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Intrinsic Cramer-Rao bounds and subspace estimation accuracy

Intrinsic Cramer-Rao bounds and subspace estimation accuracy

引用

sensor array and multichannel signal processing workshop

作者： S.T. Smith Lincoln Laboratory Massachusetts Institute of Technology USA

signal processing estimation problems are traditionally posed for a set of given, if unknown, parameters, such as angle and/or Doppler. Nevertheless, there are estimation problems on manifolds where no set of intrinsic coordinates exist. One example encountered frequently is the problem of estimating a particular subspace. The set of subspaces, called the Grassmann manifold, has no fixed coordinate system associated with it. This paper addresses the problem of applying classical Cramer-Rao analysis to determine tire fundamental bounds of estimation accuracy on arbitrary manifolds. Coordinate-free versions of the Cramer-Rao bound are derived to accomplish this. These bounds are then applied to the specific problem of estimating the subspace given an independent collection of data snapshots. The root-mean-square-error of the standard method of estimating subspaces using singular valve decomposition is compared to the intrinsic Cramer-Rao bound by varying both the SNR of the unknown subspace and the sample support. It will be seen that this SVD-based method yields accuracies very close to Cramer-Rao bound, establishing that the principal invariant subspace provides an excellent estimator of an unknown subspace, a conclusion that would not in general be possible without coordinate-free Cramer-Rao bounds.

关键词： Covariance matrix Symmetric matrices Laboratories signal processing Yield estimation Interference Military computing Singular value decomposition Contracts Equations

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Approximate maximum likelihood DOA estimation in multiplicative noise environments

Approximate maximum likelihood DOA estimation in multiplicat...

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sensor array and multichannel signal processing workshop

作者： O. Besson F. Vincent P. Stoica A.B. Gershman Department of Avionics and Systems ENSICA Toulouse France Department of Electrical and Computer Engineering McMaster University Hamilton Canada

We consider the problem of localizing a source by means of a uniform linear array of sensors when the received signal is corrupted by multiplicative noise. Since the exact maximum likelihood (ML) estimator is computationally intensive, two approximate solutions are proposed, originating from the analysis of the high and low signal to noise ratio (SNR) cases, respectively. First, starting with the no additive noise case, a very simple approximate ML (AML/sub 1/) estimator is derived. A theoretical expression for its asymptotic variance in the presence of additive noise is derived. It shows that the AML/sub 1/ estimator has a performance close to the Cramer-Rao bound (CRB) for moderate to high SNR. Next, the low SNR case is considered and the corresponding AML2 solution is derived. It is shown that the approximate ML criterion can be concentrated with respect to (w.r.t.) both the multiplicative and additive noise powers, leaving out a 2-D minimization problem instead of a 4-D problem required by the exact ML. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis.

关键词： Maximum likelihood estimation Direction of arrival estimation Working environment noise sensor arrays signal to noise ratio Scattering Integrated circuit noise Integrated circuit modeling Additive noise Parameter estimation

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Subband STAP processing, the fifth generation

Subband STAP processing, the fifth generation

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sensor array and multichannel signal processing workshop

作者： A.O. Steinhardt N.B. Pulsone DARPA Tactical Technology Office Arlington VA USA MIT Lincoln Laboratories Lexington MA USA

Adaptive array processing has moved through several stages of evolution. First there was spatial only adaptation, using gradient based algorithms. Second was true space-time adaptivity using time-taps on multiple channels. Third came more rapid convergence, using sample matrix inversion strategies. Fourth came dimensionally large system solutions, which focused on the need for reduced DOF such as beamspace, eigenspace, MUSIC, ESPRIT, BASS-ALE, etc. This paper argues that we are on the threshold of the fifth generation of STAP; mainly STAB in the subband domain. Subband STAP, is an elegant and computationally efficient solution to the need for increasing bandwidth in radar and sonar processing as well as mobile communications. We begin by motivating the need for wider bandwidths, from a SAR imaging perspective. Next, we show that the computational burden of wideband STAP is untenable for existing and emerging military requirements. Having motivated a compelling need we then propose subband STAP as a solution, motivated from an active sensor perspective. We describe subband STAP as an extension of the familiar STAP 3D datacube (range, angle, Doppler) to a 40 hypercube (subband range, angle, subband Doppler, subband frequency). Subbanding allows us to overcome challenging wideband effects such as Doppler-frequency coupling, high-resolution range migration, target self-nulling, channel decorrelation, and dispersion. We describe the challenges of subband STAP interference rejection and subband recombination with artifacts.

关键词： Military computing Bandwidth Wideband array signal processing Multiple signal classification Radar imaging Sonar Mobile communication Radar polarimetry Hypercubes

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Multi-rate adaptive beamforming (MRABF)

Multi-rate adaptive beamforming (MRABF)

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sensor array and multichannel signal processing workshop

作者： H. Cox ORINCON Corporation Arlington VA USA

An important trend in underwater acoustics is the use of large arrays with many elements and small resolution cells in an effort to detect weak signals. Frequently, the background noise is dominated by multiple moving surface ships that act like discrete interferers. These interferers may move through many spatial resolution cells in the time required to obtain sufficient "snapshots" for covariance matrix estimation. The non-stationarity of the background limits the performance of adaptive algorithms. Reduced degree-of-freedom approaches that can track and rapidly null interferers before they move too far are of great interest. The paper presents a new class of algorithms in which a low-rank, dynamically changing interference sub-space is estimated and tracked using a short-term average. An orthogonal projection is then applied to the data to null components in the interference sub-space. A second stage of adaptive beamforming that uses a longer averaging time is then applied to the projected data. Unlike most sub-space approaches that work for strong signals, there is no requirement that the signal be contained in the interference sub-space. It is shown how multiple interferers moving rapidly across beams can be tracked and nulled to reveal the presence of a weak target not visible with conventional, adaptive, or usual sub-space methods. The effectiveness of multi-rate adaptive beamforming is illustrated by examples. It is shown that moving interferers are effectively nulled to allow detection of weak signals when other methods including MVDR, conventional, and signal subspace fail.

关键词： array signal processing Interference Spatial resolution signal detection Underwater acoustics signal resolution Acoustic signal detection Underwater tracking Background noise Marine vehicles

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Beamforming, Doppler compensation, and differential space-time coding

Beamforming, Doppler compensation, and differential space-ti...

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sensor array and multichannel signal processing workshop

作者： M.A. Ingram Kuo-Hui Li A. van Nguyen T. Pratt School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA USA Information Technology and Telecommunication Laboratory Georgia Tech Research Institute Georgia Institute of Technology Atlanta GA USA

We consider the design of two beams, formed at the base station, that will serve as the two channels for differential space-time block coding in a high-mobility outdoor scenario. The mobile is assumed to have one omnidirectional antenna. In one approach, we consider selecting assuming no interference, the two most powerful beams produced by an RF beamformer. In the other approach, we make a compromise between power and Doppler spectrum partitioning. One channel is a beam that points directly at the mobile. The other beam is the difference of left and right beams, symmetric about the mobile. These left and right beams are Doppler compensated prior to forming their difference. Using computer simulation, we find that selecting beams based on power is more effective than selecting beams based on Doppler partitioning. We also find that using the two most powerful beams formed from eight antenna elements yields 7 dB and 8 dB SNR improvements, at 1.9 GHz and 5.8 GHz, respectively, relative to spatial diversity with two omnidirectional antennas.

关键词： array signal processing Diversity reception Block codes Downlink Space technology Base stations Mobile antennas Azimuth Chebyshev approximation Design engineering

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Joint channel estimation and detection for interference cancellation in multi-channel systems

Joint channel estimation and detection for interference canc...

引用

ieee workshop on Statistical signal and array processing

作者： C. Martin B. Ottersten Department of Signals Sensors & Systems Royal Institute of Technology Stockholm Sweden

Interference from other users and interference due to multipath propagation limit the capacity of wireless communication networks. As the number of users and the demand for new services in the networks increases, co-channel interference will be a limiting factor. This paper proposes an iterative structured multichannel receiver algorithm that jointly estimates the communication channels and desired data while canceling interference. A general way of adding training redundancy to a data frame is also introduced. From simulations the proposed method is shown to achieve low bit error rates also in the presence of strong interference. These simulations also show that by distributing the training information in a data burst elaborately further improvements in performance are achievable.

关键词： Channel estimation Interference cancellation Intersymbol interference Radio transmitters Intelligent networks Wireless sensor networks Iterative algorithms Antenna arrays Receiving antennas Transmitting antennas

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Design tradeoffs in a hardware implementation of the k-means clustering algorithm

Design tradeoffs in a hardware implementation of the k-means...

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sensor array and multichannel signal processing workshop

作者： M. Leeser J. Theiler M. Estlick J.J. Szymanski Department of Electrical and Computer Engineering Northeastern University Boston MA USA Space and Remote Sensing Sciences Group Los Alamos National Laboratory Los Alamos NM USA

Hyperspectral imagery provides exquisitely detailed information but poses a serious challenge to the image analyst. Massive quantities of data must be reduced in a way that identifies useful features. Pixel clustering algorithms provide one approach: each pixel is assigned to a class based on the spectral similarity of that pixel to other members of the class. An image where each pixel is represented by its class provides a single picture (not hundreds of channels) for the analyst to interpret. Opportunities for fine-grain parallelism in this computationally intensive calculation motivate the consideration of specialized hardware. We are developing an FPGA-based implementation of the k-means clustering algorithm, because FPGAs can provide considerable speedup yet are sufficiently flexible to permit the testing of variants and tradeoffs. Assigning pixels to classes requires a definition of spectral similarity. The standard choice is the Euclidean distance. We consider two alternative distances: the Manhattan (sum of the absolute coordinate differences) and the Max (maximum of the absolute differences). The Euclidean distance is optimal in the sense of minimizing within-class variance, but requires computing many squares. The Manhattan and Max distances eliminate this squaring, and furthermore reduce the number of bits needed to store intermediate calculations. We conducted two sets of experiments to assess the tradeoff between quality of clustering and efficiency of hardware implementation. The first considered an idealized setup for assessing mis-classification rates and their effect on within-class variance. The second evaluated within-class variance for real 224-channel AVIRIS data sets. Both experiments confirmed that the highest quality clusters are achieved using the Euclidean metric, and quantified the difference.

关键词： Hardware Euclidean distance Image analysis Clustering algorithms Hyperspectral sensors Hyperspectral imaging Information analysis Pixel Parallel processing Concurrent computing

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Experimental results on multichannel adaptive frame synchronisation for HF modems with co-channel interference

Experimental results on multichannel adaptive frame synchron...

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ieee workshop on signal processing Advances in Wireless Communications (SPAWC)

作者： Y.I. Abramovich C. Demeure A.Y. Gorokhov P. Chevalier Cooperative Research Centre for Sensor Signal and Infomation Processing Odessa State Polytechnic University Australia Thomson CSF France Département Signal Télécom Paris Odessa State Polytechnic University Paris France

A novel algorithm for recurrent adaptive spatial and temporal processing for HF modem synchronisation and multipath resolution has been developed and experimentally tested under a cooperative agreement between the Odessa State Polytechnic University (Ukraine) and Thomson-CSF Communication (France). HF modem signals have been transmitted from Coulommiers (France) and received by the 12-element uniform antenna array with digital multichannel receivers in Odessa (Ukraine). Co-channel interference situations with different signal-to-interference ratios have been employed to evaluate the efficiency of the proposed technique. Experimental results obtained are in agreement with theoretical expectations and demonstrate the practicality of reliable co-channel interference suppression.

关键词： Modems Jamming Interchannel interference signal processing Antenna arrays Spatial resolution signal resolution Testing

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Novel approach to rank determination of multichannel data covariance matrices

Novel approach to rank determination of multichannel data co...

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Proceedings of the 1996 8th ieee signal processing workshop on Statistical signal and array processing, SSAP'96

作者： Djuric, Petar M. State Univ of New York at Stony Brook Stony Brook United States

The rank selection problem of a multichannel data covariance matrix is addressed by the Bayesian methodology. A maximum a posteriori solution is derived, and a bootstrap technique for its implementation proposed. Our rule is tested on simulated sensor array data that represent random signals embedded in white Gaussian noise. The tests include comparisons with the popular AIC and MDL criteria. The results show that the Bayesian rule outperforms them, particularly for low signal-to-noise ratios and small direction-of-arrival separations.

关键词： signal processing

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A novel approach to rank determination of multichannel data covariance matrices

A novel approach to rank determination of multichannel data ...

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ieee workshop on Statistical signal and array processing

作者： P.M. Djuric Department of Electrical Engineering State University of New York Stony Brook Stony Brook NY USA

The rank selection problem of a multichannel data covariance matrix is addressed by Bayesian methodology. A maximum a posteriori solution is derived, and a bootstrap technique for its implementation proposed. Our rule is tested on simulated sensor array data that represent random signals embedded in white Gaussian noise. The tests include comparisons with the popular AIC and MDL criteria. The results show that the Bayesian rule outperforms them, particularly for low signal-to-noise ratios and small direction-of-arrival separations.

关键词： Covariance matrix sensor arrays Eigenvalues and eigenfunctions Testing Bayesian methods Gaussian noise array signal processing Parameter estimation signal to noise ratio signal processing

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