the efficiency of primitive recursive functions using denotational semantics tools colson and others studied primitive recursive p r algorithms proving the ultimate obstinacy property which has as a consequence that many computations cannot be efficiently implemented in a language that faithfully expresses the classical definition of p r functions as shown by ritchie and meyer the class of p r functions can also be characterised by the programming language loop our purpose is to show that the informal but precise operational description of loop and its variants is sufficient to prove non trivial time lower bounds of p r algorithms in particular we present a simple proof of a property which is similar to ultimate obstinacy namely that every p r program that implements a non trivial function must execute x i c times the body of some loop instruction where x i is the initial contents of some fixed input register and c does not depend on the input values this and other lower bounds were obtained without using the lambda calculus or systems with functional parameters such as godel system t if the conditional break and the decrement instructions are included in the loop language the ultimate obstinacy property does not hold in this case we use another approach for obtaining lower bounds the unconditional break instruction does not avoid the obstinacy property it is equivalent in function and efficiency to the conditional instruction if then else the efficient implementation of other functions like step x step 0 0 step x 1 for x 1 and min x y is also studied

a subspace approach to adaptive narrow band interference suppression in dsss we address the problem of suppression of a digital narrow band interferer in direct sequence spread spectrum dsss communications we focus on the adaptive suppression method proposed by honig madhow and verdti see ieee trans inform theory vol 41 p 944 960 1995 for wide band interference applying it to a narrow band interferer we identify the eigenspaces of the system dynamics to analyze the convergence of the adaptive version of the minimum mean square error mmse algorithm for this application using this subspace approach we are able to 1 significantly decrease the convergence times via a new constraint on the step size in adaptation 2 introduce a simple parameterization of the mean output energy moe and signal to interference ratio sir to compare performance of various receivers and 3 identify modes of operation where the algorithm will cease to effectively cancel interference we propose a new adaptive receiver that avoids the convergence anomalies identified while capitalizing on the new step size for faster convergence simulation results to support theoretical results are presented

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

detection and localization of multiple sources in noise with unknown covariance the authors present a novel technique for the detection and localization of multiple sources in the presence of noise with unknown and arbitrary covariance the technique is applicable to coherent and noncoherent signals and to arbitrary array geometry and is based on rissanen s minimum description length mdl principle 1989 for model selection its computational load is comparable to that of analogous techniques for white noise simulation results demonstrating the performance of this technique are included

basic notions of universal algebra for language theory and graph grammars abstract this paper reviews the basic properties of the equational and recognizable subsets of general algebras these sets can be seen as generalizations of the context free and regular languages respectively this approach based on universal algebra facilitates the development of the theory of formal languages so as to include the description of sets of finite trees finite graphs finite hypergraphs tuples of words partially commutative words also called traces and other similar finite objects

quiver theoretical approach to dynamical yang baxter maps abstract a dynamical yang baxter map introduced by shibukawa is a solution of the set theoretical analogue of the dynamical yang baxter equation in this paper we initiate a quiver theoretical approach for the study of dynamical yang baxter maps our key observation is that the category of dynamical sets over a set introduced by shibukawa to establish a categorical framework to deal with dynamical yang baxter maps can be embedded into the category of quivers with vertices by using this embedding we shed light on shibukawa s classification result of a certain class of dynamical yang baxter maps and extend his construction to obtain a new class of dynamical yang baxter maps we also discuss a relation between shibukawa s bialgebroid associated to a dynamical yang baxter map and hayashi s weak bialgebra associated to a star triangular face model

3d compatible ternary systems and yang baxter maps according to shibukawa ternary systems defined on quasi groups and satisfying certain conditions provide a way of constructing dynamical yang baxter yb maps after noting that these conditions can be interpreted as three dimensional compatibility of equations on quad graphs we investigate when the associated dynamical yb maps are in fact parametric yb maps in some cases these maps can be obtained as reductions of higher dimensional maps through compatible constraints conversely parametric yb maps on quasi groups with an invariance condition give rise to three dimensional compatible systems the application of this method on spaces with certain quasi group structures provides new examples of multi parametric yb maps and three dimensional compatible systems

estimation of the directions of arrival of signals in unknown correlated noise i the map approach and its implementation the authors propose a method of direction of arrival doa estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary other than being positive definite they examine the projection of the data onto the noise subspace the conditional probability density function pdf of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed the a posteriori pdf of the signal parameters alone is then obtained by assigning a noninformative a priori pdf to the unknown noise covariance matrix and integrating out this quantity a simple criterion for the maximum a posteriori map estimate of the doas of the signals is established some properties of this criterion are discussed and an efficient numerical algorithm for the implementation of this criterion is developed the advantage of this method is that the noise covariance matrix does not have to be known nor must it be estimated

complex factor analysis and extensions many subspace based array signal processing algorithms assume that the noise is spatially white in this case the noise covariance matrix is a multiple of the identity and the eigenvectors of the data covariance matrix are not affected by it if the noise covariance is an unknown arbitrary diagonal e g for an uncalibrated array the eigenvalue decomposition leads to incorrect subspace estimates and it has to be replaced by a more general factor analysis decomposition fa which then reveals all relevant information we consider this data model and several extensions where the noise covariance matrix has a more general structure such as banded sparse block diagonal and cases where we have multiple data covariance matrices that share the same noise covariance matrix starting from a nonlinear weighted least squares formulation we propose new estimation algorithms for both classical fa and its extensions the optimization is based on gauss newton gradient descent generally this leads to an iteration involving the inversion of a very large matrix using the structure of the problem we show how this can be reduced to the inversion of a matrix with dimension equal to the number of unknown noise covariance parameters this results in new algorithms that have faster numerical convergence and lower complexity compared to several maximum likelihood based algorithms that could be considered state of the art the new algorithms scale well to large dimensions and can replace eigenvalue decompositions in many applications even if the noise can be assumed to be white

frt construction for dynamical yang baxter maps abstract notions of an h x bialgebroid and of its dynamical representation are proposed the dynamical representations of each h x bialgebroid form a tensor category every dynamical yang baxter map r satisfying suitable conditions a generalization of the set theoretical solution to the quantum yang baxter equation gives birth to an h x bialgebroid a r the categories of l operators for r and of dynamical representations of a r are isomorphic as tensor categories

intensional aspects of function definitions abstract in this work a notion of function definition is introduced this notion is a generalization of equational definitions of functions we distinguish between two properties of function definitions extensional and intensional a property is extensional or intensional if it concerns the extension or intension of function definitions respectively the typical problem is that of representability given a restricted notion of function definition a function f and an intensional property p is it possible to find a definition of f which has property p the question which properties are to be considered to be intensional is discussed as an application three restricted notions of function definitions are studied these are herbrand godel kleene systems primitive recursive definitions and recursive definitions we show how these differ when considering a particular intensional property

maximum likelihood estimation for array processing in colored noise direction of arrival estimation of multiple sources using a uniform linear array in noise with unknown covariance is considered the noise is modeled as a spatial autoregressive process with unknown parameters both stochastic and deterministic signal models are considered for the random signal case an approximate maximum likelihood estimator of the signal and noise parameters is derived it requires numerical maximization of a compressed likelihood function over the unknown arrival angles analytical expressions for the mles of the signal covariance and the ar parameters are given similar results for the case of deterministic signals are also presented

solutions of the quantum dynamical yang baxter equation and dynamical quantum groups the quantum dynamical yang baxter qdyb equation is a useful generalization of the quantum yang baxter qyb equation this generalization was introduced by gervais neveu and felder unlike the qyb equation the qdyb equation is not an algebraic but a difference equation with respect to a matrix function rather than a matrix the qdyb equation and its quasiclassical analogue the classical dynamical yang baxter equation arise in several areas of mathematics and mathematical physics conformal field theory integrable systems representation theory the most interesting solution of the qdyb equation is the elliptic solution discovered by felder in this paper we prove the first classification results for solutions of the qdyb equation these results are parallel to the classification of solutions of the classical dynamical yang baxter equation obtained in our previous paper all solutions we found can be obtained from felder s elliptic solution by a limiting process and gauge transformations fifteen years ago the quantum yang baxter equation gave rise to the theory of quantum groups namely it turned out that the language of quantum groups hopf algebras is the adequate algebraic language to talk about solutions of the quantum yang baxter equation in this paper we propose a similar language originating from felder s ideas which we found to be adequate for the dynamical yang baxter equation this is the language of dynamical quantum groups or hopf algebroids which is the quantum counterpart of the language of dynamical poisson groupoids introduced in our previous paper

pilot designs for consistent frequency offset estimation in ofdm systems this paper presents pilot designs for consistent frequency offset estimation of orthogonal frequency division multiplexing systems in frequency selective fading channels we describe two design approaches namely consistency in the probabilistic sense and absolute consistency existing preambles and pilot designs in the literature do not guarantee the absolute consistency we derive general criteria for both approaches present sufficient conditions on the pilot structures over the maximum carrier frequency offset cfo estimation range half of the sampling rate and derive simple pilot designs satisfying these conditions we also extend the sufficient conditions to any arbitrary but fixed cfo estimation range and present some generalized design patterns furthermore the cfo estimation performances of distinct consistent pilot designs can be quite different at moderate or low signal to noise ratio snr due to different statistics of outliers which also yields a link failure we develop efficient pilot design criteria that provide both consistency and robustness against outliers at moderate to low snr our consistent pilot designs facilitate flexible and economical implementation while our robust pilot designs enable wireless links with less outage and better resilience

a transform based covariance differencing approach for some classes of parameter estimation problems a method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance the proposed algorithm does not require multiple estimates of the signal covariance matrix instead it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner the noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible this is illustrated by applying the algorithm to the problems of bearing estimation resolution of overlapping echos and transient response analysis simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods

optimal utilization of signal free samples for array processing in unknown colored noise fields many algorithms for direction of arrival doa estimation require the noise covariance matrix to be known or to possess a known structure in many cases the noise covariance is in fact estimated from separate measurements this paper addresses the combined effects of finite sample sizes both in the estimated noise covariance matrix and in the data with signals present it is assumed that a batch of signal free samples is available in addition to the signal containing samples no assumption is made on the structure of the noise covariance in this paper the asymptotic covariance of the weighted subspace fitting wsf algorithm is derived for the case in which the data are whitened using an estimated noise covariance the expression obtained suggests an optimal weighting that improves performance compared to the standard choice in addition a new method based on covariance matching is proposed both methods are asymptotically statistically efficient the cramer rao lower bound crb on the covariance of the estimate for the data model is also derived monte carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results

bounds for maximum likelihood regular and non regular doa estimation in k distributed noise we consider the problem of estimating the direction of arrival of a signal embedded in k distributed noise when secondary data which contains noise only are assumed to be available based upon a recent formula of the fisher information matrix fim for complex elliptically distributed data we provide a simple expression of the fim with the two data sets framework in the specific case of k distributed noise we show that under certain conditions the fim for the deterministic part of the model can be unbounded while the fim for the covariance part of the model is always bounded in the general case of elliptical distributions we provide a sufficient condition for unboundedness of the fim accurate approximations of the fim for k distributed noise are also derived when it is bounded additionally the maximum likelihood estimator of the signal doa and an approximated version are derived assuming known covariance matrix the latter is then estimated from secondary data using a conventional regularization technique when the fim is unbounded an analysis of the estimators reveals a rate of convergence much faster than the usual t 1 simulations illustrate the different behaviors of the estimators depending on the fim being bounded or not

maximum likelihood estimation of signals in autoregressive noise time series modeling as the sum of a deterministic signal and an autoregressive ar process is studied maximum likelihood estimation of the signal amplitudes and ar parameters is seen to result in a nonlinear estimation problem however it is shown that for a given class of signals the use of a parameter transformation can reduce the problem to a linear least squares one for unknown signal parameters in addition to the signal amplitudes the maximization can be reduced to one over the additional signal parameters the general class of signals for which such parameter transformations are applicable thereby reducing estimator complexity drastically is derived this class includes sinusoids as well as polynomials and polynomial times exponential signals the ideas are based on the theory of invariant subspaces for linear operators the results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems the authors briefly discuss some applications such as spectral analysis broadband transient detection using line array data and fundamental frequency estimation for periodic signals

hopf algebroids with bijective antipodes axioms integrals and duals abstract motivated by the study of depth 2 frobenius extensions we introduce a new notion of hopf algebroid it is a 2 sided bialgebroid with a bijective antipode which connects the two left and right handed structures while all the interesting examples of the hopf algebroid of j h lu turn out to be hopf algebroids in the sense of this paper there exist simple examples showing that our definition is not a special case of lu s our hopf algebroids however belong to the class of l hopf algebras proposed by p schauenburg after discussing the axioms and some examples we study the theory of non degenerate integrals in order to obtain duals of hopf algebroids

low complexity nonlinear least squares carrier offset estimator for ofdm identifiability diversity and performance orthogonal frequency division multiplexing ofdm transforms frequency selective channels into multiple low rate flat fading subchannels carrier frequency offset between transmitter and receiver local oscillators must be estimated and compensated at the receiver to maintain orthogonality of these subchannels in this paper we derive the nonlinear least squares nls estimator for carrier frequency synchronization that exploits receiver diversity and known ofdm signal subspace structure due to the placement of unmodulated virtual subcarriers the resulting estimator benefits from the high resolution subspace method without the computational overhead associated with subspace decomposition fundamental estimator performance relationships against parameters such as signal to noise ratio snr frequency selective fading and diversity branch correlation are derived in particular we derive the cramer rao bound crb for the mean square error mse of the carrier frequency offset estimator numerical studies are presented to verify the results

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

blind channel estimation for amplify and forward two way relay networks employing m psk modulation we consider the problem of channel estimation for amplify and forward af two way relay networks twrns most works on this problem focus on pilot based approaches which impose a significant training overhead that reduces the spectral efficiency of the system to avoid such losses we propose blind channel estimation algorithms for af twrns that employ constant modulus cm signaling our main algorithm is based on the deterministic maximum likelihood dml approach assuming m psk modulation we show that the resulting estimator is consistent and approaches the true channel with high probability at high snr for modulation orders higher than 2 for bpsk however the dml algorithm performs poorly and we propose an alternative algorithm that yields much better performance by taking into account the bpsk structure of the data symbols for comparative purposes we also investigate the gaussian maximum likelihood gml approach which treats the data symbols as gaussian distributed nuisance parameters we derive the cramer rao bound and use monte carlo simulations to investigate the mean squared error mse performance of the proposed algorithms we also compare the symbol error rate ser performance of the dml algorithm with that of the training based least squares ls algorithm and demonstrate that the dml offers a superior tradeoff between accuracy and spectral efficiency

cisoid parameter estimation in the colored noise case asymptotic cramer rao bound maximum likelihood and nonlinear least squares the problem of estimating the parameters of complex valued sinusoidal signals cisoids for short from data corrupted by colored noise occurs in many signal processing applications we present a simple formula for the asymptotic large sample cramer rao bound crb matrix associated with this problem the maximum likelihood method mlm which estimates both the signal and noise parameters attains the performance corresponding to the asymptotic crb as the sample length increases more interestingly we show that a computationally much simpler nonlinear least squares method nlsm which estimates the signal parameters only achieves the same performance in large samples

hopf algebroids and rigid tensor categories associated with dynamical yang baxter maps abstract we construct hopf algebroids by means of dynamical yang baxter maps set theoretic solutions to a version of the quantum dynamical yang baxter equation this hopf algebroid with suitable properties implies two rigid tensor categories one is a category consisting of finite dimensional dynamical representations the other is a category consisting of l operators on finite dimensional spaces they are isomorphic to each other

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

ml estimation of time and frequency offset in ofdm systems we present the joint maximum likelihood ml symbol time and carrier frequency offset estimator in orthogonal frequency division multiplexing ofdm systems redundant information contained within the cyclic prefix enables this estimation without additional pilots simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

direction estimation in partially unknown noise fields the problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered the unknown noise covariance is assumed to obey a linear parametric model using this model the maximum likelihood directions parameter estimate is derived and a large sample approximation is formed it is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ml aml estimator furthermore a closed form expression of the cramer rao bound on the direction parameter is provided a perturbation analysis with respect to a small error in the assumed noise model is carried out and an expression of the asymptotic bias due to the model mismatch is given computer simulations and an application of the proposed technique to a full scale passive sonar experiment is provided to illustrate the results

on primitive recursive algorithms and the greatest common divisor function we establish linear lower bounds for the complexity of non trivial primitive recursive algorithms from piecewise linear given functions the main corollary is that logtime algorithms for the greatest common divisor from such givens such as stein s cannot be matched in efficiency by primitive recursive algorithms from the same given functions the question is left open for the euclidean algorithm which assumes the remainder function