in the spectral factor can be controlled by the approximation degree

on a simple unital projectionless c algebra we construct a unital separable c algebra z as an analog of the hyperfinite type ii 1 factor besides being nuclear simple projectionless and infinite dimensional z has a unique tracial state and is kk equivalent to inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the algebra of complex numbers it is shown that unital endomorphisms on z are approximately inner and that z is isomorphic to the infinite tensor product of its replicas it is also shown that a z a for certain interesting classes of unital simple nuclear c algebras a of real rank zero

absorption probabilities for a random walk between two partially absorbing boundaries i a biased random walk on a linear lattice bounded by one or two partially absorbing boundaries is considered at the boundaries the particle is either lost from the system or turned back and reduces to the classical problem of a random walk with absorbing and or reflecting barriers the probabilities of ultimate absorption at the boundaries are obtained as well as the conditional mean for the number of steps before stopping given the absorption at a specified barrier the symmetries for the conditional mean are also given previous formulae are found to be in error

computing the minimum phase filter using the ql factorization we investigate the ql factorization of a time invariant convolutive filtering matrix and show that this factorization not only provides the finite length equivalent to the minimum phase filter but also gives the associated all pass filter the convergence properties are analyzed and we derive the exact convergence rate and an upper bound for a simple single input single output system with filter length finally this upper bound is used to derive an approximation of the convergence rate for systems of arbitrary length implementation wise the method has the advantage of being numerically stable and straight forward to extend to the multiple input multiple output case furthermore due to the existence of fast ql factorization methods it is possible to compute the filters efficiently

low complexity equalization of ofdm in doubly selective channels orthogonal frequency division multiplexing ofdm systems may experience significant inter carrier interference ici when used in time and frequency selective or doubly selective channels in such cases the classical symbol estimation schemes e g minimum mean squared error mmse and zero forcing zf estimation require matrix inversion that is prohibitively complex for large symbol lengths an analysis of the ici generation mechanism leads us to propose a novel two stage equalizer whose complexity apart from the fft is linear in the ofdm symbol length the first stage applies optimal linear preprocessing to restrict ici support and the second stage uses iterative mmse estimation to estimate finite alphabet frequency domain symbols simulation results indicate that our equalizer has significant performance and complexity advantages over the classical linear mmse estimator in doubly selective channels

the classification of simple separable unital z stable locally ash algebras let a be a unital simple separable locally approximately subhomogeneous c algebra locally ash algebra it is shown that a qa q can be tracially approximated by unital elliott thomsen algebras with trivial k1k1 group where q is the universal uhf algebra in particular it follows that a is classifiable by the elliott invariant if a is jiang su stable

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

classification of simple c algebras with unique traces we classify certain almost multiplicative morphisms up to approximate unitary equivalence and use this result to prove the following let a and b be two unital separable simple c algebras of real rank zero stable rank one with weakly unperforated k 0 groups and with unique normalized quasi traces suppose that both a and b are locally ah and k a k a 1 a k b k b 1 b then a is isomorphic to b

on a markov chain roulette type game a markov chain on non negative integers which arises in a roulette type game is discussed the transition probabilities are p01 pnj nj pi i w q pi i 1 p 1 q 1 w n 0 1 n w j n and i 1 2 n w using formulae for the determinant of a partitioned matrix a closed form expression for the solution of the markov chain roulette type game is deduced the present analysis is supported by two mathematical models from tumor growth and war with bargaining

one dimensional drift diffusion between two absorbing boundaries application to granular segregation motivated by a novel method for granular segregation we analyse the one dimensional drift diffusion between two absorbing boundaries the time evolution of the probability distribution and the rate of absorption are given by explicit formulae the splitting probability and the mean first passage time are also calculated applying the results we find optimal parameters for segregating binary granular mixtures

convergence properties of adaptive equalizer algorithms in this paper we provide a thorough stability analysis of two well known adaptive algorithms for equalization based on a novel least squares reference model that allows to treat the equalizer problem equivalently as system identification problem while not surprising the adaptive minimum mean square error mmse equalizer algorithm behaves l2 stable for a wide range of step sizes the even older zero forcing zf algorithm however behaves very differently we prove that the zf algorithm generally does not belong to the class of robust algorithms but can be convergent in the mean square sense we furthermore provide conditions on the upper step size bound to guarantee such mean squares convergence we specifically show how noise variance of added channel noise and the channel impulse response influences this bound simulation examples validate our findings

joint optimization of fir prefilter and channel estimate for sequence estimation we provide simple analytical results for the coefficients of a finite impulse response fir prefilter and the effective channel impulse response ir for use in cellular communication systems we show that using a fir filter with both causal and anticausal filter taps it is possible to find the jointly optimized impulse response such that the signal to noise ratio is maximized in the least squares sense we show via computer simulation for 8 ary phase shift keying in enhanced data rates for global evolution edge that the joint optimization of the prefilter and ir produces results similar to the minimum mean square error decision feedback equalizer prefilter in thermal noise but yields gain in colored noise

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

a universal multicoefficient theorem for the kasparov groups that holds in the same generality as the universal coefficient theorem of rosenberg and schochet there are advantages in some circumstances to using hom k a k b in place of kk a b these advantages derive from the fact that k a can be equipped with order and scale structures similar to those on k0 a with this additional structure the module k a becomes a powerful invariant of c algebras we show that it is a complete invariant for the class of real rank zero ad algebras the ad algebras are a certain kind of approximately subhomogeneous c algebras which may have torsion in k1 ell in addition to classifying these algebras we calculate their automorphism groups up to approximately innerautomorphisms

reduced complexity decoding of space time trellis codes in the frequency selective channel an iterative approach is developed for decoding space time trellis codes sttcs in frequency selective multiple input multiple output mimo channels the method uses the partitioned viterbi algorithm pva as an equaliser for the mimo system it is used iteratively with a sttc decoder that provides soft outputs using the soft output viterbi algorithm sova it is shown through simulation that the iterative procedure achieves a performance within 2 0 db of maximum likelihood ml decoding at a fer of 10 2 but suffers a small diversity loss it is also shown that the complexity of the iterative approach is lower than that of ml decoding

simulation models with correct statistical properties for rayleigh fading channels in this paper new sum of sinusoids statistical simulation models are proposed for rayleigh fading channels these new models employ random path gain random initial phase and conditional random doppler frequency for all individual sinusoids it is shown that the autocorrelations and cross correlations of the quadrature components and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly even if the number of sinusoids is as small as a single digit integer moreover the probability density functions of the envelope and phase the level crossing rate the average fade duration and the autocorrelation of the squared fading envelope which contains fourth order statistics of the new simulators asymptotically approach the correct ones as the number of sinusoids approaches infinity while good convergence is achieved even when the number of sinusoids is as small as eight the new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels multiple input multiple output channels and diversity combining scenarios statistical properties of one of the new simulators are evaluated by numerical results finding good agreements

mimo equalization with state space channel models state space models are proposed to represent multiple input multiple output mimo frequency selective wireless channels with the motivation of better model approximation and more robust channel equalization performance when the order of the channel model is lower that of the true channel we develop a simple framework under which the equalizers for state space channel models can be designed using the existing methods for designing equalizers for finite impulse response fir models in particular a mimo minimum mean squared error decision feedback equalizer is developed for state space models when only estimates of the channel are available to the receiver the equalization performance is affected by the channel estimation accuracy because reduced order state space models can provide lower h 2 channel estimation error than reduced length fir models state space based equalizers typically exhibit significantly smaller symbol error rate than fir based ones thus state space channel models can be a more robust choice than fir models in the presence of model order selection error numerical simulation also shows that adaptive state space based receivers have slower but comparable convergence rates compared to fir based adaptive equalizers

prefiltered space time m bcjr equalizer for frequency selective channels this paper addresses the problem of soft equalization for space time coded transmissions over frequency selective fading channels the structure of the space time code is embedded in the channel impulse response for efficient joint equalization and decoding the proposed equalization decoding approach uses a prefilter to concentrate the effective channel power in a small number of taps followed by a reduced complexity maximum a posteriori probability map equalizer decoder to produce soft decisions the prefilter introduces residual intersymbol interference which degrades the performance of map when applied to the trellis of the shortened channel however the shape of the overall shortened channel impulse response allows the m algorithm to approximate the prefiltered map performance with a small number of states based on this general framework we investigate several enhancements such as using different prefilters for the forward and backward recursions concatenating two trellis steps during decoding and temporal oversampling the performance is evaluated through simulations over the edge typical urban channel

early appraisal of the fixation probability in directed networks in evolutionary dynamics the probability that a mutation spreads through the whole population having arisen from a single individual is known as the fixation probability in general it is not possible to find the fixation probability analytically given the mutant s fitness and the topological constraints that govern the spread of the mutation so one resorts to simulations instead depending on the topology in use a great number of evolutionary steps may be needed in each of the simulation events particularly in those that end with the population containing mutants only we introduce two techniques to accelerate the determination of the fixation probability the first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably this technique is computationally advantageous for some of the so called layered networks the second technique which is not restricted to layered networks consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation for advantageous mutations in large populations and regardless of the network s topology we demonstrate both analytically and by means of simulations that using a threshold of about n r ensuremath 1 1 4 mutants where n is the number of simulation events and r is the ratio of the mutants fitness to that of the remainder of the population leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full fledged simulations we have observed speedups of two orders of magnitude for layered networks with 10 text 000 nodes

realizable linear and decision feedback equalizers properties and connections recently there has been renewed interest in the use of infinite impulse response iir linear equalizers les for digital communication channels as a means for both improving performance and blindly initializing decision feedback structures dfes theoretical justification for such an approach is usually given assuming unconstrained filters which are not causal and therefore not implementable in practice we present an analysis of realizable i e causal stable and of finite degree minimum mean square error mmse equalizers for single input multiple output channels both in the le and dfe cases focusing on their structures and filter orders as well as the connections between them the dfe resulting from rearranging the mmse le within a decision feedback loop is given special attention it is shown that although this dfe does not in general coincide with the mmse dfe it still enjoys certain optimality conditions the main tools employed are the wiener theory of minimum variance estimation and kalman filtering theory which show interesting properties of the mmse equalizers not revealed by previous polynomial approaches

fast techniques for computing finite length mimo mmse decision feedback equalizers multiple input multiple output mimo digital communication systems have received great attention due to their potential of increasing the overall system throughput in such systems mimo decision feedback equalization dfe schemes are often used to mitigate intersymbol interference isi resulting from channel multipath propagation in this context the existing computationally efficient methods for exact estimation of the dfe filters under minimum mean square error criteria mmse dfe rely on fast cholesky decomposition and backsubstitution or levinson techniques these methods may still present several difficulties in implementation as the demand on higher transmission rates increases and thus a simple solution is necessary in this paper new procedures for fast computation of the mimo mmse dfe are presented the new algorithms are obtained from a simple observation namely that the optimal feedforward filter fff is related to the well known kalman gain matrix commonly encountered in fast recursive least squares adaptive algorithms for which fast recursions exist and are readily applicable moreover the feedback filter can be easily computed via stable fast mimo convolution techniques as a result the proposed method is less complex more structured and can be as reliable in finite precision as known approaches in the literature

throughput maximizing fir transmit filters for linear dispersive channels optimum finite impulse response transmit filters for symbol by symbol transmission on linear dispersive additive gaussian noise channels are derived by maximizing the channel throughput subject to a fixed average input energy constraint this maximized throughput is compared to that achievable with water pour and flat transmit filters the effect of transmit filter optimization on the receiver performance is investigated by considering the popular minimum mean square error decision feedback equalizer receiver structure

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

mmse decision feedback equalizers finite length results this paper extends a number of results on the infinite length minimum mean square error decision feedback equalizer mmse dfe reported by cioffi dudevoir eyuboglu and forney see ieee trans commun 1995 to the finite length case cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite length mmse dfe our objective throughout the paper is to establish finite length analogs of the well known infinite length mmse dfe results similarities and differences between the two cases are examined and delineated finally convergence of our derived finite length results to their well established infinite length counterparts is shown

minimum mean squared error impulse response shortening for discrete multitone transceivers we reformulate the minimum mean squared error mmse solution for time domain equalization teq in multitone transceivers we show that the maximum shortening signal to noise ratio mssnr and minimum intersymbol interference min isi teqs are particular cases of our new formulation with good channel estimation the mmse teq achieves near optimal rate performance our algorithm is less sensitive to channel estimation errors than other methods

on the robustness of the finite length mmse dfe with respect to channel and second order statistics estimation errors the finite length minimum mean square error decision feedback equalizer mmse dfe is an efficient structure mitigating intersymbol interference isi introduced by practically all communication channels at high enough symbol rates the filters constituting the mmse dfe as well as related performance measures can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second order statistics sos in practice we estimate the unknown quantities and thus inevitable estimation errors arise we model the estimation errors as small perturbations and we derive a second order approximation to the excess mse furthermore we derive second order approximations to the mean excess mse in terms of the parameter estimation error covariance matrices and simple and informative bounds revealing the factors that govern the behavior of mmse dfe under mismatch simulations confirm that the derived second order approximations provide accurate estimates of the mmse dfe performance degradation due to mismatch

compact group actions on uhf algebras obtained by folding the interval we show that for any integer p greater than one there exists a c algebra which is not af such that mp a mp where mp mp is the uhf algebra of type p using this construction of uhf algebras as inductive limits of subhomogeneous algebras on an interval embedded in each other via a folding operation on the interval we exhibit actions of compact groups on uhf algebras whose fixed point algebras are not af in particular for any compact group g e there exists an action of g on mp whose fixed point algebra is not af

time varying versus time invariant finite length mmse dfe on stationary dispersive channels a time varying structure and a time invariant structure for the finite length minimum mean square error decision feedback equalizer mmse dfe are presented and their performances are compared on a stationary channel impaired by intersymbol interference isi and additive gaussian noise the time varying structure has an innovations error sequence but incurs a throughput loss on isi channels because of its block processing nature conditions under which the time invariant structure exhibits near optimal performance are described both structures converge to the canonical mmse dfe of cioffi et al see ibid vol 43 p 2582 94 1995 and vol 43 p 2595 2604 1995 as their filters lengths become infinite

doubly selective channel estimation using exponential basis models and subblock tracking three versions of a novel adaptive channel estimation approach exploiting the over sampled complex exponential basis expansion model ce bem is presented for doubly selective channels where we track the bem coefficients rather than the channel tap gains since the time varying nature of the channel is well captured in the ce bem by the known exponential basis functions the time variations of the unknown bem coefficients are likely much slower than those of the channel and thus more convenient to track we propose a subblockwise tracking scheme for the bem coefficients using time multiplexed tm periodically transmitted training symbols three adaptive algorithms including a kalman filtering scheme based on an assumed autoregressive ar model of the bem coefficients and two recursive least squares rls schemes not requiring any model for the bem coefficients are investigated for bem coefficient tracking simulation examples illustrate the superior performance of our approach over several existing doubly selective channel estimators

adaptive linear equalization combined with noncoherent detection for mdpsk signals a novel noncoherent receiver for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented the noncoherent receiver consists of a linear equalizer and a decision feedback differential detector a significant performance gain over a previously proposed noncoherent receiver can be observed for an infinite number of feedback symbols the optimum equalizer coefficients can be calculated analytically and the performance of the proposed receiver approaches that of a coherent linear minimum mean squared error equalizer moreover a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed

adaptive tracking of linear time variant systems by extended rls algorithms we exploit the one to one correspondences between the recursive least squares rls and kalman variables to formulate extended forms of the rls algorithm two particular forms of the extended rls algorithm are considered one pertaining to a system identification problem and the other pertaining to the tracking of a chirped sinusoid in additive noise for both of these applications experiments are presented that demonstrate the tracking superiority of the extended rls algorithms compared with the standard rls and least mean squares lms algorithms

on the classification of nuclear c algebras two of the most influential works on c algebras from the mid seventies brown douglas and fillmore s 6 and elliott s 21 both contain uniqueness and existence results in the now standard sense which we shall outline below these papers served as keystones for two separate theories kk theory and the classification program which for many years parted ways with only moderate interaction but with this common origin in mind it is not surprising that recent years have seen a fruitful interaction which has been one of the main engines behind rapid progress in the classification program in the present paper we take this interaction even further combining a concept of quasidiagonality for representations and a new characterization of equivalence in the cuntz picture of kk theory we achieve a general uniqueness result and from the quasidiagonality notion we derive a corresponding general existence result by comparing well known realizations of the kk groups these results are then employed to obtain new classification results for certain classes of quasidiagonal c algebras introduced by h lin an important novel feature of these classes is that they are defined by a certain local approximation property rather than by an inductive limit construction we emphasize that our fundamental uniqueness result does not depend on the universal coefficient theorem uct nor on nuclearity of the c algebras involved on the other hand when we refine the uniqueness result for use in classification we need to gradually add such conditions on the c algebras it is to be expected that requirements of this type are necessary but we have found that holding them back as long as possible leads to more conceptual proofs while clarifying the role of the uct and nuclearity in classification further since uniqueness results answer fundamental questions about kk and k theory they are of interest in themselves we have pursued this theme in 14 and defer to this paper the proof of the new characterization of kk theory which lies behind our uniqueness results our existence and uniqueness results are in the spirit of the classical ext theory from 6 the main complication overcome in the paper is to control the stabilization which is necessary when one works with finite c algebras in the infinite case where programs of this type have already been successfully carried out stabilization is unnecessary yet our methods are sufficiently versatile to allow us to reprove from a handful of basic results the classification of purely infinite nuclear c algebras of kirchberg and phillips

the kk lifting problem for dimension drop interval algebras abstract in this paper we investigate the kk theory of generalized dimension drop interval algebras with possibly different dimension drops at the endpoints with special emphasis on the problem which kk class is representable by a homomorphism between two such c algebras allowing the tensor product with a matrix algebra for the codomain algebra this lifting problem makes sense in its own right in kk theory and also has application to the classification of c algebras which are inductive limits of these building blocks it turns out that when the dimension drops at the two endpoints are different there exist kk elements which preserve the order structure defined by m dadarlat and t a loring in 4 on the mod p k theory but cannot be lifted to a homomorphism this is different from the equal dimension drop case as shown by s eilers in 6

frequency selective fading channel estimation with a polynomial time varying channel model a rectangular windowed least squares estimator using a polynomial model of the time varying channel taps is proposed for estimating the impulse response of a frequency selective fading channel this method provides a significant improvement in mean square identification error msie over the conventional least mean squares lms and the exponentially weighted recursive least squares ew rls algorithms without a polynomial model a detailed study of the effects of channel parameters such as the fading rate and the signal to noise ratio on the proposed method is carried out the performance of the method depends on the window size of the least squares estimator and the polynomial order being used algorithms to obtain the approximately optimal window size and polynomial order are proposed and are shown to perform well

application of fast subspace decomposition to signal processing and communication problems the authors previously described a class of fast subspace decomposition fsd algorithms though these algorithms can be applied to solve a variety of signal processing and communication problems with significant computational reduction they focus their discussion on two typical applications i e sensor array processing and time series analysis in many cases replacing the usual eigenvalue decomposition evd or singular value decomposition svd by the fsd is quite straightforward however the fsd approach can exploit more structure of some special problems to further simplify the implementation they first discuss the implementation details of the fsd such as how to choose an optimal starting vector how to handle correlated noise and how to exploit additional matrix structure for further computational reduction then they describe an fsd approach targeted at data matrices rectangular n spl times m n spl ges m which requires only o nmd flops where d denotes the signal subspace dimension versus a regular o nm sup 2 m sup 3 svd the computational reduction is substantial in typical scenarios i e d spl lt m spl les n in the spectrum estimation problems the data matrix has additional structure such as toeplitz or hankel they finally show how the fsd can exploit such structure for further computational reduction

efficiently computed reduced parameter input aided mmse equalizers for ml detection a unified approach a unified approach for computing the optimum settings of a length n sub f input aided equalizer that minimizes the mean square error between the equalized channel impulse response and a target impulse response of a given length n sub b is presented this approach offers more insight into the problem easily accommodates correlation in the input and noise sequences leads to significant computational savings and allows us to analyze a variety of constraints on the target impulse response besides the standard unit tap constraint in particular we show that imposing a unit energy constraint results in a lower mean square error at a comparable computational complexity furthermore we show that under the assumed constraint of finite length filters the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance we describe a new characterization of the optimum delay and show how to compute it finally we derive reduced parameter pole zero models of the equalizer that achieve the high performance of a long all zero equalizer at a much lower implementation cost

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

iterative decoding of coded thp with quantized output this paper proposes an improved receiver for the tomlinson harashima precoder thp in this paper we demonstrate that most of the capacity loss associated with conventional thp is due to the suboptimal receiver which is a simple modulo operation we then demonstrate how this loss can can be avoided with the optimization of the receiver in the suboptimal receiver the modulo operation ignores the dependency between the implicitly added sequence of symbols removed by it we then implement a thp with quantized outputs the quantized outputs enable to implement a maximum a posteriori probability map receiver that exploits the dependency between the received symbols the map receiver is named enhanced modulo operation emod and operates as an inner decoder within an iterative scheme either with outer low density parity check ldpc code or outer turbo code simulation results show considerable gains relative to coded conventional thp and also relative to the turbo equalizer te which does not use a precoder in the transmitter

on the frequency count for a random walk with absorbing boundaries a carcinogenesis example i a nonhomogeneous random walk on non negative integers with transition probabilities p0i delta 0i pni delta ni pi i 1 lambda i pi i 1 mu i and pi i rho i lambda i mu i rho i 1 is studied in particular when the transition probabilities are independent of position a general expression for the joint probability generating function jpgf of the frequency count of the stages 1 2 n 1 is derived the appropriate marginal forms of this jpgf yield the pgf of the frequency count at any pair of stages and at any particular single stage some moment formulae associated with the frequency count are derived a random walk conditional on absorption at a specified boundary is also considered the random walk model proposed is eminently suitable for the example of carcinogenesis

low complexity equalization of time varying channels with precoding this correspondence deals with time varying tv single input multiple output simo channels which are both frequency selective due to high data rate and time selective due to mobility a complex exponential basis expansion model ce bem is used to model the channel we consider a block transmission system where on the transmit side a precoder is employed to enable the maximum available diversity for a ce bem channel after direct decoding on the receive side the resulting channel resembles a finite impulse response fir filter on both block and symbol level we therefore propose an equalizer that bears a structure analogous to the effective channel in comparison with a standard block minimum mean square error decision feedback equalizer bmmse dfe that involves the inversion of a large size matrix the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available the equalizer taps and the information symbol estimates are refined recursively by means of normalized least mean squares nlms adaptation

fast adaptive equalization diversity combining for time varying dispersive channels we examine adaptive equalization and diversity combining methods for fast rayleigh fading frequency selective channels we assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation for the feedforward channel estimation we propose a novel reduced dimension channel estimation procedure where the number of unknown parameters are reduced using a priori information of the transmit shaping filter s impulse response fewer unknown parameters require a shorter training sequence we obtain least squares maximum likelihood and maximum a posteriori map estimators for the reduced dimension channel estimation problem for symbol detection we propose the use of a matched filtered diversity combining decision feedback equalizer dfe instead of a straightforward diversity combining dfe the matched filter form has lower computational complexity and provides a well conditioned matrix inversion to cope with fast time varying channels we introduce a new dfe coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error mmse criterion we refer to this as the non toeplitz dfe nt dfe we also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation with performance close to the optimal nt dfe

at structure of ah algebras with the ideal property and torsion free k theory abstract let a be an ah algebra that is a is the inductive limit c algebra of a 1 1 2 a 2 2 3 a 3 a n with a n i 1 t n p n i m n i c x n i p n i where x n i are compact metric spaces t n and n i are positive integers and p n i m n i c x n i are projections suppose that a has the ideal property each closed two sided ideal of a is generated by the projections inside the ideal as a closed two sided ideal suppose that sup n i dim x n i this condition can be relaxed to a certain condition called very slow dimension growth in this article we prove that if we further assume that k a is torsion free then a is an approximate circle algebra or an a t algebra that is a can be written as the inductive limit of b 1 b 2 b n where b n i 1 s n m n i c s 1 one of the main technical results of this article called the decomposition theorem is proved for the general case i e without the assumption that k a is torsion free this decomposition theorem will play an essential role in the proof of a general reduction theorem where the condition that k a is torsion free is dropped in the subsequent paper gong et al preprint 31 of course in that case in addition to space s 1 we will also need the spaces t ii k t iii k and s 2 as in gong 2002 29