blind channel equalization and spl epsiv approximation algorithms we show that a blind equalizer can be obtained without estimating any statistics based on the received data if the constellation alphabet is known the idea is to formulate the blind channel equalization problem into a quadratic optimization with binary constraints then efficient spl epsiv approximation algorithms are presented and applied to find the equalizer coefficients the proposed approach blindly equalizes the channel at symbol baud rates does not rely on estimating any statistics applies to nonminimum phase channels and converges to an spl epsiv neighborhood of a global optimum simulation results support the theoretical analysis

blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

imprecise weights in weber facility location problem abstract this paper presents a method for locating multiple facilities on a plane bounded by a convex polygon under the criterion minimize the sum of all the transportation cost where the cost per unit distances are known imprecisely assuming some fuzzy aspiration levels for each of the goals and basing these on a comparison of flat fuzzy numbers the original fuzzy problem is transferred into a crisp satisfactory model to determine a suitable solution we will maximize the minimum of the surpluses over the aspiration levels rectilinear distance norm has been taken as the scenario and may be considered as in an urban setting this induces the problem with a non linear objective function which is equivalent to a linear program a numerical example has been given to illustrate the solution procedure

fuzzy logic based algorithms for maximum covering location problems this paper concerns a class of maximum covering location problems in networks in uncertain environments it is assumed that a relative weights of demand nodes are either deterministic or imprecise described by linguistic expressions and b potential facility site locations are limited to network nodes the concept of coverage is extended to include a degree of node coverage which means that the borders between the subset of covered demand nodes and the subset of uncovered demand nodes are inexact the acceptable service distance travelling times from a facility site to demand nodes are modelled by fuzzy sets three new algorithms for choosing the best facility locations are developed which assume that 1 demands at all nodes are equally important 2 relative weights of demand at nodes are deterministic and 3 weights of demand at nodes are imprecise and described by linguistic terms respectively the algorithms are based on searching among potential facility nodes by applying comparison operations on discrete fuzzy sets it is shown how to extend the proposed algorithms from one site to multi site covering problems illustrative examples of selecting locations for logistics centres in a distribution company are given

deterministic cca based algorithms for blind equalization of fir mimo channels in this paper a new deterministic technique for blind equalization of multiple input multiple output mimo channels is presented the proposed method relies on the channel order diversity of the finite impulse response mimo channel and it does not make any assumption about the spectra or the finite alphabet property of the sources assuming that the lengths of the single input multiple output channels are known or estimated a priori it is able to extract the sources up to a scale and rotation matrix ambiguity which only affects to those sources associated to single input multiple output simo channels with equal lengths unlike previously proposed techniques the method described in this paper obtains the equalizers and the best linear combination of their outputs in a single step and thus optimally the reformulation of the proposed method as a set of nested canonical correlation analysis problems is exploited to obtain efficient batch and adaptive equalization algorithms finally the performance of the proposed algorithms is evaluated by means of some simulation examples

a discrete location model with fuzzy accessibility measures abstract in crisply defined discrete location problems a number of facilities are to be located at specific points within an area according to precisely quantified criteria however in many location problems especially those associated with social policies non crisply defined criteria are used such as how near or accessible a facility is or how important certain issues are etc in these cases a fuzzy sets approach is more appropriate this paper presents an application of the set partitioning set covering with equality constraints type of integer programming formulation to a discrete location problem with fuzzy accessibility criteria the solution method suggested uses the symmetry of the objectives and the constraints introduced by bellman and zadeh

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

approximating pareto frontier using a hybrid line search approach the aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach but it is well known that this technique sometimes fail in different aspects for determining the pareto frontier this paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point once the first pareto solution is obtained a simplified version of the former one is used in the context of pareto dominance to obtain a set of efficient points which will assure a thorough distribution of solutions on the pareto frontier in the current form the proposed technique is well suitable for problems having multiple objectives it is not limited to bi objective problems and require the functions to be continuous twice differentiable in order to assess the effectiveness of this approach some experiments were performed and compared with two recent well known population based metaheuristics namely parego and nsga ii when compared to parego and nsga ii the proposed approach not only assures a better convergence to the pareto frontier but also illustrates a good distribution of solutions from a computational point of view both stages of the line search converge within a short time average about 150ms for the first stage and about 20ms for the second stage apart from this the proposed technique is very simple easy to implement and use to solve multiobjective problems

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

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

blind identification of fir systems driven by markov like input signals we propose a new algorithm for the blind identification and equalization of finite impulse response fir systems using the second order statistics of the received signal the new algorithm is set in the same context as the algorithms of tong et al 1994 and moulines et al 1995 however unlike those earlier approaches it is designed to allow correlated input signals specifically the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially numerical simulations compare the equalization performance of the new algorithm to those of tong and moulines it is shown that our algorithm yields consistently lower bit error rates at a wide variety of signal to noise ratios and at various equalizer lengths moreover the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated

ranking the sequences of fuzzy values when ranking fuzzy values there is an ambiguity in selecting the most preferred ranked sequence from a collection of candidate sequences because every sequence has a possibility to which the preference relations in the sequence are correct in this paper we propose a method for ranking the sequences of fuzzy values that assigns a preference degree to each ranked sequence each preference degree indicates the relative preference of the given sequence over the other sequences the proposed method gives information regarding which sequence could be classified as the most preferred sequence and which sequences as alternatives

fuzzy location problems on networks location problems concern a wide set of fields where it is usually assumed that exact data are known however in real applications the location of the facility considered can be full of linguistic vagueness that can be appropriately modelled using networks with fuzzy values thus fuzzy location problems on networks arise this paper deals with their general formulation and the description of the ways to solve them namely we show the variety of problems that can be considered in this context and for some of them we propose the most operative approaches for their solution

sensitivity to basis mismatch in compressed sensing the theory of compressed sensing suggests that successful inversion of an image of the physical world broadly defined to include speech signals radar sonar returns vibration records sensor array snapshot vectors 2 d images and so on for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis provided that the image is sparse in an apriori known basis for imaging problems in spectrum analysis and passive and active radar sonar this basis is usually taken to be a dft basis however in reality no physical field is sparse in the dft basis or in any apriori known basis no matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity in this paper we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases we start by analyzing the effect of basis mismatch on the best k term approximation error which is central to providing exact sparse recovery guarantees we establish achievable bounds for the l1 error of the best k term approximation and show that these bounds grow linearly with the image or grid dimension and the mismatch level between the assumed and actual bases for sparsity we then derive bounds with similar growth behavior for the basis pursuit l1 recovery error indicating that the sparse recovery may suffer large errors in the presence of basis mismatch although we present our results in the context of basis pursuit our analysis applies to any sparse recovery principle that relies on the accuracy of best k term approximations for its performance guarantees we particularly highlight the problematic nature of basis mismatch in fourier imaging where spillage from off grid dft components turns a sparse representation into an incompressible one we substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch for problem sizes common to radar and sonar

application of decision analysis techniques to the weber facility location problem a location problem with future uncertainties about the data is considered several possible scenarios about the future values of the parameters are postulated however it is not clear which of these scenarios will actually happen we find the location that will best accommodate the possible scenarios four rules utilized in decision theory are examined the expected value rule the optimistic rule the pessimistic rule and the minimax regret rule the solution for the squared euclidean distance is explicitly found algorithms are suggested for general convex distance metrics an example problem is solved in detail to illustrate the findings and computational experiments with randomly generated problems are reported

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

on the robustness of type 1 and interval type 2 fuzzy logic systems in modeling research on the robustness of fuzzy logic systems flss an imperative factor in the design process is very limited in the literature specifically when a system is subjected to small deviations of the sampling points operating points it is of great interest to find the maximum tolerance of the system which we refer to as the system s robustness in this paper we present a methodology for the robustness analysis of interval type 2 flss it2 flss that also holds for t1 flss hence making it more general a procedure for the design of robust it2 flss with a guaranteed performance better than or equal to their t1 counterparts is then proposed several examples are performed to demonstrate the effectiveness of the proposed methodologies it was concluded that both t1 and it2 flss can be designed to achieve robust behavior in various applications and preference one or the other in general is application dependant it2 flss having a more flexible structure than t1 flss exhibited relatively small approximation errors in the several examples investigated the methodologies presented in this paper lay the foundation for the design of flss with robust properties that will be very useful in many practical modeling and control applications

blind and semi blind fir multichannel estimation global identifiability conditions two channel estimation methods are often opposed training sequence methods that use the information induced by known symbols and blind methods that use the information contained in the received signal and possibly hypotheses on the input symbol statistics but without integrating the information from known symbols if present semi blind methods combine both training sequence and blind information and are more powerful than the two methods separately we investigate the identifiability conditions for blind and semi blind finite impulse response fir multichannel estimation in terms of channel characteristics received data length and input symbol excitation modes as well as number of known symbols for semi blind estimation two models corresponding to two different cases of a priori knowledge on the input symbols are studied the deterministic model in which the unknown symbols are considered as unknown deterministic quantities and the gaussian model in which they are considered as gaussian random variables this last model includes the methods using the second order statistics of the received data semi blind methods appear superior to blind and training sequence methods and allow the estimation of any channel with only few known symbols furthermore the gaussian model appears more robust than the deterministic one as it leads to less demanding identifiability conditions

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

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

an efficient subspace method for the blind identification of multichannel fir systems we present a novel method for the blind identification of linear single input multiple output simo finite impulse response fir systems based on second order statistics our approach called the truncated transfer matrix method ttm proceeds in two major steps first the svd analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second the block toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations the proposed ttm method is analytical no optimization procedure involved and it is robust to noise we find that the method comes with an increased computational cost but it significantly outperforms state of the art second order methods in low signal to noise ratio snr situations

strict identifiability of multiple fir channels driven by an unknown arbitrary sequence the problem of blind identification of multiple finite impulse response fir channels driven by a common input arises in a wide range of applications it has received increasing attention in the signal processing community a system of multiple fir channels driven by an unknown input is said to be strictly identifiable if in the absence of noise the given channel outputs can only be realized by a unique up to a constant system impulse response and a unique input sequence we show necessary and sufficient conditions for strict identifiability and establish a connection among strict identifiability a cross relation based cr based identifiability and a fisher information based fi based identifiability

blind mimo system estimation based on parafac decomposition of higher order output tensors we present a novel framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs samples of the system frequency response are obtained based on parallel factorization parafac of three or four way tensors constructed based on respectively third or fourth order cross spectra of the system outputs the main difficulties in frequency domain methods are frequency dependent permutation and filtering ambiguities we show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity important features of the proposed approach are that it does not require channel length information needs no phase unwrapping and unlike the majority of existing methods needs no prewhitening of the system outputs

numerical methods for interval and fuzzy number comparison based on the probabilistic approach and dempster shafer theory there are many different methods for interval and fuzzy number comparison proposed in the literature which provide the results of comparison in the form of a real or boolean value in this paper we use the dempster shafer theory of evidence with its probabilistic interpretation to justify and construct the method which provides the result of comparison in the form of an interval or fuzzy number the complete and consistent set of expressions for inequality and equality relations between intervals and fuzzy numbers has been obtained in the framework of the probabilistic approach these relations make it possible to compare intervals and fuzzy numbers with real values and may be considered as an asymptotic limit of the results we obtain using the dempster shafer theory a natural fuzzy extension of the proposed approach is considered and discussed using some illustrative examples

identification of 2 d noncausal gauss markov random fields parameter identification of multidimensional noncausal markov random fields is an important paradigm in multidimensional signal processing and modeling and the solutions to this problem are employed in many areas of image processing an original procedure for estimating the model parameters of discrete index 2 d noncausal gauss markov random fields gmrfs from noisy observations is proposed valid for both finite and infinite lattices and for any kind of boundary conditions starting from a suitable local representation of the gmrf and taking into account the symmetry property of so called field potentials a linear equation set relating the model parameters to the 2 d autocorrelation function known or estimated of the observed field is derived its solution gives the parameter estimates of the gmrf together with the estimate of the possibly unknown variance of the observation noise

the stability of nonlinear least squares problems and the cramer rao bound a number of problems of interest in signal processing can be reduced to nonlinear parameter estimation problems the traditional approach to studying the stability of these estimation problems is to demonstrate finiteness of the cramer rao bound crb for a given noise distribution we review an alternate deterministic notion of stability for the associated nonlinear least squares nls problem from the realm of nonlinear programming i e that the global minimizer of the least squares problem exists and varies smoothly with the noise furthermore we show that under mild conditions identifiability of the parameters along with a finite crb for the case of gaussian noise is equivalent to the deterministic stability of the nls problem finally we demonstrate the application of our result which is general to the problems of multichannel blind deconvolution and sinusoid retrieval to generate new stability results for these problems with little additional effort

on the computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

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

robust recovery of stream of pulses using convex optimization abstract this paper considers the problem of recovering the delays and amplitudes of a weighted superposition of pulses this problem is motivated by a variety of applications such as ultrasound and radar we show that for univariate and bivariate stream of pulses one can recover the delays and weights to any desired accuracy by solving a tractable convex optimization problem provided that a pulse dependent separation condition is satisfied the main result of this paper states that the recovery is robust to additive noise or model mismatch

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

data efficient blind ofdm channel estimation using receiver diversity we investigate non data aided channel estimation for cyclically prefixed orthogonal frequency division multiplexing ofdm systems by exploiting channel diversity using only two receive antennas a blind deterministic algorithm is proposed identifiability conditions are derived that guarantee the perfect channel retrieval in the absence of noise in the presence of noise the proposed method has the desired property of being data efficient only a single ofdm block is needed to achieve good estimation performance for a wide range of snr values the algorithm is also robust to input symbols as it does not have any restriction on the input symbols with regard to their constellation or their statistical properties in addition this diversity based algorithm is computationally efficient and its performance compares favorably to most existing blind algorithms

blind identification equalization using deterministic maximum likelihood and a partial prior on the input a semi deterministic maximum likelihood dml approach is presented to solve the joint blind channel identification and blind symbol estimation problem for single input multiple output systems a partial prior on the symbols is incorporated into the criterion which improves the estimation accuracy and brings robustness toward poor channel diversity conditions at the same time this method introduces fewer local minima than the use of a full prior statistical ml in the absence of noise the proposed batch algorithm estimates perfectly the channel and symbols with a finite number of samples based on these considerations an adaptive implementation of this algorithm is proposed it presents some desirable properties including low complexity robustness to channel overestimation and high convergence rate

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

sufficient conditions for regularity and strict identifiability in mimo systems we consider regularity and identifiability of convolutive multi input multi output mimo systems with additive white gaussian noise modeling the source and finite impulse response fir channel sequences as deterministic unknowns in the blind context the mimo system is not locally identifiable hence its fisher information matrix fim is not regular in fact the dimension of the complex valued blind fim null space is at least the number of sources squared because the fim is singular additional information about the system is required to resolve the degrees of uncertainty and thereby obtain a valid cramer rao bound crb therefore it is of interest to know under what conditions the blind fim nullity reaches its lower bound we develop sufficient conditions for the complex fim to attain its minimum nullity refining previous necessary conditions and extending single input multi output simo results we show that the sufficient conditions for the complex fim to have minimum nullity are also equivalent to sufficient conditions for mimo strict identifiability these provide sufficient conditions on the richness of the sources the required diversity and the source lengths under these conditions additional constraints such as training may be employed to yield an identifiable system with no ambiguities remaining

on the stable resolution limit of total variation regularization for spike deconvolution the stability of spike deconvolution which aims at recovering point sources from their convolution with a point spread function psf is known to be related to the separation between those sources when the observations are noisy it is critical to ensure support stability where the deconvolution does not lead to spurious or oppositely missing estimates of the point sources in this paper we study the resolution limit of stably recovering the support of two closely located point sources using the beurling lasso estimator which is a convex optimization approach based on total variation regularization we establish a sufficient separation criterion between the sources depending only on the psf above which the beurling lasso estimator is guaranteed to return a stable estimate of the point sources with the same number of estimated elements as that of the ground truth our result highlights the impact of psf on the resolution limit in the noisy setting which was not evident in previous studies of the noiseless setting towards the end we show that the same resolution limit applies to resolving two close located sources in conjunction of other well separated sources

a semiblind channel estimation approach for mimo ofdm systems in this paper a very efficient semiblind approach that uses a training based least square criterion along with a blind constraint is proposed for multiple input multiple output orthogonal frequency division multiplexing mimo ofdm channel estimation the blind constraint is derived from the linear prediction of the received mimo ofdm signal and is used in conjunction with a weighting factor in the semiblind cost function an appealing scheme for the determination of the weighting factor is presented as a part of the proposed approach a perturbation analysis of the proposed method is conducted to justify the superiority of the semiblind solution and to obtain a closed form expression for the mean square error mse of the blind constraint further facilitating the calculation of the weighting factor the proposed method is validated through computer simulation based experimentations showing a very high estimation accuracy of the semiblind solution in terms of the mse of the channel estimate

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

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

a cholesky factorization based approach for blind fir channel identification for blind channel identification various techniques including transmitter induced cyclostationarity based approaches have been proposed in literature to induce cyclostationarity at the transmitter zero padding to every symbol packet can be considered some subspace methods are proposed for the channel estimation by exploiting the induced cyclostationarity due to zero padding the covariance matrix of received signal vectors can have a special structure utilizing this structure we can estimate channel impulse responses through factorization in this correspondence we propose a factorization based approach to estimate channel impulse responses in general the proposed factorization based approach can work with a small number of samples and becomes much more computationally efficient than the subspace method when the length of packets is long

multichannel blind deconvolution of nonminimum phase systems using filter decomposition in this paper we present a new filter decomposition method for multichannel blind deconvolution of nonminimum phase systems with this approach we decompose a doubly finite impulse response filter into a cascade form of two filters a causal finite impulse response fir filter and an anticausal fir filter after introducing a lie group to the manifold of fir filters we discuss geometric properties of the fir filter manifold using the nonholonomic transform we derive the natural gradient on the fir manifold by simplifying the mutual information rate we present a very simple cost function for blind deconvolution of nonminimum phase systems subsequently the natural gradient algorithms are developed both for the causal fir filter and for the anticausal fir filter simulations are presented to illustrate the validity and favorable learning performance of the proposed algorithms

compressed sensing off the grid this paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples unlike previous work in compressed sensing the frequencies are not assumed to lie on a grid but can assume any values in the normalized frequency domain 0 1 an atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies which is then reformulated as an exact semidefinite program even with this continuous dictionary it is shown that o slog s log n random samples are sufficient to guarantee exact frequency localization with high probability provided the frequencies are well separated extensive numerical experiments are performed to illustrate the effectiveness of the proposed method

multistep linear predictors based blind identification and equalization of multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider the estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers we extend the multistep linear prediction approach to mimo channels where the multichannel transfer function need not be column reduced moreover we allow infinite impulse response iir channels as well as the case where the subchannel transfer functions have common zeros in the past this approach has been confined to simo finite impulse response fir channels with no common subchannel zeros a related existing approach applicable to mimo channels is restricted to fir column reduced systems with equal length subchannels in our approach the knowledge of the nature of the underlying model fir or iir or the model order is not required our approach works when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data illustrative computer simulation examples are provided

deterministic linear prediction methods for blind channel estimation based on dual concept of zero forcing equalization this paper investigates a class of second order blind channel estimation algorithms based on deterministic linear prediction which includes double sided as well as forward and backward single sided for single input multiple output simo finite impulse response fir channels by introducing the dual problem of well known zero forcing equalization concept we first derive a double sided deterministic linear prediction d dlp algorithm that has good channel estimation performance with the knowledge of exact channel order by further exploiting the interference subspace cancellation technique and the triangular block toeplitz structure of a portion of the channel filtering matrix upper left or lower right part we obtain the forward and backward single sided deterministic linear prediction fs dlp and bs dlp algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate moreover a channel order estimation method is also studied based on results from both fs dlp and bs dlp simulation examples are finally presented to demonstrate the potential of the proposed methods

towards a mathematical theory of super resolution this paper develops a mathematical theory of super resolution broadly speaking super resolution is the problem of recovering the fine details of an object the high end of its spectrum from coarse scale information only from samples at the low end of the spectrum suppose we have many point sources at unknown locations in 0 1 and with unknown complex valued amplitudes we only observe fourier samples of this object up to a frequency cutoff fc we show that one can super resolve these point sources with infinite precision i e recover the exact locations and amplitudes by solving a simple convex optimization problem which can essentially be reformulated as a semidefinite program this holds provided that the distance between sources is at least 2 fc this result extends to higher dimensions and other models in one dimension for instance it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well we also show that the theory and methods are robust to noise in particular in the discrete setting we develop some theoretical results explaining how the accuracy of the super resolved signal is expected to degrade when both the noise level and the super resolution factor vary 2014 wiley periodicals inc

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

a multidimensional phase locked loop for blind multiuser detection this paper concerns the problem of blind multiuser detection a special case of the blind source separation problem in which the source signals have finite alphabets specifically we address the problem of identifying and resolving the n spl times n unitary matrix ambiguity u that results from whitening the receiver observations where n is the number of sources we propose the multidimensional phase locked loop mpll as a generalization of a scalar decision directed pll to vector valued signals the mpll adapts an estimate of u according to the recursion u spl circ sub k 1 u spl circ sub k r sub k where r sub k is an n dimensional householder like rotation depending on only the kth receiver observation the o n sup 2 complexity of an efficient implementation of the algorithm is extremely low nevertheless simulation results demonstrate good convergence properties and superior steady state performance when compared with prior techniques the algorithm is also able to accommodate large alphabets and shaped alphabets

the gradual covering decay location problem on a network abstract in covering problems it is assumed that there is a critical distance within which the demand point is fully covered while beyond this distance it is not covered at all in this paper we define two distances within the lower distance a demand point is fully covered and beyond the larger distance it is not covered at all for a distance between these two values we assume a gradual coverage decreasing from full coverage at the lower distance to no coverage at the larger distance

cross relation based blind simo identifiability in the presence of near common zeros and noise the blind identification of single input multiple output simo systems is often performed by exploiting a cross relation cr between channel pairs it has been shown that this property allows an estimation of channel impulse responses up to a common gain factor if certain identifiability conditions are met in this case the estimated channels can be evaluated by a gain compensated system distance known as normalized projection misalignment npm current algorithms for blind channel identification however suffer in the presence of insufficient channel diversity and observation noise in this paper we first demonstrate that in the absence of noise the cr identification error for channels with exact common zeros is given by a single channel pole zero transfer function next we extend our analysis to the realistic case of near common zeros and noise for which we show that the effective error can still be approximated by a common transfer function as long as the distance between the channel zeros remains below a signal to noise ratio dependent threshold a finite impulse response fir modeling of the error then enables us to define a common filter error compensated system distance termed normalized filter projection misalignment nfpm which establishes a natural extension to the npm analysis by finally considering realistic channels which we blindly estimate with the adaptive multichannel least mean square mclms algorithm we demonstrate that the nfpm reliably reaches the noise floor confirming that the effective error can be approximated by a common fir filter

blind channel identification subspace tracking method without rank estimation subspace ss methods are an effective approach for blind channel identification however these methods also have two major disadvantages 1 they require accurate channel length estimation and or rank estimation of the correlation matrix which is difficult with noisy channels and 2 they require a large amount of computation for the singular value decomposition svd which makes it inconvenient for adaptive implementation although many adaptive subspace tracking algorithms can be applied the computational complexity is still o m sup 3 where m is the data vector length in this paper we introduce new recursive subspace algorithms using ulv updating and successive cancellation techniques the new algorithms do not need to estimate the rank of the correlation matrix furthermore the channel length can be overestimated initially and be recovered at the end by a successive cancellation procedure which leads to more convenient implementations the adaptive algorithm has computations of o m sup 2 in each recursion the new methods can be applied to either the single user or the multiuser cases simulations demonstrate their good performance

a blind approach to closed loop identification of hammerstein systems this paper is a continuing study of the blind approach for the hammerstein identification in sun et al 1999 and bai and fu 2002 in the framework of a closed loop sampled data system the output is sampled faster than the updating period of the input the parameters of the linear dynamics are consistently estimated from the information of the output only after which the unmeasurable inner signal is uniquely reconstructed the noise effect is explicitly considered in both the parameter and inner signal estimation the estimation of the system orders and time delay are studied on the basis of two groups of basic equations obtained by polyphase decomposition the proposed blind approach is validated and illustrated by a simulated numerical example

blind identification of time varying channels using multistep linear predictors blind estimation of a class of single input multiple output simo time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the multistep linear predictors based method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for channel identifiability are investigated the proposed method requires the knowledge of the active basis functions in the ce bem it is not as sensitive to overestimation of the channel length as some of the existing methods computer simulation examples are presented to illustrate the approach and to compare it with three existing approaches

blind identification of simo systems and simultaneous estimation of multiple time delays from hos based inverse filter criteria higher order statistics based inverse filter criteria ifc have been effectively used for blind equalization of single input multiple output simo systems recently chi and chen reported a relationship between the unknown simo system and the optimum equalizer designed by the ifc for finite signal to noise ratio snr in this paper based on this relationship an iterative fast fourier transform fft based nonparametric blind system identification bsi algorithm and an fft based multiple time delay estimation mtde algorithm are proposed with a given set of non gaussian measurements the proposed bsi algorithm allows the unknown simo system to have common subchannel zeros and its performance estimation accuracy is superior to that of the conventional ifc based methods the proposed mtde algorithm can simultaneously estimate all the p 1 time delays with respect to a reference sensor with space diversity of sensors exploited therefore its performance estimation accuracy is robust to the nonuniform distribution of snrs of p spl ges 2 sensors due to channel fading some simulation results are presented to support the efficacy of the proposed bsi algorithm and mtde algorithm