improving inductive logic programming by using simulated annealing in inductive logic programming ilp algorithms that are purely of the bottom up or top down type encounter several problems in practice since a majority of them are greedy ones these algorithms stop when finding clauses in local optima according to the quality measure used for evaluating the results moreover when learning clauses one by one the induced clauses become less and less interesting as the algorithm is progressing to cover few remaining examples in this paper we propose a simulated annealing framework to overcome these problems using a refinement operator we define neighborhood relations on clauses and on hypotheses i e sets of clauses with these relations and appropriate quality measures we show how to induce clauses in a coverage approach or to induce hypotheses directly by using simulated annealing algorithms we discuss the necessary conditions on the refinement operators and the evaluation measures to increase the effectiveness of the algorithm implementations included a parallelized version of the algorithm are described and experimentation results in terms of convergence of the method and in terms of accuracy are presented

subspace based blind channel estimation generalization and performance analysis in this paper we present a systematic study of the subspace based blind channel estimation method we first formulate a general signal model of multiple simultaneous signals transmitted through vector channels which can be applied to a multitude of modern digital communication systems based on this model we then propose a generalized subspace based channel estimator by minimizing a novel cost function which incorporates the set of kernel matrices of the signals sharing the target channel via a weighted sum of projection errors we investigate the asymptotic performance of the proposed estimator i e bias covariance mean square error mse and cramer rao bound for large numbers of independent observations we show that the performance of the estimator can be optimized by increasing the number of kernel matrices and by using a special set of weights in the cost function finally we consider the application of the proposed estimator to a downlink code division multiple access cdma system operating in a frequency selective fading channel with negligible intersymbol interference isi the results of the computer simulations fully support our analytical developments

cooling schedules for optimal annealing a monte carlo optimization technique called simulated annealing is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima the level of randomization is determined by a control parameter t called temperature which tends to zero according to a deterministic cooling schedule we give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states in the special case that the cooling schedule has parametric form tt c log1 t the condition for convergence is that c be greater than or equal to the depth suitably defined of the deepest local minimum which is not a global minimum state

adaptive blind source separation and equalization for multiple input multiple output systems in this paper we investigate adaptive blind source separation and equalization for multiple input multiple output mimo systems we first analyze the convergence of the constant modulus algorithm cma used in mimo systems mimo cma our analysis reveals that the mimo cma equalizer is able to recover one of the input signals remove the intersymbol interference isi and suppress the other input signals furthermore for the mimo finite impulse response fir systems satisfying certain conditions the mimo cma fir equalizers are able to perfectly recover one of the system inputs regardless of the initial settings we then propose a novel algorithm for blind source separation and equalization for mimo systems our theoretical analysis proves that the new blind algorithm is able to recover all system inputs simultaneously regardless of the initial settings finally computer simulation examples are presented to confirm our analysis and illustrate the effectiveness of blind source separation and equalization for mimo systems

quadratic higher order criteria for iterative blind separation of a mimo convolutive mixture of sources this paper deals with the problem of source separation in the case when the observations result from a multiple input multiple output convolutive mixing system in a blind framework higher order contrast functions have been proved to be efficient for extracting sources inspired by a semiblind approach we propose new contrast functions for blind signal separation that make use of reference signals the main advantage of this approach consists in the quadratic form of these criteria the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available the separation of the other sources from the mixture is then carried out by an iterative deflation method furthermore these contrasts are shown to be valid for both independent identically distributed i i d and non i i d source signals the performance offered by these criteria is investigated through simulations they appear as very appealing tools compared with some classical contrast functions

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

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

ergodicity of eigenfunctions for ergodic billiards we give a simple proof of ergodicity of eigenfunctions of the laplacian with dirichlet boundary conditions on compact riemannian manifolds with piecewise smooth boundaries and ergodic billiards examples include the bunimovich stadium the sinai billiard and the generic polygonal billiard tables of kerckhoff masur and smillie

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

fir channel estimation through generalized cumulant slice weighting we study the problem of linear channel estimation with unknown channel input signals our work stems from the weighted slice algorithm in which cumulant slices of different orders are linearly combined to produce an estimate of a single input single output channel aiming to improve the reliability of estimation the new approach incorporates a certain matrix structure constraint into its weight computation criterion it provides more reliable results for channels with weak leading coefficients this generalized algorithm maintains the advantage of fonollosa and vidal s algorithm in handling the situation with channel order overestimation its natural extension to multiple input multiple output channel estimation is presented along with the channel identifiability conditions required

polyhedral billiards eigenfunction concentration and almost periodic control we study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non smooth part of the boundary called pockets we prove there are only finitely many immersed periodic tubes missing the pockets and moreover establish a new quantitative estimate for the lengths of such tubes this extends well known results in dimension 2 we then apply these dynamical results to prove a quantitative laplace eigenfunction mass concentration near the pockets of convex polyhedral billiards as a technical tool for proving our concentration results on irrational polyhedra we establish a control theoretic estimate on a product space with an almost periodic boundary condition this extends previously known control estimates for periodic boundary conditions and seems to be of independent interest

local instability of orbits in polygonal and polyhedral billiards we classify when local instability of orbits of closeby points can occur for billiards in two dimensional polygons for billiards inside three dimensional polyhedra and for geodesic flows on surfaces of three dimensional polyhedra we sharpen a theorem of boldrighini keane and marchetti we show that polygonal and polyhedral billiards have zero topological entropy we also prove that billiards in polygons are positive expansive when restricted to the set of non periodic points the methods used are elementary geometry and symbolic dynamics

non periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons this paper proves the existence of non periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons for anyn 3 there exists a corresponding convexn agon forn 3 this will be a right triangle with a small acute angle while in three dimensional space it will be a prism then agon serving as the base

optimizing least significant bit substitution using cat swarm optimization strategy embedding secret data into a cover image using simple least significant bit substitution can degrade the image quality dramatically especially when a large number of bits are substituted the exhaustive least significant bit substitution method is proposed to solve this problem however the idea has no practical application due to its long computation time this paper adopts the cat swarm optimization cso strategy to obtain the optimal or near optimal solution of the stego image quality problem the cso strategy is generated by observing the behavior of cats which has been proved to achieve better performance on finding the best global solutions we revised the cso strategy in our proposed scheme to make it practicable and suitable to solve the mentioned problem the experimental results show that the proposed scheme can obtain a better solution with less computation time

non redundant precoding based blind and semi blind channel estimation for mimo block transmission with a cyclic prefix by combining multiple input multiple output mimo communication with block transmission using a cyclic prefix cp mimo block transmission systems can not only achieve high data rates but also simplify channel estimation and equalization in this paper to provide a bandwidth efficient solution for channel estimation in mimo block transmission systems with a cp we present a framework for blind channel estimation based on a general non redundant precoding using this framework we propose a blind estimator exploiting a simplified non redundant precoding that is robust against overestimates of a true mimo channel order furthermore in the case with the number of transmit antennas greater than that of receive antennas we show under specific system conditions that the proposed blind algorithms can be used for estimation of the mimo channel without oversampling the received signals with the simplified precoding conditions established in this paper the proposed method does not impose the strict identifiability conditions on the mimo channel which are required for the existing methods furthermore the proposed estimator achieves accurate channel estimation with a small number of symbol blocks in addition we derive a simplified precoder that is optimized in the sense of minimizing the impact of unknown additive noise we discuss the tradeoff between channel estimation accuracy and bit error rate performance associated with the simplified precoder finally we develop a technique for resolving the channel ambiguity in the proposed blind estimator to create a semi blind channel estimator relying on only a few known symbols

robustness of least squares and subspace methods for blind channel identification equalization with respect to effective channel undermodeling overmodeling the least squares and the subspace methods are two well known approaches for blind channel identification equalization when the order of the channel is known the algorithms are able to identify the channel under the so called length and zero conditions furthermore in the noiseless case the channel can be perfectly equalized less is known about the performance of these algorithms in the practically inevitable cases in which the channel possesses long tails of small impulse response terms we study the performance of the mth order least squares and subspace methods using a perturbation analysis approach we partition the true impulse response into the mth order significant part and the tails we show that the mth order least squares or subspace methods estimate an impulse response that is close to the mth order significant part the closeness depends on the diversity of the mth order significant part and the size of the tails furthermore we show that if we try to model not only the large terms but also some small ones then the quality of our estimate may degrade dramatically thus we should avoid modeling small terms finally we present simulations using measured microwave radio channels highlighting potential advantages and shortcomings of the least squares and subspace methods

blind spatio temporal equalization and impulse response estimation for mimo channels using a godard cost function equalization and estimation of the matrix impulse response function of multiple input multiple output mimo digital communications channels in the absence of any training sequences is considered an iterative godard 1980 cost based approach is considered for spatio temporal equalization and mimo impulse response estimation stationary points of the cost function are investigated with particular attention to the case when finite length equalizers exist sufficient conditions are derived under which all stable local minima correspond to desirable minima the inputs are extracted and cancelled one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed

group decorrelation enhanced subspace method for identifying fir mimo channels driven by unknown uncorrelated colored sources identification of finite impulse response fir and multiple input multiple output mimo channels driven by unknown uncorrelated colored sources is a challenging problem in this paper a group decorrelation enhanced subspace gdes method is presented the gdes method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace jdes method previously reported in the literature the gdes method has a much better performance than the jdes method the correctness of the gdes method is proved assuming that 1 the channel matrix is irreducible and column reduced and 2 the source spectral matrix has distinct diagonal functions however the gdes method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix simulations show that the gdes method yields good results even when the channel matrix is not irreducible which is not possible at all for the jdes method

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

blind mimo system identification based on cumulant subspace decomposition blind identification of multiple input multiple output mimo linear systems can be achieved by utilizing higher order statistics of the output signals we study the blind identification of mimo systems whose inputs are mutually independent temporally white non gaussian source signals based on sub space analysis we develop a new linear batch algorithm to identify mimo systems from the common nullspace of a set of fourth order cumulant matrices of the channel outputs given knowledge of the channel orders the identifiability conditions required by the proposed algorithm are properly established like most subspace based approaches this new algorithm remains sensitive to channel order overestimation simulation results illustrate its performance for various channel models

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

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

adaptive power techniques for blind channel estimation in cdma systems the problem of blind adaptive channel estimation in code division multiple access cdma systems is considered motivated by the iterative power method which is used in numerical analysis for estimating singular values and singular vectors we develop recursive least squares rls and least mean squares lms subspace based adaptive algorithms in order to identify the impulse response of the multipath channel the schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind both versions rls and lms exhibit rapid convergence combined with low computational complexity with the help of simulations we demonstrate the improved performance of our methods as compared with the already existing techniques in the literature

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

blind mimo channel identification from second order statistics using rank deficient channel convolution matrix for multiuser systems several direct blind identification algorithms require that the linear multiple input multiple output mimo system have a full rank convolution matrix this condition requires that the system transfer function be irreducible and column reduced we show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios algorithms such as the outer product decomposition algorithm only require minor length adjustment to its processing window without the column reduced condition this result allows direct blind identification methods to be applicable to mimo without requiring a full rank channel convolution matrix

the growth rate for the number of singular and periodic orbits for a polygonal billiard for any simply connected polygon in the plane the number of billiard orbits which begin and end at a vertex grows subexponentially with respect to the length or to the number of reflections this implies that the numbers of isolated periodic orbits and of families of parallel periodic orbits do grow subexponentially the main technical device is a calculation showing that the topological entropy of the poincare map for the billiard flow is equal to zero

deterministic blind identification of iir systems with output switching operations in this paper a deterministic blind identification approach is proposed for linear output switching systems which are modeled by multiple infinite impulse response iir dynamic functions by adopting a new over sampling strategy the concerned single input single output siso output switching system is equivalently transformed into a time invariant multi input multi output mimo system further by exploring the mutual relations among the multiple inputs the time invariant mimo system model and subsequently the output switching system model are identified uniquely up to a scalar constant using the proposed identification approach sufficient identifiability conditions are provided for output switching systems and numerical simulations are carried out to validate the proposed approach

regularity and strict identifiability in mimo systems we study finite impulse response fir multi input multi output mimo systems with additive noise treating the finite length sources and channel coefficients as deterministic unknowns considering both regularity and identifiability in blind estimation the ambiguity set is large admitting linear combinations of the sources we show that the fisher information matrix fim is always rank deficient by at least the number of sources squared and develop necessary and sufficient conditions for the fim to achieve its minimum nullity tight bounds are given on the required source data lengths to achieve minimum nullity of the fim we consider combinations of constraints that lead to regularity i e to a full rank fim and thus a meaningful cramer rao bound exploiting the null space of the fim we show how parameters must be specified to obtain a full rank fim with implications for training sequence design in multisource systems together with constrained cramer rao bounds crbs this approach provides practical techniques for obtaining appropriate mimo crbs for many cases necessary and sufficient conditions are also developed for strict identifiability id the conditions for strict id are shown to be nearly equivalent to those for the fim nullity to be minimized

on blind multiuser forward link channel estimation by the subspace method identifiability results blind channel estimation for periodic sequence ds cdma systems can be cast into the framework of structured blind estimation of multi input multi output mimo fir systems where the structure is imposed by the user s signatures a possible approach to tackle this problem consists in looking for a structured solution to one of the blind mimo fir systems proposed previously this is the approach undertaken by several authors however most of them did not address identifiability issues in this paper we first recall and reformulate some general mimo fir identification results of meraim loubaton and moulines see ieee trans inform theory vol 43 p 499 511 1997 and point out some difficulties posed by the subspace approach next we use the above material in order to analyze the behavior of the subspace forward link channel estimate of cdma systems we derive new results showing that the subspace method is not robust to an over determination of the channel order greater than the spreading factor if however the over determination error is less than the spreading factor we show that the subspace estimate is consistent if the codes of the users are properly designed