when is a periodic discrete time system equivalent to a time invariant one we give the precise conditions under which a periodic discrete time linear state space system can be transformed into a time invariant one by a change of basis thus our theory is the discrete time counterpart of the classical theory of floquet transforms developed by floquet and lyapunov in the 1800s for continuous time systems we state and prove a necessary and sufficient condition for a discrete time floquet transform to exist and give a construction for the transform when it does exist our results also extend to generalized state space or descriptor systems

robust predictor feedback for discrete time systems with input delays this work studies the design problem of feedback stabilisers for discrete time systems with input delays a backstepping procedure is proposed for disturbance free discrete time systems the feedback law designed by using backstepping coincides with the predictor based feedback law used in continuous time systems with input delays however simple examples demonstrate that the sensitivity of the closed loop system with respect to modelling errors increases as the value of the delay increases the paper proposes a lyapunov redesign procedure that can minimise the effect of the uncertainty specific results are provided for linear single input discrete time systems with multiplicative uncertainty the feedback law that guarantees robust global exponential stability is a nonlinear homogeneous of degree 1 feedback law

posterior probability of discovery and expected rate of discovery for multiple hypothesis testing and high throughput assays technologies of measuring millions of quantities at once have been rapidly developed and used in biological and biomedical research and other fields in the past decade yet a key issue remains unsettled namely how to control spurious findings for the ensuing massive number of hypothesis tests an emerging consensus is to control false discovery rate fdr with fdr defined as the expected proportion of true nulls among discoveries and a discovery the rejection of a null hypothesis however the very concept of counting true nulls implicitly or explicitly is problematic for nulls are rarely true in reality we propose an approach that is philosophically different from the fdr and other approaches taking advantage of the massive measurements we can and should directly evaluate the reproducibility of a discovery by calculating the posterior probability of discovery ppd given observed data a discovery with a great ppd is deemed to be highly reproducible that is not spurious for a subset of hypot

joint angle and delay estimation using shift invariance techniques in a multipath communication scenario it is often relevant to estimate the directions and relative delays of each multipath ray we derive a closed form subspace based method for the simultaneous estimation of these parameters from an estimated channel impulse response using knowledge of the transmitted pulse shape function the algorithm uses a two dimensional 2 d esprit like shift invariance technique to separate and estimate the phase shifts due to delay and direction of incidence with automatic pairing of the two parameter sets improved resolution is obtained by enlarging the data matrix with shifted and conjugated copies of itself

identifiability results for blind beamforming in incoherent multipath with small delay spread several explicit identifiability results are derived for deterministic blind beamforming in incoherent multipath with small delay spread for example it is shown that if the sum of spatial and fractional sampling diversities exceeds two times the total number of paths then identifiability can be guaranteed even for one symbol snapshot the tools come from the theory of low rank three way array decomposition commonly referred to as parallel factor analysis parafac and data smoothing in one and two dimensions new results regarding the kruskal rank of certain structured matrices are also included and they are of interest in their own right

prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

wideband spectrum sensing based on sub nyquist sampling in this paper we consider the problem of locating multiple active spectrum subbands in a wide range of frequency bands a major challenge associated with such wideband spectrum sensing is that it is either infeasible or too expensive to perform nyquist sampling on the wideband signal in this paper we propose a sensing scheme based on a sub nyquist sampling method called multicoset sampling which is similar to the polyphase implementation of the nyquist sampling but requires less a d converters in contrast to the traditional sub nquist approaches where the wideband signal is first reconstructed from the sub nyquist samples we develop a method that directly estimates the power spectrum of the wideband signal of interest using the sub nyquist samples by exploiting its statistical properties we also characterize the statistical distribution of the proposed power spectrum estimator based on which we obtain a constant false alarm energy detector for the frequency bins simulation results are provided to demonstrate the effectiveness of the proposed multiband spectrum sensing method based on sub nyquist sampling

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

parafac based blind estimation of possibly underdetermined convolutive mimo systems in this paper we consider the problem of blind identification of a convolutive multiple input multiple output mimo system with no outputs and ni inputs while many methods have been proposed to blindly identify convolutive mimo systems with no ges ni overdetermined very scarce results exist for the case of underdetermined all of which refer to systems that either have some special structure or special and values in this paper we show that as long as independent of whether the system is overdetermined or underdetermined we can always find the appropriate order of statistics that guarantees identifiability of the system response within trivial ambiguities we also propose an algorithm to reach the solution that consists of parallel factorization parafac of a way tensor containing th order statistics of the system outputs followed by an iterative scheme for a certain order of statistics we provide the description of the class of identifiable mimo systems we also show that this class can be expanded by applying parafac decomposition to a pair of tensors instead of one tensor the proposed approach constitutes a novel scheme for estimation of underdetermined systems and improves over existing approaches for overdetermined systems

reduction model approach for linear time varying systems with delays we study stabilization problems for time varying linear systems with constant input delays our reduction method ensures input to state stability with respect to additive uncertainties under arbitrarily long delays it applies to rapidly time varying systems and gives a lower bound on the admissible rapidness parameters we also cover slowly time varying systems including upper bounds on the allowable slowness parameters we illustrate our work using a pendulum model

blind parafac receivers for ds cdma systems this paper links the direct sequence code division multiple access ds cdma multiuser separation equalization detection problem to the parallel factor parafac model which is an analysis tool rooted in psychometrics and chemometrics exploiting this link it derives a deterministic blind parafac ds cdma receiver with performance close to non blind minimum mean squared error mmse the proposed parafac receiver capitalizes on code spatial and temporal diversity combining thereby supporting small sample sizes more users than sensors and or less spreading than users interestingly parafac does not require knowledge of spreading codes the specifics of multipath interchip interference doa calibration information finite alphabet constant modulus or statistical independence whiteness to recover the information bearing signals instead parafac relies on a fundamental result regarding the uniqueness of low rank three way array decomposition due to kruskal 1977 1988 and generalized herein to the complex valued case that guarantees identifiability of all relevant signals and propagation parameters these and other issues are also demonstrated in pertinent simulation experiments

uni mode uniqueness conditions for candecomp parafac decomposition of n way arrays with linearly dependent loadings abstract guo miron brie and stegeman x guo s miron d brie a stegeman uni mode and partial uniqueness conditions for candecomp parafac of three way arrays with linearly dependent loadings siam j matrix anal appl 33 2012 111 129 give three sufficient conditions for the three way candecomp parafac cp model which ensure uniqueness in one of the three modes uni mode uniqueness in this paper we generalize these uniqueness conditions to n 3 based on these conditions a partial uniqueness condition is given which allows collinear loadings in only one mode

reduction model approach for linear time varying systems with input delays based on extensions of floquet theory we solve stabilization problems for linear time varying systems under input delays we show how changes of coordinates lead to systems with time invariant drifts which are covered by the reduction model method and which lead to the problem of stabilizing a time varying system without delay for continuous time periodic systems we can use floquet theory to find the changes of coordinates we also prove an analogue for discrete time systems through a discrete time extension of floquet theory

a candecomp parafac perspective on uniqueness of doa estimation using a vector sensor array we address the uniqueness problem in estimating the directions of arrival doas of multiple narrowband and fully polarized signals impinging on a passive sensor array composed of identical vector sensors the data recorded on such an array present the so called multiple invariances which can be linked to the candecomp parafac cp model cp refers to a family of low rank decompositions of three way or higher way mutidimensional data arrays where each dimension is termed as a mode a sufficient condition is derived for uniqueness of the cp decomposition of a three way three mode array in the particular case where one of the three loading matrices each associated to one mode involved in the decomposition has full column rank based on this upper bounds on the maximal number of identifiable doas are deduced for the two typical cases i e the general case of uncorrelated or partially correlated sources and the case where the sources are coherent

local stabilization of nonlinear systems through the reduction model approach we study a general class of nonlinear systems with input delays of arbitrary size we adapt the reduction model approach to prove local asymptotic stability of the closed loop input delayed systems using feedbacks that may be nonlinear our lyapunov krasovskii functionals make it possible to determine estimates of the basins of attraction for the closed loop systems

doa estimation of quasi stationary signals with less sensors than sources and unknown spatial noise covariance a khatri rao subspace approach in real world applications such as those for speech and audio there are signals that are nonstationary but can be modeled as being stationary within local time frames such signals are generally called quasi stationary or locally stationary signals this paper considers the problem of direction of arrival doa estimation of quasi stationary signals specifically in our problem formulation we assume i sensor array of uniform linear structure ii mutually uncorrelated wide sense quasi stationary source signals and iii wide sense stationary noise process with unknown possibly nonwhite spatial covariance under the assumptions above and by judiciously examining the structures of local second order statistics soss we develop a khatri rao kr subspace approach that has two notable advantages first through an identifiability analysis it is proven that this kr subspace approach can operate even when the number of sensors is about half of the number of sources the idea behind is to make use of a virtual array structure provided inherently in the local sos model of which the degree of freedom is about twice of that of the physical array second the kr formulation naturally provides a simple yet effective way of eliminating the unknown spatial noise covariance from the signal soss extensive simulation results are provided to demonstrate the effectiveness of the kr subspace approach under various situations

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

blind signal separation via tensor decomposition with vandermonde factor canonical polyadic decomposition several problems in signal processing have been formulated in terms of the canonical polyadic decomposition of a higher order tensor with one or more vandermonde constrained factor matrices we first propose new relaxed uniqueness conditions we explain that under these conditions the number of components may simply be estimated as the rank of a matrix we propose an efficient algorithm for the computation of the factors that only resorts to basic linear algebra we demonstrate the use of the results for various applications in wireless communication and array processing

robustness of adaptive control under time delays for three dimensional curve tracking we analyze the robustness of a class of controllers that enable three dimensional curve tracking by a free moving particle the free particle tracks the closest point on the curve by building a strict lyapunov function and robustly forward invariant sets we show input to state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty input delays and a class of polygonal state constraints including adaptive tracking and parameter identification under unknown control gains such an understanding may provide certified performance when the control laws are applied to real life systems

hankel matrix nuclear norm regularized tensor completion for n dimensional exponential signals signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry biology and medical imaging for fast data acquisition or other inevitable reasons however only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic but existing approaches cannot efficiently recover n dimensional exponential signals with n geq 3 in this paper we study the problem of recovering n dimensional particularly n geq 3 exponential signals from partial observations and formulate this problem as a low rank tensor completion problem with exponential factor vectors the full signal is reconstructed by simultaneously exploiting the candecomp parafac tensor structure and the exponential structure of the associated factor vectors the latter is promoted by minimizing an objective function involving the nuclear norm of hankel matrices experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank

almost sure identifiability of multidimensional harmonic retrieval two dimensional 2 d and more generally multidimensional harmonic retrieval is of interest in a variety of applications including transmitter localization and joint time and frequency offset estimation in wireless communications the associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be resolved for a given sample size consider a mixture of 2 d exponentials each parameterized by amplitude phase and decay rate plus frequency in each dimension suppose that i equispaced samples are taken along one dimension and likewise j along the other dimension we prove that if the number of exponentials is less than or equal to roughly ij 4 then assuming sampling at the nyquist rate or above the parameterization is almost surely identifiable this is significant because the best previously known achievable bound was roughly i j 2 for example consider i j 32 our result yields 256 versus 32 identifiable exponentials we also generalize the result to n dimensions proving that the number of exponentials that can be resolved is proportional to total sample size

blind separation of synchronous co channel digital signals using an antenna array i algorithms we propose a maximum likelihood ml approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site the spatial response of the array is assumed to be known imprecisely or unknown we exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal uniqueness of the estimates is established for bpsk signals we introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner computationally efficient algorithms for both block and recursive estimation of the signals are presented this new approach is applicable to an unknown array geometry and propagation environment which is particularly useful in wireless communication systems simulation results demonstrate its promising performance