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41
Spatial Diversity in Radars  Models and Detection Performance
, 2004
"... Inspired by recent advances in multipleinput multipleoutput (MIMO) communications, this proposal introduces the statistical MIMO radar concept. To our knowledge, this is the first time that the statistical MIMO is being proposed for radar. The fundamental di#erence between statistical MIMO and oth ..."
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Cited by 49 (13 self)
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Inspired by recent advances in multipleinput multipleoutput (MIMO) communications, this proposal introduces the statistical MIMO radar concept. To our knowledge, this is the first time that the statistical MIMO is being proposed for radar. The fundamental di#erence between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance. Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated. Radar targets generally consist of many small elemental scatterers that are fused by the radar waveform and the processing at the receiver, to result in echoes with fluctuating amplitude and phase. It is well known that in conventional radar, slow fluctuations of the target radar cross section (RCS) result in target fades that degrade radar performance. By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance. In this paper, we focus on the application of the target spatial diversity to improve detection performance. The optimal detector in the NeymanPearson sense is developed and analyzed for the statistical MIMO radar. It is shown that the optimal detector consists of noncoherent processing of the receiver sensors' outputs and that for cases of practical interest, detection performance is superior to that obtained through coherent processing. An optimal detector invariant to the signa...
Estimating Evoked Dipole Responses in Unknown Spatially Correlated Noise with EEG/MEG Arrays
, 2000
"... We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current ..."
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Cited by 21 (4 self)
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We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current dipoles at fixed locations and the head as a spherical conductor. We permit the dipoles' moments to vary with time by modeling them as linear combinations of parametric or nonparametric basis functions. We estimate the dipoles' locations and moments and derive the CramrRao bound for the unknown parameters. We also propose an MLbased method for scanning the brain response data, which can be used to initialize the multidimensional search required to obtain the true dipole location estimates. Numerical simulations demonstrate the performance of the proposed methods. Index TermsCramrRao bound, dipole source, EEG, evoked responses, maximum likelihood parameter estimation, MEG, sensor arr...
CramérRao Bounds for Parametric Shape Estimation in Inverse Problems
 IEEE Trans. on Image Processing
, 2003
"... We address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems, when the boundaries are parameterized by a finite number of unknown variables. Our model applies to multiple unknown objects, each with its own unknown ..."
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Cited by 11 (3 self)
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We address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems, when the boundaries are parameterized by a finite number of unknown variables. Our model applies to multiple unknown objects, each with its own unknown gray level, or color, and boundary parameterization, on an arbitrary known background. While such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the CramerRao lower bounds, very few results have been reported due to the di#culty of computing the derivatives of a functional with respect to shape deformation. In this paper, we provide a general formula for computing CramerRao lower bounds in inverse problems where the observations are related to the object by a general linear transform, followed by a possibly nonlinear and noisy measurement system.
CramérRao Bounds for 2D Target Shape Estimation in Nonlinear Inverse Scattering Problems with Application to Passive Radar
 IEEE Trans. on Antennas and Propagat
, 2001
"... We present new methods for computing fundamental performance limits for twodimensional (2D) parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging. We evaluate CramrRao lower bounds (CRB) on shape estimation accuracy using the domain der ..."
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Cited by 11 (4 self)
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We present new methods for computing fundamental performance limits for twodimensional (2D) parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging. We evaluate CramrRao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for any unbiased estimator, and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator (MLE). The resultant CRBs are used to define an asymptotic global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target and facilitate geometric inferences. Numerical simulations are performed using the layer approach and the Nystrm method for computation of domain derivatives and using Fourier descriptors for target shape parameterization. This analysis demonstrates the accuracy and generality of the proposed methods. Index TermsCramrRao bounds, Fourier descriptors, global confidence regions, nonlinear inverse scattering, passive radar imaging, shape estimation. I.
SpaceTime AutoRegressive Filtering For Matched Subspace STAP
"... Practical STAP implementations rely on reduceddimension processing, using techniques such as principle components or partially adaptive filters. The dimension reduction not only decreases the computational load, it also reduces the sample support required for estimating the interference statisti ..."
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Cited by 9 (5 self)
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Practical STAP implementations rely on reduceddimension processing, using techniques such as principle components or partially adaptive filters. The dimension reduction not only decreases the computational load, it also reduces the sample support required for estimating the interference statistics. This results because the clutter covariance is implicitly assumed to possess a certain (nonparametric) structure. In this paper, we demonstrate how imposing a parametric structure on the clutter and jamming can lead to a further reduction in both computation and secondary sample support. Our approach, referred to as SpaceTime AutoRegressive (STAR) filtering, is applied in two steps: First, a structured subspace orthogonal to that in which the clutter and interference reside is found; Second, a detector matched to this subspace is used to determine whether or not a target is present. Using a realistic simulated data set for circular array STAP, we demonstrate that this approach achieves significantly lower SINR loss with a computational load that is less than that required by other popular approaches. The STAR algorithm also yields excellent performance with very small secondary sample support, a feature that is particularly attractive for applications involving nonstationary clutter.
ML Estimator and Hybrid Beamformer for Multipath and Interference Mitigation in GNSS Receivers
"... Abstract—This paper addresses the estimation of the codephase (pseudorange) and the carrierphase of the direct signal received from a directsequence spreadspectrum satellite transmitter. The signal is received by an antenna array in a scenario with interference and multipath propagation. These ..."
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Cited by 9 (5 self)
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Abstract—This paper addresses the estimation of the codephase (pseudorange) and the carrierphase of the direct signal received from a directsequence spreadspectrum satellite transmitter. The signal is received by an antenna array in a scenario with interference and multipath propagation. These two effects are generally the limiting error sources in most highprecision positioning applications. A new estimator of the code and carrierphases is derived by using a simplified signal model and the maximum likelihood (ML) principle. The simplified model consists essentially of gathering all signals, except for the direct one, in a component with unknown spatial correlation. The estimator exploits the knowledge of the directionofarrival of the direct signal and is much simpler than other estimators derived under more detailed signal models. Moreover, we present an iterative algorithm, that is adequate for a practical implementation and explores an interesting link between the ML estimator and a hybrid beamformer. The mean squared error and bias of the new estimator are computed for a number of scenarios and compared with those of other methods. The presented estimator and the hybrid beamforming outperform the existing techniques of comparable complexity and attains, in many situations, the Cramér–Rao lower bound of the problem at hand. Index Terms—Adaptive arrays, adaptive estimation, array signal processing, beamforming, beam steering, bias, calibration, Code division multiaccess, Cramér–Rao bounds, delay estima
Array signal processing in the known waveform and steering vector case
 in Proc. ICASSP
"... Abstract—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 ar ..."
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Cited by 8 (3 self)
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Abstract—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 closedform expressions for the expected values and meansquared 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 signaltonoise 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 modelmismatched ML (M3L) method, which ignores the temporal correlation of the interference and noise. Index Terms—Asymptotic analysis, capon, interference suppression, maximum likelihood, multichannel autoregressive random process, parameter estimation, quadrupole resonance. I.
STAP for GPS Receiver Synchronization
"... A spacetime adaptive processing (STAP) algorithm for delay tracking and acquisition of the GPS signature sequence with interference rejection capability is developed. The interference can consist of both broadband and narrowband jammers, and is mitigated in two steps. The narrowband jammers are mod ..."
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Cited by 4 (0 self)
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A spacetime adaptive processing (STAP) algorithm for delay tracking and acquisition of the GPS signature sequence with interference rejection capability is developed. The interference can consist of both broadband and narrowband jammers, and is mitigated in two steps. The narrowband jammers are modeled as vector autoregressive (VAR) processes and rejected by temporal whitening. The spatial nulling is implicitly achieved by estimating a sample covariance matrix and feeding its inverse into the extended Kalman filter (EKF). The EKF estimates of the code delay and the fading channel are used for a ttest for acquisition detection. Computer simulations demonstrate robust performance of the algorithm in severe jamming, and also show that the algorithm outperforms the conventional delaylocked loop (DLL). Manuscript received November 20, 2002; revised August 7, 2003; released for publication September 30, 2003.
Codetiming synchronization in DSCDMA systems using spacetime diversity
"... The synchronization of a desired user transmitting a known training sequence in a directedsequence (DS) asyncx;#D5T csyncx;#D5T multipleacqkx (CDMA) system is addressed. It is assumed that the reck;9B cck;9B of an arbitrary 11 antenna array and works in a nearfar,frequenc99IqID5TT9#9Dc slowly fa ..."
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Cited by 3 (1 self)
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The synchronization of a desired user transmitting a known training sequence in a directedsequence (DS) asyncx;#D5T csyncx;#D5T multipleacqkx (CDMA) system is addressed. It is assumed that the reck;9B cck;9B of an arbitrary 11 antenna array and works in a nearfar,frequenc99IqID5TT9#9Dc slowly fadingcdingDT The estimator that we propose is derived by applying the maximum likelihood (ML)princ#qx to a signal model inwhic thecDkkT#fD5T9 of all the 13 interfering cerfering (e.g.,multipleac5Tf interferenc5 externalinterferenc and noise) is modeled as a Gaussian term with an unknown and arbitraryspacaryD9 cacaryD9f matrix. The maincnDTxT#fD59 of this paper is the fac that 15 the estimator makese#csDf use of thestrucxk9 of the signals in both thespac and time domains.
CramérRao Bounds for Parametric Estimation of Target Boundaries in Nonlinear Inverse Scattering Problems
 IEEE Trans. on Antennas and Propagat
, 1999
"... We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate CramerRao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scatte ..."
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Cited by 3 (3 self)
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We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate CramerRao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for any unbiased estimator, and under fairly mild regularity conditions, is asymptotically achieved by the maximum likelihood estimator (MLE), hence serving as a predictor of the high signalto noise ratio performance of the MLE. Furthermore, the resultant CRB's are used to define a global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target, and facilitate geometric inferences. Numerical simula...