coded continuous phase modulation with low complexity noncoherent reception coded continuous phase modulation based on a feedback free modulator with noncoherent detection is discussed low complexity receiver processing is achieved by using only two or three linear filters for demodulation and applying noncoherent sequence estimation with reduced state viterbi decoding and simple branch metric calculation overall the proposed noncoherent receiver provides significant advantages over previously presented approaches

the helmholtz machine discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning one fruitful approach is to build a parameterized stochastic generative model independent draws from which are likely to produce the patterns for all but the simplest generative models each pattern can be generated in exponentially many ways it is thus intractable to adjust the parameters to maximize the probability of the observed patterns we describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations our method can be viewed as a form of hierarchical self supervised learning that may relate to the function of bottom up and top down cortical processing pathways

designing structured tight frames via an alternating projection method tight frames also known as general welch bound equality sequences generalize orthonormal systems numerous applications including communications coding and sparse approximation require finite dimensional tight frames that possess additional structural properties this paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems ieps which includes the frame design problem to apply this method one needs only to solve a matrix nearness problem that arises naturally from the design specifications therefore it is the fast and easy to develop versions of the algorithm that target new design problems alternating projection will often succeed even if algebraic constructions are unavailable to demonstrate that alternating projection is an effective tool for frame design the paper studies some important structural properties in detail first it addresses the most basic design problem constructing tight frames with prescribed vector norms then it discusses equiangular tight frames which are natural dictionaries for sparse approximation finally it examines tight frames whose individual vectors have low peak to average power ratio par which is a valuable property for code division multiple access cdma applications numerical experiments show that the proposed algorithm succeeds in each of these three cases the appendices investigate the convergence properties of the algorithm

cohomology of infinitesimal and discrete groups an infinitesimal algebraic group over a field k is a connected algebraic group scheme whose coordinate ring is a finite dimension al k algebra if one begins with a reductive algebraic group g defined over fp then one has a close relationship between the representation theory of g that of its infinitesimal subgroups g defined as the kernels of the frobenius endomorphisms rr g g and that of its finite chevalley subgroups g fq of fq rational points q pd a basic theorem of cline et al i 9 theorem 6 6 relates the cohomology of g in a rational representation to that of the finite groups g fq related work of cline et al 6 and of the authors 1 16 relates the cohomology of g to that of its infinitesimal subgroups a determination of the cohomology of the first infinitesimal subgroup g 1 of g with trivial coefficients has enabled the authors in 14 to make certain explicit cohomology calculations for the finite groups g fq with certain nontrivial coefficients in this paper we continue our study of infinitesimal subgroups of simple algebraic groups by proving various qualitative properties of their cohomology and by extending our computational knowledge in particular we provide a computation which applies in a range of degrees to chevalley groups over the prime field we also investigate the cohomology of infinitesimal subgroups of nilpotent groups enabling us for example to determine the cohomology of their lie algebras in certain cases we apply this lie algebra cohomology computation to determine the integral cohomology of various torsion free nilpotent groups modulo small prime torsion thereby extending a theorem of dwyer 12 in more detail the paper begins in sect 1 with a spectral sequence converging to the cohomology of the first infinitesimal subgroup g which was previously studied in 14 from this spectral sequence it easily follows that h g1 m is a noetherian h g1 k module for each finite dimensional rational gl module m we then apply the work of andersen and jantzen 1 on the gl cohomology of induced modules to obtain the analogous result for the second infinitesimal subgroup gz our analysis also permits a determination of the generic

poly mathbb z group actions on kirchberg algebras ii this is the second part of our serial work on the classification of poly mathbb z group actions on kirchberg algebras based on technical results obtained in our previous work we completely reduce the problem to the classification of continuous fields of kirchberg algebras over the classifying spaces as an application we determine the number of cocycle conjugacy classes of outer mathbb z n actions on the cuntz algebras

a particle algorithm for sequential bayesian parameter estimation and model selection we describe a particle algorithm for the sequential bayesian estimation of unknown static parameters the algorithm combines sequential importance sampling sis and markov chain monte carlo mcmc to achieve computational efficiency and stability in its most general form the algorithm has three components i sis ii a rejuvenation test and iii mcmc measurements are processed sequentially with an artificial time line if there is no natural one associated with the measurements by sis which is computationally inexpensive after each measurement is processed the rejuvenation test checks whether the resulting sis particles have to be rejuvenated when indicated by the test the particles are completely rejuvenated by mcmc which removes errors that accumulate from sis due to the finite number of particles thus ensuring stability whenever possible the sis particles can be used to advantage in the mcmc there is flexibility in the choice of the rejuvenation test as well as the mcmc method with potential to increase the usefulness of the algorithm in particular by using reversible jump mcnic with multiple models the algorithm can perform simultaneous model selection and parameter estimation in this paper we use a rejuvenation test based on a kullback leibler distance that is easy to compute and our choice of mcnic is independent metropolis hastings with a gaussian proposal density with these choices we illustrate the use of the algorithm in two signal processing applications passive source localization with angle of arrival and simultaneous weak signal detection and parameter estimation involving both simulated and real data the results demonstrate the algorithm s stability its built in protection against model overfitting and tolerance to model mismatch

codes based on a trellis cut set transformation ii codes for noncoherent detection for pt i see ibid vol 46 p 610 20 1998 we continue the study of cut set trellis section t sub cb codes begun in part i and show that such codes are well suited for use with multiple symbol noncoherent detection and conventional two symbol differential detection the information bit assignment for a cut set trellis section can be modified to make the resulting code noncatastrophic for noncoherent detection by this procedure many existing two dimensional 2 d and multidimensional mpsk and qam trellis codes designed for coherent detection can be easily converted into codes for both coherent and noncoherent detection compared to m dpsk trellis codes it is shown that 2 d mpsk cut set trellis section codes have improved performance for multiple symbol noncoherent detection and comparable performance for conventional two symbol differential detection thus cut set trellis section codes are a class of universal channel codes since a single encoder performs well for coherent detection multiple symbol noncoherent detection and conventional two symbol differential detection

cohomology of nilpotent groups of class 2 abstract we compute the cohomology rings of a number of nilpotent groups of class 2 for appropriate coefficients and we do some more sample calculations of various cohomology groups the basic tool is a suitable small free resolution for an arbitrary nilpotent group of class 2 constructed in a previous paper

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

bayesian sequential parameter estimation by cognitive radar with multiantenna arrays in this paper we consider the problem of bayesian sequential parameter estimation of extended targets for cognitive radar with multi antenna arrays using adaptive waveforms the target is modeled as a complex gaussian random process using iterative waveform transmission the cognitive radar estimates the target s characteristic parameters and updates its probabilistic model based on new measurements the adaptive waveform is designed by minimizing the conditional entropy from the posterior density of the model parameters we analyze the performance of the developed bayesian sequential estimation algorithm and derive expressions for the signal to noise ratio gain the asymp totical posterior cramer rao bound and the mutual information gain the analysis and numerical simulations demonstrate that the adaptive sequential bayesian estimator yields accelerated convergence of the estimate towards its true value and a smaller estimation error compared with the conventional bayesian esti mator that uses fixed waveform transmission under gaussian or non gaussian noise

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

toward a fundamental theory of optimal feature selection part ii implementation and computational complexit certain algorithms and their computational complexity are examined for use in a vlsi implementation of the real time pattern classifier described in part i of this work the most computationally intensive processing is found in the classifier training mode wherein subsets of the largest and smallest eigenvalues and associated eigenvectors of the input data covariance pair must be computed it is shown that if the matrix of interest is centrosymmetric and the method for eigensystem decomposition is operator based the problem architecture assumes a parallel form such a matrix structure is found in a wide variety of pattern recognition and speech and signal processing applications each of the parallel channels requires only two specialized matrix arithmetic modules these modules may be implemented as linear arrays of processing elements having at most o n elements where n is the input data vector dimension the computations may be done in o n time steps this compares favorably to o n3 operations for a conventional or general rotation based eigensystem solver and even the o 2n2 operations using an approach incorporating the fast levinson algorithm for a matrix of toeplitz structure since the underlying matrix in this work does not possess a toeplitz structure some examples are provided on the convergence of a conventional iterative approach and a novel two stage iterative method for eigensystem decomposition

doubly constrained robust capon beamformer the standard capon beamformer scb is known to have better resolution and much better interference rejection capability than the standard data independent beamformer when the array steering vector is accurately known however the major problem of the scb is that it lacks robustness in the presence of array steering vector errors in this paper we will first provide a complete analysis of a norm constrained capon beamforming nccb approach which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise our analysis of nccb is thorough and sheds more light on the choice of the norm constraint than what was commonly known we also provide a natural extension of the scb which has been obtained via covariance matrix fitting to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector viz a constant norm constraint and a spherical uncertainty set constraint which we refer to as the doubly constrained robust capon beamformer dcrcb nccb and dcrcb can both be efficiently computed at a comparable cost with that of the scb performance comparisons of nccb dcrcb and several other adaptive beamformers via a number of numerical examples are also presented

polycyclic by finite groups admit a bounded degree polynomial structure for a polycyclic by finite group gamma of hirsch length h an affine resp polynomial structure is a representation of gamma into rm aff bbb r h resp rm p bbb r h the group of polynomial diffeomorphisms letting gamma act properly discontinuously on bbb r h recently it was shown by counter examples that there exist groups gamma even nilpotent ones which do not admit an affine structure thus giving a negative answer to a long standing question of john milnor we prove that every polycyclic by finite group gamma admits a polynomial structure which moreover appears to be of a special simple type called canonical and as a consequence of this consists entirely of polynomials of a bounded degree the construction of this polynomial structure is a special case of an iterated seifert fiber space construction which can be achieved here because of a very strong and surprising cohomology vanishing theorem

the uniqueness of polynomial crystallographic actions let gamma be a polycyclic by finite group it is proved in 8 that gamma admits a polynomial action of bounded degree on mathbb r n which is properly discontinuous and such that the quotient gamma backslash mathbb r n is compact we prove here that such an action is unique up to conjugation by a polynomial transformation of mathbb r n

polynomial structures for nilpotent groups if a polycyclic by finite rank k group admits a faithful affine representation making it acting on rk properly discontinuously and with compact quotient we say that admits an affine structure in 1977 john milnor questioned the existence of affine structures for such groups very recently examples have been obtained showing that even for torsion free finitely generated nilpotent groups n affine structures do not always exist it looks natural to consider affine structures as examples of polynomial structures of degree one we introduce the concept of a canonical type polynomial structure for polycyclic by finite groups using the algebraic framework of the seifert fiber space construction and a nice cohomology vanishing theorem we prove the existence and uniqueness up to conjugation of canonical type polynomial structures for virtually finitely generated nilpotent groups applying this uniqueness to a result going back to mal cev it follows that for torsion free finitely generated nilpotent groups each canonical polynomial structure is expressed in polynomials of limited degree the minimal degree needed for obtaining a polynomial structure will determine the affine defect number we prove that the known counterexamples to milnor s question have the smallest possible affine defect i e affine defect number equal to one

adaptive iterative detectors for phase uncertain channels via variational bounding the problem of iterative detection decoding of data symbols transmitted over an additive white gaussian noise awgn channel in the presence of phase uncertainty is addressed in this paper by modelling the phase uncertainty either as an unknown deterministic variable process or random variable process with a known a priori probability density function a number of non bayesian and bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem in this paper a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique especially applying the generic variational bayesian vb framework efficient iterative joint estimation and detection decoding schemes are derived for the constant phase model as well as for the dynamic phase model in addition the relation of the vb based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation maximization em algorithm is provided performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors furthermore an incremental scheduling of the vb or em algorithm is shown to reduce the overall complexity of the receiver

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

quantizing for minimum average misclassification risk in pattern classification a decision rule is a labeled partition of the observation space where labels represent classes a way to establish a decision rule is to attach a label to each code vector of a vector quantizer vq when a labeled vq is adopted as a classifier we have to design it in such a way that high classification performance is obtained by a given number of code vectors in this paper we propose a learning algorithm which optimizes the position of labeled code vectors in the observation space under the minimum average misclassification risk criterion

on the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues we derive some basic results on the geometry of semidefinite programming sdp and eigenvalue optimization i e the minimization of the sum of the k largest eigenvalues of a smooth matrix valued function we provide upper bounds on the rank of extreme matrices in sdps and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue optimization in the spectrum of an optimal matrix the kth and k 1 st largest eigenvalues tend to be equal and frequently have multiplicity greater than two this clustering is intuitively plausible and has been observed as early as 1975 when the matrix valued function is affine we prove that clustering must occur at extreme points of the set of optimal solutions if the number of variables is sufficiently large we also give a lower bound on the multiplicity of the critical eigenvalue these results generalize to the case of a general matrix valued function under appropriate conditions

unified optimization framework for multi static radar code design using information theoretic criteria in this paper we study the problem of code design to improve the detection performance of multi static radar in the presence of clutter i e a signal dependent interference to this end we briefly present a discrete time formulation of the problem as well as the optimal detector in the presence of gaussian clutter due to the lack of analytical expression for receiver operation characteristic roc code design based on roc is not feasible therefore we consider several popular information theoretic criteria including bhattacharyya distance kullback leibler kl divergence j divergence and mutual information mi as design metrics the code optimization problems associated with different information theoretic criteria are obtained and cast under a unified framework we propose two general methods based on majorization minimization to tackle the optimization problems in the framework the first method provides optimal solutions via successive majorizations whereas the second one consists of a majorization step a relaxation and a synthesis stage moreover derivations of the proposed methods are extended to tackle the code design problems with a peak to average ratio power par constraint using numerical investigations a general analysis of the coded system performance computational efficiency of the proposed methods and the behavior of the information theoretic criteria is provided

aspherical manifolds with virtually 3 step nilpotent fundamental group a closed aspherical manifold of dimension 3 4 with virtually 3 step nilpotent fundamental group supports a complete affinely flat structure topological and seifert bundle classifications are given for a special case called seifert relatives of flat riemannian manifolds we use the seifert fiber space construction as a main tool 0 introduction it is well known that given a torsion free virtually poly z group ir there exists a closed smooth k r 1 manifold eg a double coset space of a lie group a question we are interested in is whether such a manifold is homeomorphic to a quotient of r by an action of a discrete group of affine motions the best known result seems to be j scheuneman s 18 stating that the answer is yes if ir is 3 step nilpotent in this paper we generalize this to virtually 3 step nilpotent groups in dimension 3 4 the main idea is to refine the seifert fiber space construction of p conner and f raymond 4 this gives rise to an embedding of such ir into the group of affine motions so that rm ir is compact then we apply t farrell and w c hsiang s theorem 6 stating that any two closed aspherical manifolds with isomorphic fundamental groups which are virtually nilpotent are homeomorphic in dimension 3 4 this paper is organized as follows in section 1 we refine the seifert fiber space construction by restricting the coefficient module to some submodules of m w rk the main result is that if the first coboundary homomorphism 6 of certain cohomology exact sequence is surjective then one can convert the algebraic object group into a geometric one group action manuscript received november 23 1981 manuscript revised may 14 1981 this is a part of the author s ph d thesis at the university of michigan 1981 the second part geometric realization will appear as a separate article elsewhere the author wishes to express his sincere appreciation to professor frank raymond for his guidance in this work

a coordinate descent framework to design low psl isl sequences this paper is focused on the design of phase sequences with good aperiodic autocorrelation properties in terms of peak sidelobe level and integrated sidelobe level the problem is formulated as a biobjective pareto optimization forcing either a continuous or a discrete phase constraint at the design stage an iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems that are nonconvex and np hard in general each iteration of the devised method requires the solution of a nonconvex min max problem it is handled either through a novel bisection or an fft based method respectively for the continuous and the discrete phase constraint additionally a heuristic approach to initialize the procedures employing the l p norm minimization technique is proposed simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase binary case

conditional posterior cramer rao lower bounds for nonlinear sequential bayesian estimation the posterior cramerrao lower bound pcrlb for sequential bayesian estimators which was derived by tichavsky in 1998 provides a performance bound for a general nonlinear filtering problem however it is an offline bound whose corresponding fisher information matrix fim is obtained by taking the expectation with respect to all the random variables namely the measurements and the system states as a result this unconditional pcrlb is not well suited for adaptive resource management for dynamic systems the new concept of conditional pcrlb is proposed and derived in this paper which is dependent on the actual observation data up to the current time and is implicitly dependent on the underlying system state therefore it is adaptive to the particular realization of the underlying system state and provides a more accurate and effective online indication of the estimation performance than the unconditional pcrlb both the exact conditional pcrlb and its recursive evaluation approach including an approximation are derived further a general sequential monte carlo solution is proposed to compute the conditional pcrlb recursively for nonlinear non gaussian sequential bayesian estimation problems the differences between this new bound and existing measurement dependent pcrlbs are investigated and discussed illustrative examples are also provided to show the performance of the proposed conditional pcrlb

information theoretic bounds on target recognition performance based on degraded image data this paper derives bounds on the performance of statistical object recognition systems wherein an image of a target is observed by a remote sensor detection and recognition problems are modeled as composite hypothesis testing problems involving nuisance parameters we develop information theoretic performance bounds on target recognition based on statistical models for sensors and data and examine conditions under which these bounds are tight in particular we examine the validity of asymptotic approximations to probability of error in such imaging problems problems involving gaussian poisson and multiplicative noise and random pixel deletions are considered as well as least favorable gaussian clutter a sixth application involving compressed sensor image data is considered in some detail this study provides a systematic and computationally attractive framework for analytically characterizing target recognition performance under complicated non gaussian models and optimizing system parameters

a symbol by symbol channel estimation receiver for space time block coded systems and its performance analysis on the nonselective rayleigh fading channel we present a symbol by symbol channel estimation receiver for an orthogonal space time block coded system and derive its analytical performance on a slow nonselective rayleigh fading channel exact closed form expressions for its bit error probability bep performance for m ary phase shift keying modulations are obtained which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error our bep expressions show explicitly the dependence of bep on the mean square error of the channel estimates which in turn depend on the channel fading model and the channel estimator used tight upper bounds are presented that show more clearly the dependence of the bep on various system parameters simulation results using various fading models are obtained to demonstrate the validity of the analysis

the real cohomology of virtually nilpotent groups abstract in this paper we present a method to compute the real cohomology of any finitely generated virtually nilpotent group the main ingredient in our setup consists of a polynomial crystallographic action of this group as any finitely generated virtually nilpotent group admits such an action which can be constructed quite easily the approach we present applies to all these groups our main result is an algorithmic way of computing these cohomology spaces as a first application we prove a kind of poincare duality also in the nontorsion free case and we derive explicit formulas in the virtually abelian case

space time code design for mimo detection based on kullback leibler divergence the focus of the paper is on the design of space time codes for a general multiple input multiple output detection problem when multiple observations are available at the receiver the figure of merit used for optimization purposes is the convex combination of the kullback leibler divergences between the densities of the observations under the two hypotheses and different system constraints are considered this approach permits to control the average sample number i e the time for taking a decision in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test the solutions offer an interesting insight in the optimal transmit policies encapsulated in the rank of the code matrix which rules the amount of diversity to be generated as well as in the power allocation policy along the active eigenmodes a study of the region of achievable divergence pairs whose availability permits optimization of a wide range of merit figures is also undertaken a set of numerical results is finally given in order to analyze and discuss the performance and validate the theoretical results

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

maximum likelihood digital data sequence estimation over the gaussian channel with unknown carrier phase we consider the problem of simultaneous ml estimation of data and carrier phase from a linear suppressed carrier modulated signal received in the presence of additive white gaussian noise the ml detector of the data sequence is derived and its error probability performance is analyzed the result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length a suboptimum decision aided subsequence by subsequence detector whose complexity does not increase exponentially with sequence length is proposed and its performance is analyzed

three dimensional affine crystallographic groups those groups r which act properly discontinuously and aillnely on ii with compact fundamental domain are classified first it is shown that such a group f contains a solvable subgroup of finite index thus establishing a conjecture of auslander in dimension three then unimodular simply transitive altine actions on ir are classified this leads to a classification of attine crystallographic groups acting on ir3 a characterization of which abstract groups admit such an action is given moreover it is proved that every isomorphism between virtually solvable atline crystallographic groups respectively simply transitive afline groups is induced by conjugation by a polynomial automorphism of the affrne space a characterization is given of which closed 3 manifolds can be represented as quotients of ir by groups of afftne transformations a closed 3 manifold m admits a complete atline structure if and only if m has a finite covering homeomorphic or homotopy equivaient to a 2 torus bundle over the circle

some properties of the multisurface method for pattern classification abstract fisher 2 r a fisher the use of multiple measurements in taxonomic problems ann eugenics 7 part ii 179 188 1936 introduced a criterion function for classification of two categories of patterns by a hyperplane a i x i h 0 he then found the normal vector a i that maximizes this criterion function in the present paper we generalize fisher s criterion function making it suitable for a piecewise linear classifier we build the optimal piecewise linear classifier that maximizes the generalized fisher s criterion function the basis of the method is presented in reference 1 s spivak a multisurface method for pattern classification pattern recognition 22 587 591 1989 here we explore further the properties of the method which include extracting irrelevant planes from the desired classifier and removing ineffective features from each plane it is shown that the method can be easily generalized for separation of more than two categories of patterns

functional properties of minimum mean square error and mutual information in addition to exploring its various regularity properties we show that the minimum mean square error mmse is a concave functional of the input output joint distribution in the case of additive gaussian noise the mmse is shown to be weakly continuous in the input distribution and lipschitz continuous with respect to the quadratic wasserstein distance for peak limited inputs regularity properties of mutual information are also obtained several applications to information theory and the central limit theorem are discussed

robust subspace learning and detection in laplacian noise and interference we address the problem of maximum likelihood subspace learning and detection in the presence of laplacian noise and interference whose subspace may be known or unknown for subspace learning the laplacian problem reduces to a maxmin convex mathematical program with polyhedral cost the minimization involves projection of the measurements onto a subspace orthogonal to the signal and interference spaces and has linear constraints while the maximization produces the subspace and has polyhedral constraints the laplacian noise model for subspace detection and estimation motivated by applications in functional magnetic resonance imaging and applicable in other areas yields maximum likelihood detectors and learned subspaces with unique structure due to the presence of corners in the polyhedrally convex optimization for instance the optimal learned subspace can consist of vectors whose elements take values of 1 or 1 only emergence of such a quantization attests to the robustness property of laplacian learning meaning that the solution is insensitive to perturbation in the data set the resulting detectors are similarly robust to false alarms and have computationally attractive properties

optimal transmit receiver design in the presence of signal dependent interference and channel noise optimal detection of a target return contaminated by signal dependent interference as well as additive channel noise requires the design of a transmit pulse f t and a receiver impulse response h t jointly maximizing the output signal to interference plus noise ratio sinr despite the highly nonlinear nature of this problem it has been possible to show that f t may always be chosen minimum phase a full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs f h that appears to converge satisfactorily for most values of input sinr extensive simulation reveals that the shape of f t can be a critical factor in particular the performance of a chirp like pulse is often unacceptable especially when clutter and channel noise are low pass dominant and comparable

design of optimized radar codes with a peak to average power ratio constraint this paper considers the problem of radar waveform design in the presence of colored gaussian disturbance under a peak to average power ratio par and an energy constraint first of all we focus on the selection of the radar signal optimizing the signal to noise ratio snr in correspondence of a given expected target doppler frequency algorithm 1 then through a max min approach we make robust the technique with respect to the received doppler algorithm 2 namely we optimize the worst case snr under the same constraints as in the previous problem since algorithms 1 and 2 do not impose any condition on the waveform phase we also devise their phase quantized versions algorithms 3 and 4 respectively which force the waveform phase to lie within a finite alphabet all the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints we prove that these problems are np hard and hence introduce design techniques relying on semidefinite programming sdp relaxation and randomization as well as on the theory of trigonometric polynomials providing high quality suboptimal solutions with a polynomial time computational complexity finally we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to doppler shifts

some results on matrix symmetries and a pattern recognition application this correspondence deals with various matrix symmetries frequently encountered in practice it is shown that the class of doubly symmetric matrices is not closed under multiplication whereas centrosymmetric matrices form an abelian group under addition and a non abelian group under multiplication results similar to centrosymmetric matrices are presented for the special case of centro hermitian matrices a brief discussion of a pattern recognition feature selection problem is included to demonstrate the manner in which these results may be utilized in practice for developing computationally efficient algorithms

multi parameter estimation in compound gaussian clutter by variational bayesian in this paper we consider the problem of multi parameter estimation in the presence of compound gaussian clutter for cognitive radar by the variational bayesian method the advantage of variational bayesian is that the estimation of multi variate parameters is decomposed to problems of estimation of univariate parameters by variational approximation thus enabling analytically tractable approximate posterior densities in complex statistical models consisting of observed data unknown parameters and hidden variables we derive the asymptotic bayesian cramer rao bounds and demonstrate by numerical simulations that the proposed approach leads to improved estimation accuracy than the expectation maximization method and the exact bayesian method in the case of non gaussian nonlinear signal models and small data sample size

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

a nonparametric bound for the bayes error abstract the exact computation of the bayes error probability is not possible in most recognition situations the mathematical form of the class conditional probability density functions of real world features is usually unknown we can only compute certain approximations from finite training sets this paper presents a nonparametric upper bound on the bayes wrror with a built in statistical test first the bayes error of a feature is expressed in terms of the relative extremes of the absolute value of the difference between the class conditional cumulative distributions then from the sampled distributions obtained from the training examples we can establish confidence bands for the true distributions finally an upper bound on the bayes error can be easily obtained from the confidence bands the bound has a definite statistical meaning it is as tight as allowed by a chosen confidence level it can be considered as an extension of the kolmogorov smirnov test an efficient algorithm for the bound in the univariate case is experimentally compared with other typical estimators and shown to be a practical and accurate feature celection criterion in a wide range of applications

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

variational bayesian estimation of statistical properties of composite gamma log normal distribution an iterative variational bayesian method is proposed for estimation of the statistical properties of the composite gamma log normal distribution specifically the nakagami parameter of the gamma component and the mean and variance parameters of the log normal component moreover the random hidden signal in the model plays a key role in the parameter estimation hence its density is also estimated the parameter estimation performance is analyzed by evaluation of the variational bayesian cramer rao bound from the variational posterior densities the numerical simulations show a good agreement between the bounds and the estimator variances in order to benchmark the proposed estimators the mse and relative bias of the parameter estimates are compared with those of the expectation maximization algorithm the proposed estimator has generally outperformed the benchmark algorithm the performance improvement is significant for the nakagami parameter varying from 9 db for a larger sample size to 24 db for a smaller sample size similarly the performance for the variance parameter varies from 1 5 db to 5 2 db with increasing the sample size the proposed algorithm is also tested on a simulated data set based on correlated latent variables and the estimator is found to be effective for weakly correlated data finally for the hidden signal the estimated density from the proposed method is found to be having lower kullback leibler divergence in comparison to that of the expectation maximization algorithm

mimo radar waveform design in colored noise based on information theory in this paper we consider multiple input multiple output mimo radar waveform design in colored noise two information theoretic measures are used as criterions for optimal waveform design under transmitted power constraint the first one is by maximizing the mutual information between target impulse response and target echoes the second one is by maximizing the relative entropy between two hypotheses in the first hypothesis we assume the target is not present in the echoes while in the second hypothesis we assume the target exists in the echoes we derive optimal solutions for both cases interestingly both optimal solutions require that transmitted waveform should match with the target and noise however the optimal solutions of the two problems lead to different power allocation strategies

polynomial structures on polycyclic groups we know by recent work of benoist and of burde grunewald that there exist polycyclic by finite groups g of rank h the examples given were in fact nilpotent admitting no properly discontinuous affine action on rh on the other hand for such g it is always possible to construct a properly discontinuous smooth action of g on rh our main result is that any polycyclic by finite group g of rank h contains a subgroup of finite index acting properly discontinuously and by polynomial diffeomorphisms of bounded degree on rh moreover these polynomial representations always appear to contain pure translations and are extendable to a smooth action of the whole group g

iterative maximum likelihood sequence estimation for space time coded systems in previous work on decoding space time codes it is either assumed that perfect channel state information csi is present or a channel estimate is obtained using pilot symbols and then used as if it were perfect to extract symbol estimates in the latter case a loss in performance is incurred since the resulting overall receiver is not optimal we look at maximum likelihood ml sequence estimation for space time coded systems without assuming csi the log likelihood function is presented for both quasi static and nonstatic fading channels and an expectation maximization em based algorithm is introduced for producing ml data estimates whose complexity is much smaller than a direct evaluation of the log likelihood function simulation results indicate the em based algorithm achieves a performance close to that of a receiver which knows the channel perfectly

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

on the uniqueness of some affinely flat infra nilmanifolds i p irn irk u p irn irk since pi irn irk pi irn ir k each element of i 1 ir irk is completely determined by k polynomials of total degree at most i in n variables let g be a group and suppose we have a morphism 4 g g l k ir and a homomorphism p g aff ir we can provide a g module structure for p ir f k in the following way for g e g and pepi ir irk we define

on the practical implication of mutual information for statistical decisionmaking a basic mathematical function that conjoins the two key conceptions of mutual information and bayes risk is defined based on that function some asymptotic theorems that verify an important implication of mutual information in the context of practical bayesian decisionmaking are proven

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

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

diversity integration tradeoffs in mimo detection in this paper a multiple input multiple output mimo detection problem is considered at first we derive the generalized likelihood ratio test glrt for arbitrary transmitted signals and arbitrary time correlation of the disturbance then we investigate design criteria for the transmitted waveforms in both power unlimited and power limited systems and we derive closed form formulas for the probability of false alarm and the detection probability finally we study the interplay among the rank of the optimized space time code i e the number of linearly independent transmitted waveforms the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path the results confirm that there is an inherent tradeoff between diversity and integration and that no uniformly optimum waveform design strategy exists

a per survivor phase estimation algorithm for detection of psk signals an expectation maximization em technique for maximum a posteriori map estimation of a random parameter is employed to devise a per survivor phase tracking algorithm for phase shift keyed signals transmitted over channels with phase jitter simulation results show that the proposed algorithm can provide substantial performance gains over recursive and nonrecursive phase estimators in the presence of a strong phase jitter

robust sequential approximate bayesian estimation summary an approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non normal observations the behaviour of the resulting non linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non normal error distributions illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned we consider here the problem of sequential estimation of the location vector of a linear time series model termed the dynamic linear model by harrison and stevens 1976 the straightforward exact analysis obtained by assuming normal error and prior structure is generally lost when alternative error distributions are adopted and yet considerations of realism or robustness may strongly suggest such non normal assumptions the multi state model of harrison and stevens provides an approximate analysis based on a discrete variance mixture of normal distributions an approach which has been extensively investigated in the engineering literature under the name of gaussian sum approximations see for example alspach and sorenson 1971 our aim in this paper is to provide an approximate tractible recursive updating procedure for the location parameters which is applicable to a wide range of symmetric unimodal error distributions and is both more realistic and more elegant than the discrete gaussian sum approach in particular for heavy tailed distributions our procedures provide approximate bayesian methods for time series analysis which extend considerably the work of masreliez and martin 1977 and have close connections with classical robustness ideas such as m estimation and influence functions

the mimo radar and jammer games the interaction between a smart target and a smart mimo radar is investigated from a game theory perspective since the target and the radar form an adversarial system their interaction is modeled as a two person zero sum game the mutual information criterion is used in formulating the utility functions the unilateral hierarchical and symmetric games are studied and the equilibria solutions are derived

noncoherent adaptive channel identification algorithms for noncoherent sequence estimation in this letter two novel noncoherent adaptive algorithms for channel identification are introduced the proposed noncoherent least mean square lms and noncoherent recursive least squares rls algorithms can be combined easily with noncoherent sequence estimation nse for m ary differential phase shift keying signals transmitted over intersymbol interference isi channels it is shown that the resulting adaptive noncoherent receivers are very robust against carrier phase variations for zero frequency offset the convergence speed and the steady state error of the noncoherent adaptive algorithms are similar to those of conventional lms and rls algorithms however the conventional algorithms diverge even for relatively small frequency offsets whereas the proposed noncoherent algorithms converge for relatively large frequency offsets simulations confirm the good performance of nse combined with noncoherent adaptive channel estimation in time variant fading isi channels

an adaptive receiver for space time trellis codes based on per survivor processing an adaptive receiver based on per survivor processing is proposed for detecting space time trellis codes transmitted over time selective flat fading channels and its performance is examined through simulations results suggest that the new receiver can outperform iterative approaches based on kalman filtering and the expectation maximization algorithm at the cost of increased receiver complexity

an information criterion for likelihood selection for a given source distribution we establish properties of the conditional density achieving the rate distortion function lower bound as the distortion parameter varies in the limit as the distortion tolerated goes to zero the conditional density achieving the rate distortion function lower bound becomes degenerate in the sense that the channel it defines becomes error free as the permitted distortion increases to its limit the conditional density achieving the rate distortion function lower bound defines a channel which no longer depends on the source distribution in addition to the data compression motivation we establish two results one asymptotic one nonasymptotic showing that the the conditional densities achieving the rate distortion function lower bound make relatively weak assumptions on the dependence between the source and its representation this corresponds in bayes estimation to choosing a likelihood which makes relatively weak assumptions on the data generating mechanism if the source is regarded as a prior taken together these results suggest one can use the conditional density obtained from the rate distortion function in data analysis that is when it is impossible to identify a true parametric family on the basis of physical modeling our results provide both data compression and channel coding justification for using the conditional density achieving the rate distortion function lower bound as a likelihood

the auslander conjecture for nil affine crystallographic groups let n be a simply connected connected real nilpotent lie group of finite dimension n we study subgroups in aff n n aut n acting properly discontinuously and cocompactly on n this situation is a natural generalization of the so called affine crystallographic groups we prove that for all dimensions 1 n 5 the generalized auslander conjecture holds i e that such subgroups are virtually polycyclic

per survivor processing and tentative decisions what is in between in per survivor processing psp the number of parameter estimators equals the number of retained hypothetical data sequences survivors the authors propose an algorithm which uses an arbitrary number of parameter estimators and compromises between the two extremes of tentative decisions one parameter estimator and psp specific applications to reduced state sequence estimation rsse and maximum likelihood sequence estimation mlse with adaptive tracking of a fading channel are considered

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

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

cramer rao lower bound and em algorithm for envelope based snr estimation of nonconstant modulus constellations signal to noise ratio snr estimation for linearly modulated signals is addressed in this letter focusing on envelope based estimators which are robust to carrier offsets and phase jitter and on the challenging case of nonconstant modulus constellations for comparison purposes the true cramer rao lower bound is numerically evaluated obtaining an analytical expression in closed form for the asymptotic case of high snr values which quantifies the performance loss with respect to coherent estimation as the maximum likelihood algorithm is too complex for practical implementation an expectation maximization em approach is proposed achieving a good tradeoff between complexity and performance for medium to high snrs finally a hybrid scheme based on em and moments based estimates is suggested which performs close to the theoretical limit over a wide snr range

mimo radar waveform design via alternating projection waveform design is essential to unleash the performance advantages promised by multiple input multiple output mimo radar and this topic has attracted a lot of attention in the recent years revisiting an earlier examined mimo radar waveform design problem that optimizes both minimum mean square error estimation mmse and mutual information mi in this correspondence we formulate a new waveform design problem and provide some further results which complement the previous study more specifically we present an iterative optimization algorithm based on the alternating projection method to determine waveform solutions that can simultaneously satisfy a structure constraint and optimize the design criteria numerical examples are provided which illustrate the effectiveness of the proposed approach in particular we find that the waveform solutions obtained through our proposed algorithm can achieve very close and virtually indistinguishable performance from that predicted in the previous study

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

polynomial alternatives for the group of affine motions it is known that every polycyclic by finite group even if it admits no affine structure allows a polynomial structure of bounded degree a major obstacle to a further development of the theory of these polynomial structures is that the group of the polynomial diffeomorphisms of mathbb r n in contrast to the group of affine motions is no longer a finite dimensional lie group in this paper we construct a family of finite dimensional lie groups even linear algebraic groups of polynomial diffeomorphisms which we call weighted groups of polynomial diffeomorphisms it turns out that every polycyclic by finite group admits a polynomial structure via these weighted groups in the nilpotent and other case s we can sharpen by specifying a nice set of weights the existence results obtained in earlier work we introduce unipotent polynomial structures of nilpotent groups and show how the existence of such polynomial structures is closely related to the existence of simply transitive actions of the corresponding mal cev completion this and other properties provide a strong analogy with the situation of affine structures and simply transitive affine actions considered e g in the work of fried goldman and hirsch

superrigidity of lattices in solvable lie groups let be a closed cocompact subgroup of a simply connected solvable lie groupg such that adg has the same zariski closure as adg if gln is any finite dimensional representation of we show that virtually extends to a representation ofg by combining this with work of margulis on lattices in semisimple groups we obtain a similar result for lattices in many groups that are neither solvable nor semisimple furthermore we show that if is isomorphic to a closed cocompact subgroup of another simply connected solvable lie groupg then any isomorphism from to extends to a crossed isomorphism fromg tog in the same vein we prove a more concrete form of mostow s theorem that compact solvmanifolds with isomorphic fundamental groups are diffeomorphic

toward a fundamental theory of optimal feature selection part i several authors have studied the problem of dimensionality reduction or feature selection using statistical distance measures e g the chernoff coefficient bhattacharyya distance i divergence and j divergence because they generally felt that direct use of the probability of classification error expression was either computationally or mathematically intractable we show that for the difficult problem of testing one weakly stationary gaussian stochastic process against another when the mean vectors are similar and the covariance matrices patterns differ the probability of error expression may be dealt with directly using a combination of classical methods and distribution function theory the results offer a new and accurate finite dimensionality information theoretic strategy to feature selection and are shown by use of examples to be superior to the well known kadota shepp approach which employs distance measures and asymptotics in its formulation the present part i deals with the theory part ii deals with the implementation of a computer based real time pattern classifier which takes into account a realistic quasi stationarity of the patterns

minimal models formality and hard lefschetz properties of solvmanifolds with local systems for a simply connected solvable lie group g with a cocompact discrete subgroup gamma we consider the space of differential forms on the solvmanifold g gamma with values in a certain flat bundle so that this space has a structure of a differential graded algebra dga we construct sullivan s minimal model of this dga this result is an extension of nomizu s theorem for ordinary coefficients in the nilpotent case by using this result we refine hasegawa s result of formality of nilmanifolds and benson gordon s result of hard lefschetz properties of nilmanifolds

feature extraction based on decision boundaries a novel approach to feature extraction for classification based directly on the decision boundaries is proposed it is shown how discriminantly redundant features and discriminantly informative features are related to decision boundaries a procedure to extract discriminantly informative features based on a decision boundary is proposed the proposed feature extraction algorithm has several desirable properties 1 it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem and 2 it finds the necessary feature vectors the proposed algorithm does not deteriorate under the circumstances of equal class means or equal class covariances as some previous algorithms do experiments show that the performance of the proposed algorithm compares favorably with those of previous algorithms