a computationally efficient two step implementation of the glrt in this paper the performance of a new two step adaptive detection algorithm is analyzed the two step glrt consists of an initial adaptive matched filter amf test followed by a generalized likelihood ratio test glrt analytical expressions are provided for the probability of false alarm p sub fa and the probability of detection p sub d in unknown complex gaussian interference the analysis shows that the two step glrt significantly reduces the computational load over the glrt while maintaining detection and sidelobe rejection performance commensurate with the glrt the two step glrt detection algorithm is also compared with another two step detection algorithm the adaptive sidelobe blanker asb both the two step glrt and the asb are characterized in terms of the mainbeam detection performance and the rejection of sidelobe targets we demonstrate that for a given p sub fa the two step glrt has a broad range of threshold pairs one threshold for the amf test and one for the glrt that provide performance identical to the glrt this is in contrast with the asb where the threshold pairs that maximize the p sub d are a function of the target s signal to interference plus noise ratio sinr hence for a fixed pair of thresholds the two step glrt can provide slightly better mainbeam detection performance than the asb in the transition region from low to high detection probabilities

maximum likelihood estimation of a structured covariance matrix with a condition number constraint in this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications when a limited number of training data is present we determine the maximum likelihood ml estimator of the covariance matrix starting from a set of secondary data assuming a special covariance structure i e the sum of a positive semi definite matrix plus a term proportional to the identity and a condition number upper bound constraint we show that the formulated constrained optimization problem falls within the class of maxdet problems and develop an efficient procedure for its solution in closed form remarkably the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix at the analysis stage we assess the performance of the proposed algorithm in terms of achievable signal to interference plus noise ratio sinr both for a spatial and a doppler processing the results show that interesting sinr improvements with respect to some existing covariance matrix estimation techniques can be achieved

derivation of the bias of the normalized sample covariance matrix in a heterogeneous noise with application to low rank stap filter in a previous work we have developed a low rank lr spatio temporal adaptive processing stap filter when the disturbance is modeled as the sum of a low rank spherically invariant random vector sirv clutter and a zero mean white gaussian noise this lr stap filter is built from the normalized sample covariance matrix nscm and exhibits good robustness properties to secondary data contamination by target components in this correspondence we derive the bias of the nscm with this noise model we show that the eigenvectors estimated from the nscm are unbiased the new expressions of the expectation of nscm eigenvalues are also given from these results we also show that the estimate of the clutter subspace projector based on the nscm used in our lr stap is a consistent estimate of the true one results on numerical data validates the theoretical approach

detection of an unknown rank one component in white noise we consider the detection of an unknown and arbitrary rank one signal in a spatial sector scanned by a small number m of beams we address the problem of finding the maximal invariant for the problem at hand and show that it consists of the ratio of the eigenvalues of a wishart matrix to its trace next we derive the generalized likelihood ratio test glrt along with expressions for its probability density function pdf under both hypotheses special attention is paid to the case m 2 where the glrt is shown to be a uniformly most powerful invariant umpi numerical simulations attest to the validity of the theoretical analysis and illustrate the detection performance of the glrt

adaptive detection of point like targets in spectrally symmetric interference we address adaptive radar detection of targets embedded in ground clutter dominated environments characterized by a symmetrically structured power spectral density at the design stage we leverage on the spectrum symmetry for the interference to come up with decision schemes capable of capitalizing the a priori information on the covariance structure to this end we prove that the detection problem at hand can be formulated in terms of real variables and then we apply design procedures relying on the glrt the rao test and the wald test specifically the estimates of the unknown parameters under the target presence hypothesis are obtained through an iterative optimization algorithm whose convergence and quality guarantee is thoroughly proved the performance analysis both on simulated and on real radar data confirms the superiority of the considered architectures over their conventional counterparts which do not take advantage of the clutter spectral symmetry

a unifying framework for adaptive radar detection in homogeneous plus structured interference part i on the maximal invariant statistic this paper deals with the problem of adaptive multidimensional multichannel signal detection in homogeneous gaussian disturbance with unknown covariance matrix and structured deterministic interference the aforementioned problem corresponds to a generalization of the well known generalized multivariate analysis of variance gmanova in this part i of the paper we formulate the considered problem in canonical form and after identifying a desirable group of transformations for the considered hypothesis testing we derive a maximal invariant statistic mis for the problem at hand furthermore we provide the mis distribution in the form of a stochastic representation finally strong connections to the mis obtained in the open literature in simpler scenarios are underlined

adaptive detection and estimation in the presence of useful signal and interference mismatches this paper considers adaptive detection and estimation in the presence of useful signal and interference mismatches we assume a homogeneous environment where the random disturbance components from the primary and secondary data share the same covariance matrix moreover the data under test contains a deterministic interference vector in addition to the possible useful signal we focus on the situation where an energy fraction of both the useful signal and the deterministic interference may lie outside their nominal subspaces conical uncertainty model under these conditions we devise a procedure for the computation of the joint maximum likelihood ml estimators of the useful signal and interference vectors resorting to a suitable rank one decomposition of a semidefinite program sdp problem optimal solution hence we use the aforementioned estimators for the synthesis of adaptive receivers based on different generalized likelihood ratio test glrt criteria at the analysis stage we assess the performance of the new detectors in comparison with some decision rules available in open literature

adaptive double subspace signal detection in gaussian background part ii partially homogeneous environments in this part of the paper we continue to study the problem of detecting a double subspace signal in gaussian noise precisely we address the detection problem in partially homogeneous environments where the primary and secondary data share the same covariance matrix up to an unknown scaling factor we derive the generalized likelihood ratio test glrt rao test wald test and their two step versions we also introduce three spectral norm tests snts all these detectors possess the constant false alarm rate cfar property moreover various kinds of special cases of these detectors are given at the stage of performance evaluation we consider two cases one is the case of no signal mismatch the other is more general namely the case of signal mismatch including the column space signal mismatch and row space signal mismatch

subspace based adaptive generalized likelihood ratio detection subspace based adaptive detection performance is examined for the generalized likelihood ratio detector based on wilks spl lambda statistic the problem considered here is detecting the presence of one or more signals of known shape embedded in gaussian distributed noise with unknown covariance structure the data is mapped into a subspace prior to detection the probability of false alarm is independent of the subspace transformation and depends only on subspace dimension the probability of detection depends on the subspace transformation through a nonadaptive signal to noise ratio snr parameter subspace processing results in an snr loss that tends to decrease performance and a gain in statistical stability that tends to increase performance it is shown that the statistical stability effect dominates the snr loss for short data records and subspace detectors can require substantially less snr than full space detectors for equivalent performance a method for designing the subspace transformation to minimize the snr loss is proposed and illustrated through simulations

adaptive array detection of uncertain rank one waveforms adaptive array detection of known within a complex scaling rank one space time waveforms in unknown spatial noise has received considerable attention the two published solutions are the adaptive matched filter and the glrt we expand on this work to consider the case of rank one waveforms that are uncertain i e only partially known more precisely we model the space time steering vector as the kronecker product of two vectors each of which is unknown but is known to lie in a known subspace applications for such a model include detection in the presence of multipath and spectral or polarization diversity in both radar processing and wireless communication using the principle of invariance we construct detectors based on the maximal invariant we show that the snr required to achieve a given detection probability for a given false alarm rate is only weakly impacted by waveform uncertainty thus our detector approaches the performance of earlier detectors which entail known waveforms

on the statistical invariance for adaptive radar detection in partially homogeneous disturbance plus structured interference this paper deals with the problem of adaptive vector subspace signal detection in partially homogeneous gaussian disturbance and structured unknown deterministic interference within the framework of invariance theory it is first proved that the maximal invariant statistic mis for the problem at hand is scalar valued and coincides with the well known adaptive normalized matched filter evaluated after data projection in the complementary subspace of the interfering signal second the statistical characterization of the mis under both hypotheses is derived then it is shown the statistical equivalence of two step generalized likelihood ratio test rao and wald tests as well as the more recently considered durbin and gradient test to the above statistic finally simulation results are provided to confirm our findings and analyze the performance trend of the mis with the relevant parameters

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

a generalized version of ace and performance analysis this paper considers the problem of detecting a signal that belongs to an unknown one dimensional subspace of mathbb c n times 1 in additive interference plus noise whose covariance matrix is unknown the interference plus noise is assumed to be modeled as a complex multivariate zero mean random vector whose covariance matrix bf r is estimated from signal free training vectors the hypothesis test labeled the generalized adaptive coherence estimator gace involves two test vectors both of which contain the unknown signal the test statistic reduces to the ace test statistic as the signal to interference plus noise ratio of any one of the test vectors increases without limit in the limit of large number of training samples the gace test statistic reduces to the magnitude square of the inner product of a signal vector in additive statistically independent white noise vectors analytical expressions for the probability of false alarm and the probability of detection of the gace test are derived and the test is shown to have the constant false alarm rate cfar property sample results to illustrate the performance of the detector are provided and compared with the performance of the generalized likelihood ratio test glrt for the specific problem along with results on the sequential application of the glrt and gace

estimates of the green function for x elliptic operators in this note we establish two sided pointwise estimates near the pole of the green function for x elliptic operators in divergence form enjoying the doubling condition and the poincare inequality as a step towards this result we also prove a nonhomogeneous harnack inequality some representation formulas and a result on approximation by regular domains

a wiener test a la landis for evolutive hormander operators abstract in this paper we prove a wiener type characterization of boundary regularity in the spirit of a classical result by landis for a class of evolutive hormander operators we actually show the validity of our criterion for a larger class of degenerate parabolic operators with a fundamental solution satisfying suitable two sided gaussian bounds our condition is expressed in terms of a series of balayages or as it turns out to be equivalently riesz potentials

random distortion testing and optimality of thresholding tests this paper addresses the problem of testing whether the mahalanobis distance between a random signal and a known deterministic model 0 exceeds some given non negative real number or not when has unknown probability distribution and is observed in additive independent gaussian noise with positive definite covariance matrix when is deterministic unknown we prove the existence of thresholding tests on the mahalanobis distance to 0 that have specified level and maximal constant power mcp the mcp property is a new optimality criterion involving wald s notion of tests with uniformly best constant power ubcp on ellipsoids for testing the mean of a normal distribution when the signal is random with unknown distribution constant power maximality extends to maximal constant conditional power mccp and the thresholding tests on the mahalanobis distance to 0 still verify this novel optimality property our results apply to the detection of signals in independent and additive gaussian noise in particular for a large class of possible model mismatches mccp tests can guarantee a specified false alarm probability in contrast to standard neyman pearson tests that may not respect this constraint

comparison of glr and invariant detectors under structured clutter covariance this paper addresses a target detection problem in radar imaging for which the covariance matrix of unknown gaussian clutter has block diagonal structure this block diagonal structure is the consequence of a target lying along a boundary between two statistically independent clutter regions here we design adaptive detection algorithms using both the generalized likelihood ratio glr and the invariance principles there has been considerable interest in applying invariant hypothesis testing as an alternative to the glr test this interest has been motivated by several attractive properties of invariant tests including exact robustness to variation of nuisance parameters and possible finite sample min max optimality however in our deep hide target detection problem there are regimes for which neither the glr nor the invariant tests uniformly outperforms the other we discuss the relative advantages of glr and invariance procedures in the context of this radar imaging and target detection application

iterative generalized likelihood ratio test for mimo radar we consider a multiple input multiple output mimo radar system where both the transmitter and receiver have multiple well separated subarrays with each subarray containing closely spaced antennas because of this general antenna configuration both the coherent processing gain and the spatial diversity gain can be simultaneously achieved we compare several spatial spectral estimators including capon and apes for target detection and parameter estimation we introduce a generalized likelihood ratio test glrt and a conditional generalized likelihood ratio test cglrt for the general antenna configuration based on glrt and cglrt we then propose an iterative glrt iglrt procedure for target detection and parameter estimation via several numerical examples we show that iglrt can provide excellent detection and estimation performance at a low computational cost

adaptive detection in gaussian interference with unknown covariance after reduction by invariance in this paper we address the problem of adaptive detection in homogeneous gaussian interference with unknown covariance matrix after reduction by invariance starting from a maximal invariant statistic which contains all the information for the synthesis of an invariant detector we devise the rao test generalized likelihood ratio test glrt and durbin test moreover we compare their decision statistics with those of the receivers designed according to the same criteria from the raw data i e before reduction by invariance we prove that the glrt in the original data space is statistically equivalent to the glrt designed after reduction by invariance under a very mild assumption and coincide with the conditional uniformly most powerful invariant c umpi test obtained conditioning on an ancillary part of the maximal invariant statistic as to the rao and durbin criteria when they are applied after reduction by invariance lead to detectors different from the counterparts devised in the raw data domain at the analysis stage the performance of the receivers devised in the invariant domain is analyzed in comparison with that of the counterparts synthesized from the original observations

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

adaptive beamformer orthogonal rejection test research in the area of signal detection in the presence of unknown interference has resulted in a number of adaptive detection algorithms examples of such algorithms include the adaptive matched filter amf the generalized likelihood ratio test glrt and the adaptive coherence estimator ace each of these algorithms results in a tradeoff between detection performance for matched signals and rejection performance for mismatch signals this paper introduces a new detection algorithm we call the adaptive beamformer orthogonal rejection test abort our test decides if an observation contains a multidimensional signal belonging to one subspace or if it contains a multidimensional signal belonging to an orthogonal subspace when unknown complex gaussian noise is present in our analysis we use a statistical hypothesis testing framework to develop a generalized likelihood ratio decision rule we evaluate the performance of this decision rule in both the matched and mismatched signal cases our results show that for constant power complex gaussian noise if the signal is matched to the steering vector abort glrt and amf give approximately equivalent probability of detection higher than that of ace which trades detection probability for an extra invariance to scale mismatch between training and test data of these four tests ace is most selective and therefore least tolerant of mismatch whereas amf is most tolerant of mismatch and therefore least selective abort and glrt offer compromises between these extremes with abort more like ace and with glrt more like amf

fast converging adaptive detection of doppler shifted range distributed targets a generalized likelihood ratio test glrt for the adaptive detection of a target or targets that are doppler shifted and distributed in range is derived the unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference which is assumed to be characterized as complex zero mean correlated gaussian random variables the target s or targets complex amplitudes are assumed to be distributed across the entire input data block sensor spl times range the unknown covariance matrix is constrained to have the reasonable form of the identity matrix the internal noise contribution plus an unknown positive semidefinite psdh matrix the external interference contribution it is shown via simulation for a variety of interference scenarios that the new detector has the characteristic of having a bounded constant false alarm rate cfar i e for our problem the probability of false alarm p sub f for a given detection threshold is bounded by the p sub f that results when no external interference is present it is also shown via simulation that the new detector converges relatively fast with respect to the number of sample vectors k necessary in order to achieve a given probability of detection p sub d

adaptive detection of a subspace signal in signal dependent interference this paper deals with the problem of adaptive detection of subspace signals embedded in thermal noise and clutter that depends on the transmitted signal to this end at the design stage we assume that the signal dependent sd clutter shares the same subspace as the target signals as customary a set of secondary data free of signal components is also assumed available two adaptive detectors referred to as the sd rao and sd wald are proposed by resorting to the rao test and wald test design criteria unlike the classical rao and wald tests which are derived by dividing the complex parameter into the real and imaginary parts the proposed detectors treat the complex parameter as a single quantity to reduce the computational burden moreover we derive the theoretical false alarm probabilities and detection probabilities and show that both the two proposed detectors exhibit the constant false alarm rate property numerical results show that the proposed detectors achieve a detection performance improvement over the conventional multidimensional detectors

on multiple covariance equality testing with application to sar change detection this paper deals with the problem of testing the equality of m covariance matrices we first identify a suitable group of transformations leaving the problem invariant and obtain the corresponding maximal invariant statistic then the generalized likelihood ratio test glrt is recalled and explicit expressions for rao wald gradient and durbin tests are provided also equivalences among them and with other well known tests proposed in open literature mostly for the real valued case are analyzed and compared finally the application of the proposed framework to the relevant signal processing application of multipass coherent change detection ccd in polarimetric synthetic aperture radar is demonstrated both on simulated and on live data

wiener criterion for x elliptic operators abstract in this note we prove a wiener criterion of regularity of boundary points for the dirichlet problem related to x elliptic operators in divergence form enjoying the doubling condition and the poincare inequality as a step towards this result we exhibit some other characterizations of regularity in terms of the capacitary potentials finally we also show that a cone type criterion holds true in our setting

adaptive subspace detectors we use the theory of generalized likelihood ratio tests glrts to adapt the matched subspace detectors msds of scharf 1991 and of scharf and frielander 1994 to unknown noise covariance matrices in so doing we produce adaptive msds that may be applied to signal detection for radar sonar and data communication we call the resulting detectors adaptive subspace detectors asds these include kelly s 1987 glrt and the adaptive cosine estimator ace of kaurt and scharh see ibid vol 47 p 2538 41 1999 and of scharf and mcwhorter see proc 30th asilomar conf signals syst comput pacific grove ca 1996 for scenarios in which the scaling of the test data may deviate from that of the training data we then present a unified analysis of the statistical behavior of the entire class of asds obtaining statistically identical decompositions in which each asd is simply decomposed into the nonadaptive matched filter the nonadaptive cosine or t statistic and three other statistically independent random variables that account for the performance degrading effects of limited training data

a unifying framework for adaptive radar detection in homogeneous plus structured interference part ii detectors design this paper deals with the problem of adaptive multidimensional multichannel signal detection in homogeneous gaussian disturbance with unknown covariance matrix and structured unknown deterministic interference the aforementioned problem extends the well known generalized multivariate analysis of variance gmanova tackled in the open literature in part i of this paper we have obtained the maximal invariant statistic mis for the problem under consideration as an enabling tool for the design of suitable detectors which possess the constant false alarm rate cfar property herein we focus on the development of several theoretically founded detectors for the problem under consideration first all the considered detectors are shown to be function of the mis thus proving their cfarness property second coincidence or statistical equivalence among some of them in such a general signal model is proved third strong connections to well known simpler scenarios analyzed in adaptive detection literature are established finally simulation results are provided for a comparison of the proposed receivers

a subspace based adaptive sidelobe blanker we propose a modified version of the adaptive sidelobe blanker asb consisting of a generalized likelihood ratio test glrt based subspace detector followed by the adaptive coherence estimator the performance analysis shows that it possesses the constant false alarm rate property with respect to the unknown covariance matrix of the noise in homogeneous environment and that it guarantees a wider range of ldquodirectivityrdquo values with respect to the plain asb the probability of false alarm and the probability of detection the latter for matched signals only have been evaluated in closed form in homogeneous environment and by resorting to monte carlo simulation for the other considered cases

separating function estimation tests a new perspective on binary composite hypothesis testing in this paper we study some relationships between the detection and estimation theories for a binary composite hypothesis test h0 against h1 and a related estimation problem we start with a one dimensional 1d space for the unknown parameter space and one sided hypothesis problems and then extend out results into more general cases for one sided tests we show that the uniformly most powerful ump test is achieved by comparing the minimum variance and unbiased estimator mvue of the unknown parameter with a threshold thus for the case where the ump test does not exist the mvue of the unknown parameter does not exist either therefore for such cases a good estimator of the unknown parameter is deemed as a good decision statistic for the test for a more general class of composite testing with multiple unknown parameters we prove that the mvue of a separating function sf can serve as the optimal decision statistic for the ump unbiased test where the sf is continuous differentiable positive for all parameters under h1 and is negative for the parameters under h0 we then prove that the ump unbiased statistic is equal to the mvue of an sf in many problems with multiple unknown parameters the ump test does not exist for such cases we show that if one detector between two detectors has a better receiver operating characteristic roc curve then using its decision statistic we can estimate the sf more e accurately in probability for example the sf is the signal to noise ratio snr in some problems these results motivate us to introduce new suboptimal sf estimator tests sfets which are easy to derive for many problems finally we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding sf

recursive estimation of the covariance matrix of a compound gaussian process and its application to adaptive cfar detection adaptive detection of signals embedded in gaussian or non gaussian noise is a problem of primary concern among radar engineers we propose a recursive algorithm to estimate the structure of the covariance matrix of either a set of gaussian vectors that share the spectral properties up to a multiplicative factor or a set of spherically invariant random vectors sirvs with the same covariance matrix and possibly correlated texture components we also assess the performance of an adaptive implementation of the normalized matched filter nmf relying on the newly introduced estimate in the presence of compound gaussian clutter dominated disturbance in particular it is shown that a proper initialization of the recursive procedure leads to an adaptive nmf with the constant false alarm rate cfar property and that it is very effective to operate in heterogeneous environments of relevant practical interest

a diagonal growth curve model and some signal processing applications we consider a variation of the growth curve gc model referred to as the diagonal growth curve dgc model where the steering vectors and waveforms are both known and the complex amplitude matrix is constrained to be diagonal a closed form approximate maximum likelihood aml estimator for this model is derived based on the maximum likelihood principle we analyze the statistical properties of this method theoretically and show that the aml estimate is unbiased and asymptotically statistically efficient for a large snapshot number via several numerical examples in array signal processing and spectral analysis we also show that the proposed aml estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods

invariant adaptive detection of range spread targets under structured noise covariance the invariance principle is adopted to develop an exhaustive study for adaptive detection of range spread targets in gaussian noise sharing a block diagonal covariance structure for this problem the usual generalized likelihood ratio principle is intractable in this paper we first determine the largest group of affine transformations that does not alter the decision problem then a maximal invariant identified by this group is derived which can characterize the totality of the invariant detectors and extends the existing results for the point target case a theoretical performance analysis of the maximal invariant is also given finally we propose two classes of invariant detectors which are distinguished by whether a constant false alarm rate cfar is maintained numerical experiments are provided for a comparison of the proposed detectors where a tradeoff between the cfarness and the improved performance has been observed and studied

adaptive radar detectors based on the observed fim modified versions of rao wald and durbin tests are considered exploiting an estimator of the fisher information matrix fim in place of the exact one they are asymptotically equivalent under some technical conditions to the standard counterparts and rely on the use of the observed fim ofim which is proportional to the negative hessian of the log likelihood the developed framework is applied to the problem of adaptive radar detection of a point like target in homogeneous or partially homogeneous interference remarkably for both the scenarios it is shown that rao wald and durbin tests with ofim are statistically equivalent to the generalized likelihood ratio test glrt for the specific detection problem namely kelly s detector for the homogeneous environment and the adaptive coherence estimator ace s kraut and l l scharf the cfar adaptive subspace detector is a scale invariant glrt ieee trans signal process vol 47 no 9 pp 2538 2541 sep 1999 also known as adaptive normalized matched filter anmf e conte m lops and g ricci asymptotically optimum radar detection in compound gaussian clutter ieee trans aerosp electron syst vol 31 no 2 pp 617 625 apr 1995 for the partially homogeneous scenario this provides a new interpretation of the mentioned glrts laying the foundations for a better understanding of their theoretical validity

diffuse multipath exploitation for adaptive radar detection we deal with the problem of detecting point like targets in diffuse multipath environments modeling the target echo as the superposition of a deterministic signal with an unknown scaling factor due to the direct path plus a zero mean complex circular symmetric gaussian random vector with an unknown covariance matrix accounting for the echoes from the glistening surface we devise a constrained generalized likelihood ratio test glrt for the resulting hypothesis testing problem enforcing the primary data covariance matrix due to both interference and multipath echoes to belong to a neighborhood of the secondary data sample covariance matrix remarkably the proposed decision scheme ensures the desirable constant false alarm rate cfar property with respect to the unknown parameters of the interference the performance assessment conducted on simulated data in terms of detection probability also in comparison with existing solutions highlights the effectiveness of the new approach to cope with diffuse multipath phenomena

potential analysis for a class of diffusion equations a gaussian bounds approach let h be a linear second order partial differential operator with non negative characteristic form in a strip s r n r we assume that h as a fundamental solution smooth out of its poles and bounded from above and from below by gaussian kernels modeled on subriemannian doubling distances in r n under these assumptions we show that h endows s with a structure of harmonic space this allows us to study boundary value problems for l with a perron wiener brelot bauer method and to obtain pointwise regularity estimates at the boundary in terms of wiener series modeled on the gaussian kernels our analysis includes the proof of a scale invariant harnack inequality for nonnegative solutions we also show an application to the real hypersurphaces of c n 1 with given levi curvature

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

the computation of characteristic classes of lattice gauge fields agl p c valued lattice gauge fieldu on a simplicial complex determines a principalgl p c bundle if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters a representative cocyclecq for theqth chern class of can be computed on each 2q simplex by takingcq to be the intersection number of a certain singular 2q cubem with a schubert type variety q in the space of allp p matrices this reduces to the solution of polynomial equations with coefficients coming fromu and thus avoids numerical integration or cooling type procedures an application of this method is suggested for the computation of the topological charge of ansu 3 valued lattice gauge field on a 4 complex

invariance and optimality of cfar detectors in binary composite hypothesis tests we investigate the relationship between constant false alarm rate cfar and invariant tests we introduce the minimal invariant group mig we show that for a family of distributions the unknown parameters are eliminated from the distribution of the maximal invariant statistic under the mig while the maximum information of the observed signal is preserved we prove that any invariant test with respect to mig is cfar and conversely for any cfar test an invariant statistic exists with respect to an mig under some mild conditions moreover for a given cfar test we propose a systematic method for deriving an enhanced test i e a function of observations exists such that the likelihood ratio lr of the maximal invariant of its mig gives an enhanced test furthermore we introduce the uniformly most powerful cfar ump cfar test as the optimal cfar bound among all cfar tests we then prove that the ump cfar test for the minimally invariant hypothesis testing problem is given by the lr of the maximal invariant under mig for some problems this test mp cfar depends on the unknown parameters of the alternative hypothesis however provides an upper performance bound for all suboptimal cfar tests we also propose three suboptimal novel cfar tests among which one is asymptotically optimal

the petrovskiĭ criterion and barriers for degenerate and singular p parabolic equations in this paper we obtain sharp petrovski criteria for the p parabolic equation both in the degenerate case p 2 and the singular case 1 p 2 we also give an example of an irregular boundary point at which there is a barrier thus showing that regularity cannot be characterized by the existence of just one barrier

wiener s criterion for the heat equation this paper establishes a necessary and sufficient condition for a boundary point of an arbitrary bounded open subset of r 1 to be regular for the heat equation our criterion is in the sense described below the exact analogue of winner s test w for boundary regularity of harmonic functions a careful statement of our result requires that we first of all introduce a great deal of terminology let 2 q r 1 n 1 denote any bounded open subset and 8 2 its topological boundary we will often write a typical point z e r 1 as z x t xer te r if ue c2 q r we may define the heat operator

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

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

rao test for adaptive detection in gaussian interference with unknown covariance matrix this paper deals with the problem of detecting a signal known up to a scaling factor in the presence of gaussian disturbance with unknown covariance matrix a new detector based on the rao test criterion is introduced and its invariance properties and constant false alarm rate cfar behavior are studied at the analysis stage the performance of the new receiver is assessed also in comparison with some classical adaptive radar detectors both in the matched as well as in the mismatched signal case remarkably the rao test may achieve a matched detection performance which is commensurate with that of the generalized likelihood ratio test glrt based detectors if a sufficient number of training data is available moreover it also exhibits better rejection capabilities of mismatched signals than the counterparts in the last part of the work a two stage detector whose second stage coincides with the rao test is devised it represents a suitable means to restore the detection performance of the plain rao test in the presence of a small number of training data finally the performance of the aforementioned two stage processor is analyzed in closed form and the cfar behavior is proved

lattice gauge fields principal bundles and the calculation of topological charge su2 valued lattice gauge fields are studied on a 4 dimensional simplicial lattice ifu has sufficiently small plaquette products then there is a unique principal su2 bundle admitting transition functions defined on the intersections of adjacent dual cells which take values within 8 ofu an algorithm is explicitly given which associates an integer to everyu off a certain set of measure zero this algorithm only involves evaluation of 4 4 determinants and the solution of quadratic equations whenu is as above the integer produced is the second chern number of i e the topological charge ofu

glrt based adaptive detection algorithms for range spread targets we address adaptive detection of a range spread target or targets embedded in gaussian noise with unknown covariance matrix to this end we assume that cells referred to in the following as secondary data that are free of signal components are available those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test in this context we design detectors relying on the generalized likelihood ratio test glrt and on a two step glrt based design procedure remarkably both criteria lead to receivers ensuring the constant false alarm rate cfar property with respect to the unknown quantities a thorough performance assessment of the proposed detection strategies together with the evaluation of their processing cost highlights that the two step design procedure is to be preferred with respect to the plain glrt in fact the former leads to detectors that achieve satisfactory performance under several situations of practical interest and are simpler to implement than those designed resorting to the latter

cfar detection strategies for distributed targets under conic constraints in this paper we deal with the problem of adaptive detection of mismatched mainlobe targets and or sidelobe interfering signals that are distributed in range to this end we investigate the impact of modeling the actual useful signal as a vector belonging to a proper cone with axis the nominal steering vector as a means to improve the robustness of the decision rule in presence of mainlobe targets similarly in order to improve the rejection capabilities of the decision rule in presence of sidelobe interferers we study the effects of replacing the usual noise only hypothesis with a noise plus interferers hypothesis where interferers belong to the complement of a cone with axis the nominal steering vector at the design stage we resort to the two step glrt based design procedure to this end we assume that a set of training data is available namely data free of signal components but sharing the same gaussian distribution of the noise in the cells under test remarkably proposed detectors possess the cfar property under the noise only hypothesis the performance assessment conducted by monte carlo simulation is aimed at assessing the effectiveness of proposed solutions also in comparison to existing ones

the complex parameter rao test the rao test is an important method in signal detection in the presence of unknown parameters the traditional approach to the problem when the unknown parameters are complex valued is to form a corresponding real valued parameter vector and then to use the real rao test alternatively we present a complex parameter rao test by reformulating the calculations with respect to the complex valued quantities directly two important examples of the application of the complex parameter rao test are given to illustrate the procedure

the adaptive coherence estimator a uniformly most powerful invariant adaptive detection statistic we show that the adaptive coherence estimator ace is a uniformly most powerful ump invariant detection statistic this statistic is relevant to a scenario appearing in adaptive array processing in which there are auxiliary signal free training data vectors that can be used to form a sample covariance estimate for clutter and interference suppression the result is based on earlier work by bose and steinhardt who found a two dimensional 2 d maximal invariant when test and training data share the same noise covariance their 2 d maximal invariant is given by kelly s generalized likelihood ratio test glrt statistic and the adaptive matched filter amf we extend the maximal invariant framework to the problem for which the ace is a glrt the test data shares the same covariance structure as the training data but the relative power level is not constrained in this case the maximal invariant statistic collapses to a one dimensional 1 d scalar which is also the ace statistic furthermore we show that the probability density function for the ace possesses the property of total positivity which establishes that it has monotone likelihood ratio thus a threshold test on the ace is ump invariant this means that it has a claim to optimality having the largest detection probability out of the class of detectors that are also invariant to affine transformations on the data matrix that leave the hypotheses unchanged this requires an additional invariance not imposed by bose and steinhardt invariance to relative scaling of test and training data the ace is invariant and has a constant false alarm rate cfar with respect to such scaling whereas kelly s glrt and the amf are invariant and cfar only with respect to common scaling

performance of the adaptive sidelobe blanker detection algorithm in homogeneous environments the adaptive sidelobe blanker asb algorithm is a two stage detector consisting of a first stage adaptive matched filter amf detector followed by a second stage detector called the adaptive coherence or cosine estimator ace only those data test cells that survive both detection thresholdings are declared signal target bearing we provide exact novel closed form expressions for the resulting probability of detection pd and false alarm pfa for the asb algorithm and demonstrate that under homogeneous data conditions with no signal array response mismatch that i the asb is a constant false alarm rate cfar algorithm ii the asb has a higher or commensurate pd for a given pfa than both the amf and the ace and iii the asb has an overall performance that is commensurate with kelly s 1986 benchmark generalized likelihood ratio test glrt a compact statistical summary is derived providing distributions and dependencies among the glrt amf and the ace decision statistics

radar detection of distributed targets in homogeneous interference whose inverse covariance structure is defined via unitary invariant functions in this paper we deal with the problem of detecting an extended target embedded in homogeneous gaussian interference with unknown but structured covariance matrix we model the possible target echo from each range bin under test as a deterministic signal with an unknown scaling factor accounting for the target response at the design stage we exploit some a priori knowledge about the operating environment enforcing the inverse interference plus noise covariance matrix to belong to a set described via unitary invariant continuous functions hence we derive the constrained maximum likelihood ml estimates of the unknown parameters under both the h0 and h1 hypotheses and design the generalized likelihood ratio test glrt for the considered decision problem at the analysis stage we assess the performance of the devised glrt for some covariance matrix uncertainty sets of practical relevance both for spatial and doppler processing the results highlight that correct use of the a priori knowledge can lead to a detection performance quite close to the optimum receiver which supposes the perfect knowledge of the interference plus noise covariance matrix

false alarm rate of the glrt for subspace signals in subspace interference plus gaussian noise in the presence of interference and gaussian noise with unknown covariance matrix a generalized likelihood ratio test glrt detector has already been developed for detecting a distributed target the target signal and interference are described with subspace models namely the target signals or interference are modeled as linear combinations of the linearly independent columns of a known subspace matrix in this paper we obtain statistical properties of this glrt detector and prove its constant false alarm rate against the noise covariance matrix moreover we derive analytical expressions for the probability of false alarm of the glrt detector specifically exact expressions for the probability of false alarm are obtained for six cases where the target subspace dimension denoted by p is 1 2 and 3 and the number of range cells denoted by h the distributed target occupies is 1 2 and 3 for the general case where p geq 4 and h geq 4 we derive an approximate expression for the probability of false alarm monte carlo simulations show that the exact expressions are valid and the accuracy of the approximate expression is acceptable for moderate or large training data size in practice these expressions can greatly facilitate the threshold setting for the glrt detector for any preassigned probability of false alarm

adaptive detection with bounded steering vectors mismatch angle we address the problem of detecting a signal of interest soi using multiple observations in the primary data in a background of noise with unknown covariance matrix we consider a situation where the signal s signature is not known perfectly but its angle with a nominal and known signature is bounded furthermore we consider a possible scaling inhomogeneity between the primary and the secondary noise covariance matrix first assuming that the noise covariance matrix is known we derive the generalized likelihood ratio test glrt which involves solving a semidefinite programming problem next we substitute the unknown noise covariance matrix for its estimate obtained from secondary data to yield the final detector the latter is compared with a detector that assumes a known signal s signature

on the relationship between the glrt and umpi tests for the detection of signals with unknown parameters the generalized likelihood ratio test glrt is widely used in signal processing applications such as image processing wireless communications medical imaging classification and signal detection however the glrt does not have many known properties other than that it is invariant uniformly most powerful invariant umpi for problems that fit the linear model and asymptotically n spl rarr spl infin umpi in general since it is invariant it belongs to the class of tests for which the umpi test is optimal in this paper we consider a general class of detection problems in which unknown signal parameters imply a problem invariance that can be described analytically by orthogonal subgroups this invariance is natural for problems with unknown signal parameters and for example include those of the matched subspace detectors of scharf and friedlander we derive the glrt and umpi detectors for this general signal class for the case of gaussian noise an expression is found that relates the two test statistics showing the umpi statistic to be the sum of two terms one of which is the glrt using this we find that the glrt and umpi tests are asymptotically equivalent as signal to noise ratio snr approaches infinity or as probability of false alarm approaches zero these results are illustrated by extending an example given by nicolls and de jager to show the analytic relationship between the glrt and umpi tests the results indicate that the performance between the tests becomes close at signal to noise ratios snrs associated with operating points of the receiver operating curve that are typically of interest in signal detection applications

harnack inequality for non divergence form operators on stratified groups we prove lower bounds for the fundamental solutions of the non divergence form operators j i j x t x i x j t and i j i j x x i x j where the x i s are hormander vector fields generating a stratified group g and a i j i j is a positive definite matrix with holder continuous entries we then prove an invariant harnack inequality for such operators as a byproduct we also study some relevant properties of the green functions on bounded domains

adaptive detection of range distributed targets a modified generalized likelihood ratio test mglrt for the adaptive detection of a target or targets that are distributed in range is derived the unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference which is assumed to be characterized as complex zero mean correlated gaussian random variables the target s or targets complex amplitudes are assumed to be distributed across the entire input data block sensor spl times range results on probabilities of false alarm and detection are derived and a bounded constant false alarm rate cfar detector is developed simulation results are presented it is shown that the derived mglrt of range distributed targets is much more effective in detecting targets distributed in range than an m out of k detector which is cascaded with a single point target kelly 1986 detector

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

performance of a class of adaptive detection algorithms in nonhomogeneous environments a two dimensional 2 d adaptive sidelobe blanker asb detection algorithm was developed through experimentation as an extenuate for false alarms caused by undernulled interference encountered when applying the adaptive matched filter amf in nonhomogeneous environments the algorithm s utility has been demonstrated empirically considering theoretic performance analyses of the asb detection algorithm as well as the amf generalized likelihood ratio test glrt and the adaptive cosine estimator ace under nonideal conditions can become fairly intractable rather quickly especially in an adaptive processing context involving covariance estimation in this paper however we have developed and exploited a theoretic framework through which the performance of these algorithms under nonhomogeneous conditions can be examined theoretically it is demonstrated through theoretic analysis that in the presence of undernulled interference the asb is a pliable false alarm regulatory far detector that maintains good target sensitivity a viable method of asb threshold selection is also presented and demonstrated

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

adaptive detection of a signal known only to lie on a line in a known subspace when primary and secondary data are partially homogeneous this paper deals with the problem of detecting a signal known only to lie on a line in a subspace in the presence of unknown noise using multiple snapshots in the primary data to account for uncertainties about a signal s signature we assume that the steering vector belongs to a known linear subspace furthermore we consider the partially homogeneous case for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels this provides an extension to the framework considered by bose and steinhardt the natural invariances of the detection problem are studied which leads to the derivation of the maximal invariant then a detector is proposed that proceeds in two steps first assuming that the noise covariance matrix is known the generalized likelihood ratio test glrt is formulated then the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector the latter is compared with a similar detector that assumes the steering vector to be known

wiener s criterion for parabolic equations with variable coefficients and its consequences dans un ensemble borne de r n 1 on etudie la regularite des points limites pour le probleme de dirichlet pour un operateur parabolique a coefficients lisses on donne une caracterisation geometrique de ces points limites qui sont reguliers

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

topology of lattice gauge fields non abelian gauge fields on a four dimensional hypercubic lattice with small action density tr u dot p for su 2 gauge fields are shown to carry an integer topological chargeq which is invariant under continuous deformations of the field a concrete expression forq is given and it is verified thatq reduces to the familiar chern number in the classical continuum limit

generalized elliptic integrals and the legendre m function abstract we study monotonicity and convexity properties of functions arising in the theory of elliptic integrals and in particular in the case of a schwarz christoffel conformal mapping from a half plane to a trapezoid we obtain sharp monotonicity and convexity results for combinations of these functions as well as functional inequalities and a linearization property

nonlinear parabolic capacity and polar sets of superparabolic functions we extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the p laplacian type we study definitions and properties of the nonlinear parabolic capacity and show that the capacity of a compact set can be represented via a capacitary potential as an application we show that polar sets of superparabolic functions are of zero capacity the main technical tools used include estimates for equations with measure data and obstacle problems

modified rao test for multichannel adaptive signal detection the problem of detecting a subspace signal is studied in colored gaussian noise with an unknown covariance matrix in the subspace model the target signal belongs to a known subspace but with unknown coordinates we first present a new derivation of the rao test based on the subspace model and then propose a modified rao test mrt by introducing a tunable parameter the mrt is more general which includes the rao test and the generalized likelihood ratio test as special cases moreover closed form expressions for the probabilities of false alarm and detection of the mrt are derived which show that the mrt bears a constant false alarm rate property against the noise covariance matrix numerical results demonstrate that the mrt can offer the flexibility of being adjustable in the mismatched case where the target signal deviates from the presumed signal subspace in particular the mrt provides better mismatch rejection capacities as the tunable parameter increases

adaptive double subspace signal detection in gaussian background part i homogeneous environments in this two part paper we consider the problem of adaptive multidimensional multichannel signal detection in gaussian noise with unknown covariance matrix the test data primary data is assumed as a collection of sample vectors arranged as the columns of a rectangular data array the rows and columns of the signal matrix are both assumed to lie in known subspaces but with unknown coordinates due to this feature of the signal structure we name this kind of signal as the double subspace signal part i of this paper focuses on the adaptive detection in homogeneous environments while part ii deals with the adaptive detection in partially homogeneous environments precisely in this part we derive the generalized likelihood ratio test glrt rao test wald test as well as their two step variations in homogeneous environments three types of spectral norm tests snts are also introduced all these detectors are shown to possess the constant false alarm rate cfar property moreover we discuss the differences between them and show how they work another contribution is that we investigate various special cases of these detectors remarkably some of them are well known existing detectors while some others are still new at the stage of performance evaluation conducted by monte carlo simulations both matched and mismatched signals are dealt with for each case more than one scenario is considered

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

a cfar adaptive subspace detector for first order or second order gaussian signals based on a single observation in this paper we consider the problem of detecting a signal in gaussian noise with unknown covariance matrix in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor one solution to this problem is the adaptive subspace detector asd with a single or multiple observations however the probabilities of false alarm and detection of this asd have not been obtained yet in this paper these expressions are derived on the basis of a single observation which are confirmed with monte carlo simulations it is shown that the asd has a constant false alarm rate property with respect to both the shared noise covariance matrix structure and the independent scaling of the noise in the test data in addition we prove that for the first order model where the signal of interest is assumed to be a deterministic but unknown vector the asd derived with the generalized likelihood ratio test is consistent with that derived with an ad hoc two step design procedure

a maximal invariant framework for adaptive detection with structured and unstructured covariance matrices we introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing this involves calculating a low dimensional basis set of functions called the maximal invariant the statistics of which are often tractable to obtain thereby making analysis feasible and facilitating the search for tests with some optimality property using this approach we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published kelly s generalized likelihood ratio glrt and robey s adaptive matched filter amf test statistics applying this framework to structured covariance matrices corresponding to stochastic interferers in a known subspace for which the glrt is unavailable we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad hoc detectors these invariant tests are unaffected by most nuisance parameters hence the variation in the level of performance is sharply reduced this framework facilitates the search for such tests even when the usual glrt is unavailable

temporal synchronization of mimo wireless communication in the presence of interference in wireless communications systems that potentially operate in interference acquisition and temporal alignment of a transmitted signal by a receiver can be the most fragile component of the link in this paper synchronization detection in the presence of interference for multiple input multiple output mimo communication is discussed here synchronization indicates signal acquisition and timing estimation at the receiver and is formulated as a binary statistical hypothesis test transmit sequences from multiple antennas are received by multiple antennas in noisy environments with spatially correlated noise interference flat fading and frequency selective channel models for both the interference and signal of interest are considered by applying well known multiple antenna approaches to the mimo synchronization problem a number of new synchronization test statistics are introduced these test statistics are motivated by minimum mean square error mmse beamformers generalized likelihood ratio test glrt least squared ls channel estimation and spatial invariance test statistics appropriate for orthogonal frequency division multiplexing ofdm systems are considered including test statistics that take advantage of cyclic prefixes and of pilot sequences within an ofdm symbol performances of various test statistics in terms of probability of missing detection for some probability of a false detection are shown to vary by multiple orders of magnitude in the presence of interference

generalized cfar property and ump invariance for adaptive signal detection in this paper we consider adaptive detection of a signal embedded in additive disturbance whose multivariate distribution belongs to a very general class including many statistical models commonly adopted for radar disturbance we introduce the concept of generalized constant false alarm rate cfar and show that a class of receivers sharing some invariances complies with the quoted property then we devise the generalized likelihood ratio test glrt and prove that under some mild technical conditions it coincides with that obtained under the gaussian assumption for the observations we also deal with the existence of the uniformly most powerful invariant umpi detector either using the wijsman theorem or directly computing the maximal invariant likelihood ratio lr at the analysis stage we focus on a compound matrix variate model for the disturbance component which is a natural generalization of the spherically invariant random vector sirv in this context we assess the performance of some well known invariant decision rules also in comparison with the most powerful invariant mpi detector the results highlight that some among the analyzed receivers exhibit a performance level very close to the mpi test

theoretical performance analysis of the w abort detector in a recent paper we introduced a modification of the adaptive beaniformer orthogonal rejection test abort for adaptive detection of signals in unknown noise by supposing under the null hypothesis the presence of signals orthogonal to the nominal steering vector in the whitened observation space we will refer to this new receiver as the whitened adaptive beamformer orthogonal rejection test w abort through monte carlo simulations this new detector was shown to provide better rejection capabilities of mismatched e g sidelobe signals than existing ones like abort or the adaptive coherence estimator ace but at the price of a certain loss in terms of detection of matched i e mainlobe signals the aim of this paper is to provide a theoretical validation of this fact we consider both the case of distributed targets and point like targets we provide a statistical characterization of the w abort test statistic under the null hypothesis and for matched and mismatched signals under the alternative hypothesis for distributed targets the probability of false alarm and the probability of detection can only be expressed in terms of multi dimensional integrals and are thus very complicated to obtain in contrast for point like targets such probabilities can be easily calculated by numerical integration techniques the theoretical expressions derived herein corroborate the simulation results obtained previously

adaptive radar detection of a subspace signal embedded in subspace structured plus gaussian interference via invariance this paper deals with adaptive radar detection of a subspace signal competing with two sources of interference the former is gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise the latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna the problem is solved via the principle of invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant a maximal invariant statistic which completely characterizes the class of invariant decision rules and significantly compresses the original data domain as well as its statistical characterization are determined thus the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules at the analysis stage the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions

cfar matched direction detector in a previously published paper by besson et al we considered the problem of detecting a signal whose associated spatial signature is known to lie in a given linear subspace in the presence of subspace interference and broadband noise of known level we extend these results to the case of unknown noise level more precisely we derive the generalized likelihood ratio test glrt for this problem which provides a constant false alarm rate cfar detector it is shown that the glrt involves the largest eigenvalue and the trace of complex wishart matrices the distribution of the glrt is derived under the null hypothesis numerical simulations illustrate its performance and provide a comparison with the glrt when the noise level is known

cfar detection of multidimensional signals an invariant approach the paper deals with constant false alarm rate cfar detection of multidimensional signals embedded in gaussian noise with unknown covariance we attack the problem by resorting to the principle of invariance which proves a valuable statistical tool for ensuring a priori namely at the design stage the cfar property in this context we determine a maximal invariant statistic with respect to a proper group of transformations that leave unaltered the hypothesis testing problem under study devise the optimum invariant detector and show that no uniformly most powerful invariant umpi test exists thus we establish the conditions an invariant detector must fulfill in order to ensure the cfar property finally we discuss several suboptimal implementable invariant receivers and remarkably show that the generalized likelihood ratio test glrt detector is a member of this class the performance analysis which has been carried out in the presence of a gaussian signal array shows that the proposed detectors exhibit a quite acceptable loss with respect to the optimum neyman pearson detector

second order complex random vectors and normal distributions complex random vectors are usually described by their covariance matrix this is insufficient for a complete description of second order statistics and another matrix called the relation matrix is necessary some of its properties are analyzed and used to express the probability density function of normal complex vectors various consequences are presented

asymptotically optimal cfar detectors this paper investigates the asymptotic optimality of the constant false alarm rate cfar tests obtained using the minimal invariant group mig reduction we show that the cfar tests obtained after mig reduction using the wald test is a separating function estimation test sfet and that the generalized likelihood ratio test glrt and the rao test are asymptotically sfet using maximum likelihood estimation mle under some mild conditions thus they are asymptotically optimal in order to find an improved test and motivated by the invariance property of the mle of induced maximal invariant we maximize the asymptotic probability of detection of the sfet using the mle after reduction we propose a systematic method allowing to derive the asymptotically optimal separating function aosf this aosf is obtained as the euclidean distance of the transformed parameters under two hypotheses such that the gradient of the transformed parameters is the cholesky decomposition of the fisher information matrix fim i e the fim is transformed into an identity matrix interestingly the aosf estimation test aosfet using mle simplifies to the wald cfar wherever the fim does not depend on the unknown parameters the simulation results show that the proposed aosfet usually outperforms the glrt wald test and rao test

an invariant approach to adaptive radar detection under covariance persymmetry in this paper we propose a systematic and unifying framework to deal with adaptive radar detection in the presence of gaussian interference sharing a persymmetric covariance structure first we determine the group of transformations which leaves the considered hypothesis testing problem unaltered then after reduction by sufficiency we determine a maximal invariant statistic which is a four dimensional vector and significantly compresses the original observation space its first two components are the one step and the two step generalized likelihood ratio test decision statistics respectively whereas its last two entries represent an ancillary statistic we provide also the exact statistical characterization of the maximal invariant which is exploited to synthesize both the optimum and the locally optimum in the low signal to interference plus noise ratio regime invariant receivers finally some sub optimum decision rules based on theoretically solid design criteria are discussed and their performances are analyzed in comparison with the benchmark invariant test