sensitivity analysis for antenna near field imaging although imaging and inverse scattering problems have been thoroughly studied during the last century there is only a partial understanding of these complex problems most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results in comparison there are very few results and a limited knowledge about the information content in the inversion data in this paper we provide a mathematical framework for sensitivity analysis of antenna near field imaging problems based on the multipole expansion of the electromagnetic field and the fisher information to quantify the quality of data by exploiting this framework a fundamental relation for accuracy and resolution is formulated based on the crameacuter rao bound crb the sensitivity analysis is illustrated using a relevant example with cylindrical measurement data

the continuum limit of critical random graphs we consider the erd s renyi random graph g n p inside the critical window that is when p 1 n n 4 3 for some fixed lambda in mathbb r we prove that the sequence of connected components of g n p considered as metric spaces using the graph distance rescaled by n 1 3 converges towards a sequence of continuous compact metric spaces the result relies on a bijection between graphs and certain marked random walks and the theory of continuum random trees our result gives access to the answers to a great many questions about distances in critical random graphs in particular we deduce that the diameter of g n p rescaled by n 1 3 converges in distribution to an absolutely continuous random variable with finite mean

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

parametric glrt for multichannel adaptive signal detection this paper considers the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance a parametric generalized likelihood ratio test glrt is developed by modeling the disturbance as a multichannel autoregressive ar process maximum likelihood ml parameter estimation underlying the parametric glrt is examined it is shown that the ml estimator for the alternative hypothesis is nonlinear and there exists no closed form expression to address this issue an asymptotic ml aml estimator is presented which yields asymptotically optimum parameter estimates at reduced complexity the performance of the parametric glrt is studied by considering challenging cases with limited or no training signals for parameter estimation such cases especially when training is unavailable are of great interest in detecting signals in heterogeneous fast changing or dense target environments but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level compared with the recently introduced parametric adaptive matched filter pamf and parametric rao detectors the parametric glrt achieves higher data efficiency offering improved detection performance in general

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

bounds on list decoding of rank metric codes so far there is no polynomial time list decoding algorithm beyond half the minimum distance for gabidulin codes these codes can be seen as the rank metric equivalent of reed solomon codes in this paper we provide bounds on the list size of rank metric codes in order to understand whether polynomial time list decoding is possible or whether it works only with exponential time complexity three bounds on the list size are proven the first one is a lower exponential bound for gabidulin codes and shows that for these codes no polynomial time list decoding beyond the johnson radius exists second an exponential upper bound is derived which holds for any rank metric code of length n and minimum rank distance d the third bound proves that there exists a rank metric code over bbfqm of length n m such that the list size is exponential in the length for any radius greater than half the minimum rank distance this implies that there cannot exist a polynomial upper bound depending only on n and d similar to the johnson bound in hamming metric all three rank metric bounds reveal significant differences to bounds for codes in hamming metric

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

a new parametric glrt for multichannel adaptive signal detection a parametric generalized likelihood ratio test glrt for multichannel signal detection in spatially and temporally colored disturbance was recently introduced by modeling the disturbance as a multichannel autoregressive ar process the detector however involves a highly nonlinear maximum likelihood estimation procedure which was solved via a two dimensional iterative search method initialized by a suboptimal estimator in this paper we present a simplified glrt along with a new estimator for the problem both the estimator and the glrt are derived in closed form at considerably lower complexity with adequate training data the new glrt achieves a similar detection performance as the original one however for the more interesting case of limited training the original glrt may become inferior due to poor initialization because of its simpler form the new glrt also offers additional insight into the parametric multichannel signal detection problem the performance of the proposed detector is assessed using both a simulated dataset which was generated using multichannel ar models and the kassper dataset a widely used dataset with challenging heterogeneous effects found in real world environments

a unified construction of space time codes with optimal rate diversity tradeoff the problem of constructing space time st block codes over a fixed desired signal constellation is considered in this situation there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code the transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal to noise ratio snr in the setting of a quasi static channel model let n sub t denote the number of transmit antennas and t the block interval for any n sub t spl les t a unified construction of n sub t spl times t st codes is provided here for a class of signal constellations that includes the familiar pulse amplitude pam quadrature amplitude qam and 2 sup k ary phase shift keying psk modulations as special cases the construction is optimal as measured by the rate diversity tradeoff and can achieve any given integer point on the rate diversity tradeoff curve an estimate of the coding gain realized is given other results presented here include i an extension of the optimal unified construction to the multiple fading block case ii a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes iii the providing of a linear dispersion form for the underlying binary block codes iv a gray mapped version of the unified construction and v a generalization of construction of the ary case corresponding to constellations of size sup k items ii and iii are aimed at simplifying the decoding of this class of st codes

parameter estimation and glrt detection in colored non gaussian autoregressive processes the problem of estimating signal and noise parameters from a mixture of nongaussian autoregressive noise with partially known deterministic signal is discussed two models are considered in order to examine different kinds of additive mixing the cramer rao bounds to the joint estimation of the signal amplitude and the noise parameters are presented a computationally simple estimator which was previously proposed for estimation in the absence of signal is extended for the two models under consideration the proposed method essentially consists of two stages of least squares estimation which is motivated by the maximum likelihood estimation the technique is applied to the problem of detecting a signal known except for amplitude in colored nongaussian noise two slightly different mixing models are used and a generalized likelihood ratio test glrt coupled with the proposed estimation scheme is used to solve the problems the results of computer simulations are presented as evidence of the validity of the theoretical productions of performance

the exploration process of inhomogeneous continuum random trees and an extension of jeulin s local time identity we study the inhomogeneous continuum random trees icrt that arise as weak limits of birthday trees we give a description of the exploration process a function defined on 0 1 that encodes the structure of an icrt and also of its width process determining the size of layers in order of height these processes turn out to be transformations of bridges with exchangeable increments which have already appeared in other icrt related topics such as stochastic additive coalescence the results rely on two different constructions of birthday trees from processes with exchangeable increments on weak convergence arguments and on general theory on continuum random trees

calculation of the fisher information matrix for multidimensional data sets data sets that are acquired in many practical systems can be described as the output of a multidimensional linear separable denominator system with gaussian measurement noise an important example is nuclear magnetic resonance nmr spectroscopy in nmr spectroscopy high accuracy parameter estimation is of central importance a classical result on the crame spl acute r rao lower bound states that the inverse of the fisher information matrix fim provides a lower bound for the covariance of any unbiased estimator of the parameter vector the calculation of the fim is therefore of central importance for an assessment of the accuracy with which parameters can be estimated it is shown how the fim can be expressed using the matrices that determine the system that generates the data set for uniformly sampled data it is shown how the fim can be expressed through the solutions of lyapunov equations the novel techniques are demonstrated with an example arising from nmr spectroscopy

on list decodability of random rank metric codes and subspace codes codes in rank metric have a wide range of applications to construct such codes with better list decoding performance explicitly it is of interest to investigate the listdecodability of random rank metric codes it is shown that if n m b is a constant then for every rank metric code in fm n q with rate r and list decoding radius must obey the gilbert varshamov bound that is r 1 1 b otherwise the list size can be exponential and hence no polynomial time list decoding is possible on the other hand for arbitrary 0 0 with e and being independent of each other with high probability a random rank metric code with rate r 1 1 b can be efficiently list decoded up to a fraction of rank errors with constant list size o 1 e we establish similar results for constant dimension subspace codes moreover we show that with high probability the list decoding radius of random fq linear rank metric codes also achieve the gilbert varshamov bound with constant list size o exp 1 e

computationally efficient angle estimation for signals with known waveforms this paper presents a large sample decoupled maximum likelihood deml angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise the deml estimator decouples the multidimensional problem of the exact ml estimator to a set of 1 d problems and hence is computationally efficient we shall derive the asymptotic statistical performance of the deml estimator and compare the performance with its cramer rao bound crb i e the best possible performance for the class of asymptotically unbiased estimators we will show that the deml estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms we will also show that for moderately correlated signals with known waveforms the deml estimator is no longer a large sample maximum likelihood ml estimator but the deml estimator may still be used for angle estimation and the performance degradation relative to the crb is small we shall show that the deml estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix finally several numerical examples showing the performance of the deml estimator are presented in this paper

uniform infinite planar triangulations the existence of the weak limit as n of the uniform measure on rooted triangulations of the sphere with n vertices is proved some properties of the limit are studied in particular the limit is a probability measure on random triangulations of the plane

invariance principles for random bipartite planar maps it is conjectured in the physics literature that properly rescaled random planar maps when conditioned to have a large number of faces should converge to a limiting surface whose law does not depend up to scaling factors on details of the class of maps that are sampled previous works on the topic starting with chassaing schaeffer have shown that the radius of a random quadrangulation with n faces converges in distribution once rescaled by n 1 4 to the diameter of the brownian snake up to a scaling constant using a bijection due to bouttier di francesco guitter between bipartite planar maps and a family of labeled trees we show the corresponding invariance principle for a class of random maps that follow a boltzmann distribution the radius of such maps conditioned to have n faces or n vertices and under a criticality assumption converges in distribution once rescaled by n 1 4 to a scaled version of the diameter of the brownian snake convergence results for the so called profile of maps are also provided as well as convergence of rescaled bipartite maps to the brownian map as introduced by marckert mokkadem the proofs of these results rely on a new invariance principle for two type spatial galton watson trees

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

a new class of rank metric codes and their list decoding beyond the unique decoding radius compared with classical block codes list decoding rank metric codes efficiently seems more difficult the evidences to support this view include 1 so far the only known efficient list decoding of rank metric codes mathcal c gives decoding radius beyond 1 r 2 with positive rate r when the ratio of the number of rows over the number of columns is extremely small 2 the johnson bound for rank metric codes does not exist as opposed to classical codes and 3 the gabidulin codes of square matrices cannot be list decoded beyond half of the minimum distance although the list decodability of random rank metric codes and the limits to the list decodability have been determined completely little work on efficient list decoding of rank metric codes has been done the only known efficient list decoding of rank metric codes mathcal c gives decoding radius up to the singleton bound 1 r varepsilon with positive rate r when rho mathcal c is extremely small i e o varepsilon 2 where rho mathcal c denotes the ratio of the number of rows over the number of columns of mathcal c it is commonly believed that it is difficult to list decode rank metric codes mathcal c with the ratio rho mathcal c close to 1 the main purpose of this paper is to explicitly construct a class of rank metric codes mathcal c with the ratio rho mathcal c up to 1 2 and efficiently list decode these codes beyond unique decoding radius 1 r 2 furthermore encoding and list decoding algorithms run in polynomial time mathrm poly n exp 1 varepsilon the list size can be reduced to o 1 varepsilon by randomizing the algorithm our key idea is to employ bivariate polynomials f x y where f is linearized in variable y and the variable x is used to fold the code in other words the rows are used to correct rank errors and the columns are used to fold the code to enlarge the decoding radius apart from the above algebraic technique we have to prune down the list the algebraic idea enables us to pin down the messages into a structured subspace whose dimension is linear in the number n of columns this periodic structure allows us to pre encode the messages to prune down the list more precisely we use subspace design introduced by guruswami and xing to obtain a deterministic algorithm with a larger constant list size and employ hierarchical subspace evasive sets introduced by guruswami et al to obtain a randomized algorithm with a smaller constant list size

analytic sequential weiss weinstein bounds in this paper we explore a sequential bayesian bound for state space models focusing on hybrid continuous and discrete random states we provide an analytic recursion for the sequential weiss weinstein sww bound for linear state space models with solutions for gaussian uniform and exponential distributions as derived as well as for a combination of these we compare the sww bound for discretized states with the corresponding bound for the continuous states the sww bound is contrasted with the sequential cramer rao bound for gaussian distributions practical issues of sww bounds are discussed and numerical simulation results provide insights into their behavior

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

scaling limits of markov branching trees with applications to galton watson and random unordered trees we consider a family of random trees satisfying a markov branching property roughly this property says that the subtrees above some given height are independent with a law that depends only on their total size the latter being either the number of leaves or vertices such families are parameterized by sequences of distributions on partitions of the integers that determine how the size of a tree is distributed in its different subtrees under some natural assumption on these distributions stipulating that macroscopic splitting events are rare we show that markov branching trees admit the so called self similar fragmentation trees as scaling limits in the gromov hausdorff prokhorov topology applications include scaling limits of consistent markov branching model and convergence of galton watson trees towards the brownian and stable continuum random trees we also obtain that random uniform unordered trees have the brownian tree as a scaling limit hence extending a result by marckert miermont and fully proving a conjecture made by aldous

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

class of widely linear complex kalman filters recently a class of widely linear augmented complex valued kalman filters kfs that make use of augmented complex statistics have been proposed for sequential state space estimation of the generality of complex signals this was achieved in the context of neural network training and has allowed for a unified treatment of both second order circular and noncircular signals that is both those with rotation invariant and rotation dependent distributions in this paper we revisit the augmented complex kf augmented complex extended kf and augmented complex unscented kf in a more general context and analyze their performances for different degrees of noncircularity of input and the state and measurement noises for rigor a theoretical bound for the performance advantage of widely linear kfs over their strictly linear counterparts is provided the analysis also addresses the duality with bivariate real valued kfs together with several issues of implementation simulations using both synthetic and real world proper and improper signals support the analysis

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

uplink synchronization in ofdma spectrum sharing systems spectrum sharing employs dynamic allocation of frequency resources for a more efficient use of the radio spectrum despite its appealing features this technology inevitably complicates the synchronization task which must be accomplished in an environment that may involve interference this paper considers the uplink of an orthogonal frequency division multiple access ofdma based spectrum sharing system and provides solutions for estimating the frequency and timing errors of multiple unsynchronized users in doing so we exploit suitably designed training blocks and apply maximum likelihood methods after modeling the interference power on each subcarrier as a random variable with an inverse gamma distribution the resulting frequency estimator turns out to be the extension to a multiuser scenario of a scheme that has previously been proposed for single user spectrum sharing systems timing recovery is more challenging and leads to a complete search over a multidimensional domain to overcome such a difficulty two alternative approaches are proposed the first one relies on a simplifying assumption about the interference distribution in the frequency domain while the second scheme operates in an iterative fashion according to the expectation maximization algorithm

pattern avoiding permutations and brownian excursion part ii fixed points permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics computer science and biology in this paper we study fixed points of both 123 and 231 avoiding permutations we find an exact description for a scaling limit of the empirical distribution of fixed points in terms of brownian excursion this builds on the connections between pattern avoiding permutations and brownian excursion developed in hoffman et al pattern avoiding permutations and brownian excursion part 1 shapes and fluctuations to appear random structures and algorithms arxiv 1406 5156 2016 and strengthens the recent results of elizalde electron j comb 18 2 17 2011 and miner and pak adv appl math 55 86 130 2014 on fixed points of pattern avoiding permutations

array signal processing in the known waveform and steering vector case the amplitude estimation of a signal that is known only up to an unknown scaling factor with interference and noise present is of interest in several applications including using the emerging quadrupole resonance qr technology for explosive detection in such applications a sensor array is often deployed for interference suppression this paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori two approaches viz the capon and the maximum likelihood ml methods are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise we derive closed form expressions for the expected values and mean squared errors mses of the two estimators a comparative study shows that the ml estimate is unbiased whereas the capon estimate is biased downwards for finite data sample lengths we show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal to noise ratio snr is high furthermore we consider a more general scenario where the interference and noise are both spatially and temporally correlated we model the interference and noise vector as a multichannel autoregressive ar random process an alternating least squares als method for parameter estimation is presented we show that in most cases the als method is superior to the model mismatched ml m sup 3 l method which ignores the temporal correlation of the interference and noise

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

on the invariance coincidence and statistical equivalence of the glrt rao test and wald test three common techniques to discriminate between alternatives in a binary hypothesis testing problem are the generalized likelihood ratio test glrt the rao test and the wald test in this paper we investigate some characteristics of the corresponding decision statistics and provide their expressions for some problems of particular interest in statistical signal processing first of all we focus on the invariance of the rao and wald tests with respect to transformations leaving the testing problem unaltered then we introduce necessary and sufficient conditions in order for their decision statistics to coincide with twice the logarithm of the glrt statistic finally we present some detection problems usually encountered in practical signal processing applications where the decision variables of the three quoted tests are equivalent namely related by strictly monotonic transformations

distributed snr estimation with power constrained signaling over gaussian multiple access channels a sensor network is used for distributed signal to noise ratio snr estimation in a single time snapshot sensors observe a signal embedded in noise and each observation is phase modulated using a constant modulus scheme and transmitted over a gaussian multiple access channel to a fusion center at the fusion center the mean and variance are estimated jointly using an asymptotically minimum variance estimator it is shown that this joint estimator decouples into simple individual estimators of the mean and the variance the constant modulus phase modulation scheme ensures a fixed transmit power robust estimation across several sensing noise distributions as well as an snr estimate that requires a single set of transmissions from the sensors to the fusion center the estimators are evaluated in terms of asymptotic variance which are then used to evaluate the performance of the snr estimator with gaussian and cauchy sensing noise distributions in the cases of total transmit power constraint as well as a per sensor power constraint for each sensing noise distribution the optimal phase transmission parameters are also determined the asymptotic relative efficiency of the estimators is evaluated it is shown that among the noise distributions considered the estimators are asymptotically efficient only when the noise distribution is gaussian simulation results corroborate analytical results

maximum rank distance codes as space time codes the critical design criterion for space time codes in asymptotically good channels is the minimum rank between codeword pairs rank codes are a two dimensional matrix code construction where by the rank is the metric of merit we look at the application of rank codes to space time code design in particular we provide construction methods of full rank codes over different complex signal constellations for arbitrary numbers of antennas and codeword periods we also derive a singleton type bound on the rate of a code for the rank metric and we show that rank codes satisfy this bound with equality

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

branching processes in levy processes the exploration process the main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure the exploration process appears as a simple local time functional of a levy process with no negative jumps whose laplace exponent coincides with the branching mechanism function this new relation between spectrally positive levy processes and continuous branching processes provides a unified perspective on both theories in particular we derive the adequate formulation of the classical ray knight theorem for such levy processes as a consequence of this theorem we show that the path continuity of the exploration process is equivalent to the almost sure extinction of the branching process

improved decoding of reed solomon and algebraic geometry codes given an error correcting code over strings of length n and an arbitrary input string also of length n the list decoding problem is that of finding all codewords within a specified hamming distance from the input string we present an improved list decoding algorithm for decoding reed solomon codes the list decoding problem for reed solomon codes reduces to the following curve fitting problem over a field f given n points x sub i spl middot y sub i sub i 1 sup n x sub i y sub i spl isin f and a degree parameter k and error parameter e find all univariate polynomials p of degree at most k such that y sub i p x sub i for all but at most e values of i spl isin 1 n we give an algorithm that solves this problem for e 1 3 where the result yields the first asymptotic improvement in four decades the algorithm generalizes to solve the list decoding problem for other algebraic codes specifically alternant codes a class of codes including bch codes and algebraic geometry codes in both cases we obtain a list decoding algorithm that corrects up to n spl radic n n d errors where n is the block length and d is the designed distance of the code the improvement for the case of algebraic geometry codes extends the methods of shokrollahi and wasserman see in proc 29th annu acm symp theory of computing p 241 48 1998 and improves upon their bound for every choice of n and d we also present some other consequences of our algorithm including a solution to a weighted curve fitting problem which may be of use in soft decision decoding algorithms for reed solomon codes

explicit codes achieving list decoding capacity error correction with optimal redundancy in this paper we present error correcting codes that achieve the information theoretically best possible tradeoff between the rate and error correction radius specifically for every 0 r 1 and epsiv 0 we present an explicit construction of error correcting codes of rate that can be list decoded in polynomial time up to a fraction 1 r epsiv of worst case errors at least theoretically this meets one of the central challenges in algorithmic coding theory our codes are simple to describe they are folded reed solomon codes which are in fact exactly reed solomon rs codes but viewed as a code over a larger alphabet by careful bundling of codeword symbols given the ubiquity of rs codes this is an appealing feature of our result and in fact our methods directly yield better decoding algorithms for rs codes when errors occur in phased bursts the alphabet size of these folded rs codes is polynomial in the block length we are able to reduce this to a constant depending on epsiv using existing ideas concerning ldquolist recoveryrdquo and expander based codes concatenating the folded rs codes with suitable inner codes we get binary codes that can be efficiently decoded up to twice the radius achieved by the standard gmd decoding

the cfar adaptive subspace detector is a scale invariant glrt the constant false alarm rate cfar matched subspace detector cfar msd is the uniformly most powerful invariant test and the generalized likelihood ratio test glrt for detecting a target signal in noise whose covariance structure is known but whose level is unknown previously the cfar adaptive subspace detector cfar asd or adaptive coherence estimator ace was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data we show here that the cfar asd is glrt when the test measurement is not constrained to have the same noise level as the training data as a consequence this glrt is invariant to a more general scaling condition on the test and training data than the well known glrt of kelly 1986

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions

coding for errors and erasures in random network coding the problem of error control in random linear network coding is considered a ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic motivated by the property that linear network coding is vector space preserving information transmission is modeled as the injection into the network of a basis for a vector space v and the collection by the receiver of a basis for a vector space u a metric on the projective geometry associated with the packet space is introduced and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space v capu is sufficiently large if the dimension of each codeword is restricted to a fixed integer the code forms a subset of a finite field grassmannian or equivalently a subset of the vertices of the corresponding grassmann graph sphere packing and sphere covering bounds as well as a generalization of the singleton bound are provided for such codes finally a reed solomon like code construction related to gabidulin s construction of maximum rank distance codes is described and a sudan style ldquolist 1rdquo minimum distance decoding algorithm is provided

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

robust precoding with limited feedback design based on precoding mse for mu miso systems for the separation of the signals in the vector broadcast channel bc some information about the channel state is necessary at the transmitter in many cases this channel state information csi must be fed back from the receivers to the transmitter we jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a precoder centric criterion i e the minimization of a mean square error mse metric appropriate for the precoder design this is in contrast to our previous works where the quantizer design was based on a csi mse metric i e based on the minimization of the mse between the true channel and the channel recovered by the transmitter using a feedback channel interestingly the estimators resulting from this joint formulation are independent of the used codebook the codebook entries are the employed precoders therefore each receiver feeds back the index of a set of precoders and the intersection of the sets gives the appropriate precoder since the quantizers of the different receivers have to work separately the metric for the computation of the partition cells cannot be expressed as a simple squared error depending on the quantizer output the proposed system based on a joint optimization clearly outperforms previous designs with separate optimization of feedback and precoding

probabilistic and fractal aspects of levy trees we investigate the random continuous trees called levy trees which are obtained as scaling limits of discrete galton watson trees we give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted trees which is equipped with the gromov hausdorff distance to construct levy trees we make use of the coding by the height process which was studied in detail in previous work we then investigate various probabilistic properties of levy trees in particular we establish a branching property analogous to the well known property for galton watson trees conditionally given the tree below level a the subtrees originating from that level are distributed as the atoms of a poisson point measure whose intensity involves a local time measure supported on the vertices at distance a from the root we study regularity properties of local times in the space variable and prove that the support of local time is the full level set except for certain exceptional values of a corresponding to local extinctions we also compute several fractal dimensions of levy trees including hausdorff and packing dimensions in terms of lower and upper indices for the branching mechanism function which characterizes the distribution of the tree we finally discuss some applications to super brownian motion with a general branching mechanism

limit of normalized quadrangulations the brownian map consider qn a random pointed quadrangulation chosen equally likely among the pointed quadrangulations with n faces in this paper we show that when n goes to qn suitably normalized converges weakly in a certain sense to a random limit object which is continuous and compact and that we name the brownian map the same result is shown for a model of rooted quadrangulations and for some models of rooted quadrangulations with random edge lengths a metric space of rooted resp pointed abstract maps that contains the model of discrete rooted resp pointed quadrangulations and the model of the brownian map is defined the weak convergences hold in these metric spaces

patterns and pattern matching in trees an analysis this paper presents general results on the probabilities of occurrences of patterns in trees which serve to analyze a commonly used pattern matching algorithm on trees it appears that for a wide class of statistics on trees pattern matching has a linear expected time complexity in contrast to a quadratic worst case behaviour the methods used are both combinatorial and analytic and prove useful in the evaluation of a wide class of tree algorithms

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

rigid body localization using sensor networks a framework for joint position and orientation estimation of a rigid body using range measurements is proposed we consider a setup in which a few sensors are mounted on a rigid body the absolute position of the rigid body is not known however we know how the sensors are mounted on the rigid body i e the sensor topology is known the rigid body is localized using noisy range measurements between the sensors and a few anchors nodes with known absolute positions and without using any inertial measurements we propose a least squares ls and a number of constrained ls estimators where the constrained estimators solve an optimization problem on the stiefel manifold as a benchmark we derive a unitarily constrained cramer rao bound finally the known topology of the sensors can be perturbed during fabrication or if the body is not entirely rigid to take these perturbations into account constrained total least squares estimators are also proposed

subspace partitioning for target detection and identification detection of a given target or set of targets from observed data is a problem countered in many applications regardless of the algorithm selected detection performance can be severely degraded when the subspace defined by the target data set is singular or ill conditioned high correlations between target components and their linear combinations lead to false positives and misidentifications especially for subspace based detectors in this paper we propose a subspace partitioning scheme that allows for detection to be performed in a number of better conditioned subspaces instead of the original subspace the proposed technique is applied to raman spectroscopic data analysis through both simulation and experimental results we demonstrate the improvement in the overall detection performance when using the proposed subspace partitioning scheme in conjunction with several subspace detection methods that are commonly used in practice

signal detection in complex structured para normal noise in this paper we address target detection in correlated non gaussian noise we introduce a new class of multivariate complex valued distributions that allows us to specify flexible non gaussian marginals as well as correlation between the variables while preserving circular symmetry for noise belonging to this class we study the fundamental problem of signal detection under different settings and develop the needed generalized likelihood ratio tests we also consider estimation of the noise parameters and derive the maximum likelihood formulations we evaluate the merit of our approach using numerical simulations on synthetic and real data and clearly demonstrate the advantage of using both correlations and non gaussianity

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

uniqueness and universality of the brownian map we consider a random planar map mn which is uniformly distributed over the class of all rooted q angulations with n faces we let mn be the vertex set of mn which is equipped with the graph distance dgr both when q 4 is an even integer and when q 3 there exists a positive constant cq such that the rescaled metric spaces mn cqn 1 4dgr converge in distribution in the gromov hausdorff sense toward a universal limit called the brownian map the particular case of triangulations solves a question of schramm

detection of gaussian constellations in mimo systems under imperfect csi this paper considers the problem of gaussian symbols detection in mimo systems in the presence of channel estimation errors under this framework we develop a computationally efficient approximations of the map detector the new detectors are based on a relaxation of the discrete nature of the digital constellation and on the channel estimation error statistics this leads to a non convex program that is solved efficiently via a hidden convexity minimization approach additionally we show that using a bayesian em approach comparable ber performance to that of the map detector can be achieved next we extend the detection scheme to the case where the noise variance is unknown we present a modified bayesian em approach with annealed gibbs sampling to perform joint noise variance estimation and symbols detection simulation results in a random mimo system show that the proposed algorithm outperforms the linear mmse receiver in terms of ber

the brownian map is the scaling limit of uniform random plane quadrangulations we prove that uniform random quadrangulations of the sphere with n faces endowed with the usual graph distance and renormalized by n 1 4 converge as n in distribution for the gromov hausdorff topology to a limiting metric space we validate a conjecture by le gall by showing that the limit is up to a scale constant the so called brownian map which was introduced by marckert mokkadem and le gall as the most natural candidate for the scaling limit of many models of random plane maps the proof relies strongly on the concept of geodesic stars in the map which are configurations made of several geodesics that only share a common endpoint and do not meet elsewhere

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

persymmetric adaptive detectors in homogeneous and partially homogeneous environments this paper addresses the problem of detecting a signal in partially homogeneous and homogeneous environments in partially homogeneous environments i e both the test data and training data share the same noise covariance matrix structure up to an unknown scaling factor a persymmetric adaptive coherence estimator per ace detector is proposed by exploiting the persymmetric structure of the covariance matrix the per ace can reduce training data requirements furthermore the expressions for the probabilities of false alarm and detection are derived along with the distribution of the loss factor in homogeneous environments a persymmetric adaptive matched filter per amf detector has been presented however its probability of detection has not been obtained yet thus we derive the expression for the probability of detection for both the per ace and per amf numerical results of these proposed expressions are confirmed with those of monte carlo trials in addition simulation results show that the proposed per ace outperforms the conventional ace in training limited scenarios

some gabidulin codes cannot be list decoded efficiently at any radius gabidulin codes can be seen as the rank metric equivalent of reed solomon codes it was recently proved using subspace polynomials that gabidulin codes cannot be list decoded beyond the so called johnson radius in another result cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials in this paper these subspace codes are used to prove two bounds on the list size in decoding certain gabidulin codes the first bound is an existential one showing that exponentially sized lists exist for codes with specific parameters the second bound presents exponentially sized lists explicitly for a different set of parameters both bounds rule out the possibility of efficiently list decoding several families of gabidulin codes for any radius beyond half the minimum distance such a result was known so far only for non linear rank metric codes and not for gabidulin codes using a standard operation called lifting identical results also follow for an important class of constant dimension subspace codes

the brownian limit of separable permutations we study random uniform permutations in an important class of pattern avoiding permutations the separable permutations we describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the brownian excursion in the recent terminology of permutons our work can be interpreted as the convergence of uniform random separable permutations towards a brownian separable permuton

dominos and the gaussian free field we define a scaling limit of the height function on the domino tiling model dimer model on simply connected regions in z 2 and show that it is the massless free field a gaussian process with independent coefficients when expanded in the eigenbasis of the laplacian

the depth first processes of galton watson trees converge to the same brownian excursion in this paper we show a strong relation between the depth first processes associated to galton watson trees with finite variance conditioned by the total progeny the depth first walk the depth first queue process the height process a consequence is that these processes suitably normalized converge to the same brownian excursion this provides an alternative proof of aldous one of the convergence of the depth first walk to the brownian excursion which does not use the existence of a limit tree the methods that we introduce allow one to compute some functionals of trees or discrete excursions for example we compute the limit law of the process of the height of nodes with a given out degree and the process of the height of nodes root of a given subtree

maximal invariants and performance of some invariant hypothesis tests for an adaptive detection problem maximal invariants for adaptive detection of a signal in unknown interference from multiple observations is derived given coherent samples from p sets of observations it is shown that a maximal invariant statistic for the detection problem is a 2p 1 dimensional vector comprising the eigenvalues of two hermitian positive definite matrices obtained from the data set two invariant detectors well known for p 1 are generalized for the case of multiple observations and closed form expressions for the probability of detection and probability of false alarm are derived along with the distributions of the signal to interference plus noise loss factors several novel invariant detectors are constructed from the maximal invariants and the receiver operating characteristics of the detectors compared

the total variance of a periodogram based spectral estimate of a stochastic process with spectral uncertainty and its application to classifier design the variance of a spectral estimate of a stochastic process is essential to the formulation and performance of a spectral classifier the overall variance of a spectral estimate originates from two sources the within class spectral uncertainty and the variance introduced in the spectral estimation procedure in this paper we derive the total variance of a periodogram based spectral estimate under some assumptions using this result we formulate a linear spectral classifier based on fisher s separability metric the classifier is used to classify two oceanographic processes ocean convection versus internal waves

local convergence for permutations and local limits for uniform rho avoiding permutations with rho 3 we set up a new notion of local convergence for permutations and we prove a characterization in terms of proportions of consecutive pattern occurrences we also characterize random limiting objects for this new topology introducing a notion of shift invariant property corresponding to the notion of unimodularity for random graphs we then study two models in the framework of random pattern avoiding permutations we compute the local limits of uniform rho avoiding permutations for rho 3 when the size of the permutations tends to infinity the core part of the argument is the description of the asymptotics of the number of consecutive occurrences of any given pattern for this result we use bijections between rho avoiding permutations and rooted ordered trees local limit results for galton watson trees the second moment method and singularity analysis

continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models given any regularly varying dislocation measure we identify a natural self similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths as an application we obtain continuum random tree limits of aldous s beta splitting models and ford s alpha models for phylogenetic trees this confirms in a strong way that the whole trees grow at the same speed as the mean height of a randomly chosen leaf

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

on the minimum mean p th error in gaussian noise channels and its applications the problem of estimating an arbitrary random vector from its observation corrupted by additive white gaussian noise where the cost function is taken to be the minimum mean p th error mmpe is considered the classical minimum mean square error mmse is a special case of the mmpe several bounds properties and applications of the mmpe are derived and discussed the optimal mmpe estimator is found for gaussian and binary input distributions properties of the mmpe as a function of the input distribution signal to noise ratio snr and order p are derived the single crossing point property scpp which provides an upper bound on the mmse and which together with the mutual information mmse relationship is a powerful tool in deriving converse proofs in multi user information theory is extended to the mmpe moreover a complementary bound to the scpp is derived as a first application of the mmpe a bound on the conditional differential entropy in terms of the mmpe is provided which then yields a generalization of the ozarow wyner lower bound on the mutual information achieved by a discrete input on a gaussian noise channel as a second application the mmpe is shown to improve on previous characterizations of the phase transition phenomenon that manifests in the limit as the length of the capacity achieving code goes to infinity as a discontinuity of the mmse as a function of snr as a final application the mmpe is used to show new bounds on the second derivative of mutual information or the first derivative of the mmse

the range of tree indexed random walk in low dimensions we study the range rn of a random walk on the d dimensional lattice z d indexed by a random tree with n vertices under the assumption that the random walk is centered and has fi nite fourth moments we prove in dimension d 3 that n d 4 rn converges in distribution to the lebesgue measure of the support of the integrated super brownian excursion ise an auxiliary result shows that the suitably rescaled local times of the tree indexed ran dom walk converge in distribution to the density process of ise we obtain similar results for the range of critical branching random walk in z d d 3 as an intermediate estimate we get exact asymptotics for the probability that a critical branching random walk starting with a single particle at the origin hits a distant point the results of the present article complement those derived in higher dimensions in our earlier work 1 introduction in the present paper we continue our study of asymptotics for the num ber of distinct sites of the lattice visited by a tree indexed random walk we consider discrete plane trees which are rooted ordered trees that can be viewed as describing the genealogy of a population starting with one ancestor or root which is denoted by the symbol given such a treet and a probability measure on z d we can consider the random walk with jump distribu tion indexed by the treet this means that we assign a random spatial location zt u 2 z d to every vertex u oft in the following way first the spatial location zt of the root is the origin of z d then we assign independently to every edge e of the tree t a random variable ye distributed according to and we let the spatial location zt u of the vertex u be the sum of the quantities ye over all edges e belonging to the simple path from to u in the tree the number of distinct spatial locations is called the range of the tree indexed random walk zt in our previous work 13 we stated the following result let be a probability distribution on z d which is symmetric with finite support and is not supported on a strict subgroup of z d and for every integer n 1 lett n be a random tree uniformly distributed over all plane trees with n vertices conditionally given t n let zt n be a random walk with jump distribution indexed byt n and let rn stand for the range of zt n then

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

linear algebraic list decoding for variants of reed solomon codes folded reed solomon rs codes are an explicit family of codes that achieve the optimal tradeoff between rate and list error correction capability specifically for any e 0 guruswami and rudra presented an no 1 e time algorithm to list decode appropriate folded rs codes of rate r from a fraction 1 r e of errors the algorithm is based on multivariate polynomial interpolation and root finding over extension fields it was noted by vadhan that interpolating a linear polynomial suffices for a statement of the above form here we give a simple linear algebra based analysis of this variant that eliminates the need for the computationally expensive root finding step over extension fields and indeed any mention of extension fields the entire list decoding algorithm is linear algebraic solving one linear system for the interpolation step and another linear system to find a small subspace of candidate solutions except for the step of pruning this subspace the algorithm can be implemented to run in quadratic time we also consider a closely related family of codes called order m derivative codes and defined over fields of large characteristic which consist of the evaluations of f as well as its first m 1 formal derivatives at n distinct field elements we show how our linear algebraic methods for folded rs codes can be used to show that derivative codes can also achieve the above optimal tradeoff the theoretical drawback of our analysis for folded rs codes and derivative codes is that both the decoding complexity and proven worst case list size bound are n 1 e by combining the above idea with a pseudorandom subset of all polynomials as messages we get a monte carlo construction achieving a list size bound of o 1 e2 which is quite close to the existential o 1 e bound however the decoding complexity remains n 1 e our work highlights that constructing an explicit subspace evasive subset that has small intersection with low dimensional subspaces an interesting problem in pseudorandomness in its own right could lead to explicit codes with better list decoding guarantees

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

the continuum random tree iii let mathscr r k k geq 1 be random trees with k leaves satisfying a consistency condition removing a random leaf from mathscr r k gives mathscr r k 1 then under an extra condition this family determines a random continuum tree mathscr l which it is convenient to represent as a random subset of l 1 this leads to an abstract notion of convergence in distribution as n rightarrow infty of rescaled random trees mathscr j n on n vertices to a limit continuum random tree mathscr l the notion is based upon the assumption that for fixed k the subtrees of mathscr j n determined by k randomly chosen vertices converge to mathscr r k as our main example under mild conditions on the offspring distribution the family tree of a galton watson branching process conditioned on total population size equal to n can be rescaled to converge to a limit continuum random tree which can be constructed from brownian excursion

on the evaluation of the polyanskiy poor verdu converse bound for finite block length coding in awgn a tight converse bound to the channel coding rate in the finite block length regime and under additive white gaussian noise conditions was recently proposed by polyanskiy poor verdu ppv the bound is a generalization of a number of other classical results and it was also claimed to be equivalent to shannon s 1959 cone packing bound in this paper we investigate methods for a reliable numerical evaluation of the bound which is troublesome even for not too large values of the block length n by compactly expressing the polyanskiy poor and verdu ppv converse bound in terms of non central chi squared distributions and by evaluating those through an integral expression and a corresponding series expansion which exploit a method proposed by temme as a result a robust evaluation method and new insights on the bound s asymptotics as well as new approximate expressions are obtained