Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random steering vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

Fringe Visibility Estimators for the Palomar Testbed Interferometer

Visibility estimators and their performance are presented for use with the Palomar Testbed Interferometer (PTI). One operational mode of PTI is single-baseline visibility measurement using pathlength modulation with synchronous readout by a NICMOS-3 infrared array. Visibility is estimated from the fringe quadratures, either incoherently, or using source phase referencing to provide a longer coherent integration time. The visibility estimators differ those used with photon-counting detectors in order to account for biases attributable to detector offsets and read noise. The performance of these estimators is affected not only by photon noise, but also by the detector read noise and errors in estimating the bias corrections, which affect the incoherent and coherent estimators differently. Corrections for visibility loss in the coherent estimators using the measured tracking jitter are also presented.Comment: PASP in press (Jan 99). 13 Pages, no figure

A Low-Cost Robust Distributed Linearly Constrained Beamformer for Wireless Acoustic Sensor Networks with Arbitrary Topology

We propose a new robust distributed linearly constrained beamformer which utilizes a set of linear equality constraints to reduce the cross power spectral density matrix to a block-diagonal form. The proposed beamformer has a convenient objective function for use in arbitrary distributed network topologies while having identical performance to a centralized implementation. Moreover, the new optimization problem is robust to relative acoustic transfer function (RATF) estimation errors and to target activity detection (TAD) errors. Two variants of the proposed beamformer are presented and evaluated in the context of multi-microphone speech enhancement in a wireless acoustic sensor network, and are compared with other state-of-the-art distributed beamformers in terms of communication costs and robustness to RATF estimation errors and TAD errors

Steering vector errors and diagonal loading

Diagonal loading is one of the most widely used and effective methods to improve robustness of adaptive beamformers. In this paper, we consider its application to the case of steering vector errors, i.e. when there exists a mismatch between the actual steering vector of interest and the presumed one. More precisely, we address the problem of optimally selecting the loading level with a view to maximise the signal to interference plus noise ratio in the presence of random steering vector errors. First, we derive an expression for the optimal loading for a given steering vector error and we show that this loading is negative. Next, this optimal loading is averaged with respect to the probability density function of the steering vector errors, yielding a very simple expression for the average optimal loading. Numerical simulations attest to the validity of the analysis and show that diagonal loading with the optimal loading factor derived herein provides a performance close to optimum

Advances in Calibration and Imaging Techniques in Radio Interferometry

This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from clarification of the fundamentals, use of standard numerical optimization techniques, and generalization or specialization to new algorithms

Simulation-based high-level synthesis of Nyquist-rate data converters using MATLAB/SIMULINK

This paper presents a toolbox for the simulation, optimization and high-level synthesis of Nyquist-rate Analog-to-Digital (A/D) and Digital-to-Analog (D/A) Converters in MATLAB®. The embedded simulator uses SIMULINK® C-coded S-functions to model all required subcircuits including their main error mechanisms. This approach allows to drastically speed up the simulation CPU-time up to 2 orders of magnitude as compared with previous approaches - based on the use of SIMULINK® elementary blocks. Moreover, S-functions are more suitable for implementing a more detailed description of the circuit. For all subcircuits, the accuracy of the behavioral models has been verified by electrical simulation using HSPICE. For synthesis purposes, the simulator is used for performance evaluation and combined with an hybrid optimizer for design parameter selection. The optimizer combines adaptive statistical optimization algorithm inspired in simulated annealing with a design-oriented formulation of the cost function. It has been integrated in the MATLAB/SIMULINK® platform by using the MATLAB® engine library, so that the optimization core runs in background while MATLAB® acts as a computation engine. The implementation on the MATLAB® platform brings numerous advantages in terms of signal processing, high flexibility for tool expansion and simulation with other electronic subsystems. Additionally, the presented toolbox comprises a friendly graphical user interface to allow the designer to browse through all steps of the simulation, synthesis and post-processing of results. In order to illustrate the capabilities of the toolbox, a 0.13)im CMOS 12bit@80MS/s analog front-end for broadband power line communications, made up of a pipeline ADC and a current steering DAC, is synthesized and high-level sized. Different experiments show the effectiveness of the proposed methodology.Ministerio de Ciencia y Tecnología TIC2003-02355RAICONI

Goldstone solar system radar signal processing

A performance analysis of the planetary radar data acquisition system is presented. These results extend previous computer simulation analysis and are facilitated by the development of a simple analytical model that predicts radar system performance over a wide range of operational parameters. The results of this study are useful to both the radar system designer and the science investigator in establishing operational radar data acquisition parameters which result in the best systems performance for a given set of input conditions

Concepts for on-board satellite image registration. Volume 2: IAS prototype performance evaluation standard definition

Problems encountered in testing onboard signal processing hardware designed to achieve radiometric and geometric correction of satellite imaging data are considered. These include obtaining representative image and ancillary data for simulation and the transfer and storage of a large quantity of image data at very high speed. The high resolution, high speed preprocessing of LANDSAT-D imagery is considered