Ivars P. Kirsteins

Data Dimension Reduction Using Krylov Subspaces: Making Adaptive Beamformers Robust to Model Order-Determination

In this work, we present a class of low-complexity reduced-dimension adaptive beamformers constructed from expanding Krylov subspaces. We demonstrate how the data dimensionality reduction obtained from Krylov pre-processing decreases the sensitivity of reduced-rank adaptive beamforming techniques to incorrect model-order selection and lessens the computational complexity of systems involving large arrays with many elements. An important advantage of the proposed dimensionality reduction scheme is that it relieves reduced-rank methods from the stringent requirement on the precise model order determination

Performance analysis of Krylov space adaptive beamformers

The performance of Krylov subspace-based dimensionality reduction for adaptive beamforming is analyzed using a simple second-order Taylor series approximation to the mean output signal-to-noise ratio (SNR). It is shown that the predicted SNRs accurately follow the experimentally measured SNR and explain the threshold effects when the angles or spacing are varied between the signal mode (subspace) and interference modes (subspace). Furthermore, we discuss how the SNR approximation can be applied to calculating the deflection of a Krylov subspace dimension-reduced Capons test statistic.

Signal detection in strong low rank compound-Gaussian interference

This paper presents the performance of the principal components inverse (PCI) method in compound-Gaussian interference. The impact of increased subspace perturbation on PCI performance and the issue of increased training data support are addressed.

Does canonical correlation analysis provide reliable information on data correlation in array processing

This work provides analytical results on the canonical correlation analysis (CCA) of data sets from two spatially separated arrays of sensors. Our case studies cover both single source and multiple source signals in either white or colored noise fields for array signal processing. We derive analytical expressions of the canonical correlation for these examples and present a computer simulation analysis of empirical canonical correlations as a function of nominal correlation, signal-to-noise ratio (SNR), and sample support. Results obtained reveal an interesting fact that the canonical coefficients from CCA provide reliable information on the spatial correlation existing among data sets from two arrays only when the SNRs at both arrays are reasonably high. When sample correlation matrices (SCM) are used in the empirical CCA, reliable correlation can be estimated from CCA asymptotically (either at high SNRs from both arrays, or with a large number of snapshots in comparison with array dimensionality).

Blind separation of signal and multipath interference for synthetic aperture sonar

Multipath interference is a major source of noise for synthetic aperture sonar systems operating in shallow water. Motivated by this problem, we present an iterative algorithm for blindly separating the signal from the multipath interference that uses differences in the temporal coherence properties of the signal and multipaths caused by sea surface roughness to estimate the optimum filter weights. The filter weights are estimated by minimizing the circular variance of the phase differences between overlapping vertical phase centers. An important advantage of this approach is that signal-free training data and accurate array calibration information are not needed. Experimentally we show that the blind separation performance is competitive with high resolution angle of arrival estimation and compares favorably to the Cramer-Rao lower bound predicted error.

Existence and estimation of impropriety in real rhythmic signals

Impropriety in complex signal processing has been studied and used primarily in a communications context, but also in some cases where complex signals are generated by adding real signals in quadrature. We discuss the meaning of impropriety, and the associated use of complementary statistics, when a real-valued random process is improper in the frequency domain. Through the use of modulation signal models, spectral impropriety can be connected explicitly to the frequency and phase of components belonging to a periodic, or more generally rhythmic, modulator waveform. We give theoretical signal models and provide an example of complementary analysis on underwater propeller noise from a merchant ship.

Multi-rank processing for passive ranging in underwater acoustic environments subject to spatial coherence loss

In this work we derive the maximum likelihood estimator for passive wavefront curvature ranging systems operating in environments subject to a spatial coherence loss. As a consequence of the spatial coherence loss, the optimum processor is no longer a rank-1 matched filter and now instead involves a multi-rank weighted combination of the data based on the coherence matrix eigenvectors and eigenvalues. We also establish an interesting connection of our proposed multi-rank processor to the conventional rank-1 processor, and to the non-coherence sub-array processor, under different operating conditions. A comparative study is carried out in evaluating the performance of the proposed processors.

Multiband analysis for colored amplitude-modulated ship noise

Propeller radiated cavitation noise is broadband yet audibly rhythmic, taking on the characteristics of amplitude-modulated noise. The study of this process is important because the shaft and blade rates, as well as other identifying features of the ship, can be inferred from the cavitation signal envelope. Unlike the conventional method for estimating the modulation frequency, this paper proposes a multirate subband method applicable to colored signals, and shows the conditions under which it is optimal in the sense of maximum likelihood. Application to actual ship noise data confirms the utility of the new method, yet also reveals previously unobserved signal dynamics, namely acoustic frequency-dependent phase shifts and amplitude variation in the modulation spectrum.

Blind separation of interference for synthetic aperture sonar and the lessons learned from real data

Multipath interference is a major source of interference for synthetic aperture sonar systems operating in shallow water at long ranges. In this paper we describe an iterative algorithm for blindly separating the signal from the multipath interference that uses differences in the temporal coherence properties of the signal and multipaths caused by sea surface roughness, the difficulties encountered in applying the algorithm to actual sea data, and the solutions and lessons learned.

Suppressing reverberation by multipath separation for improved buried object detection

This paper addresses the problem of using a vertical aperture to suppress the interference caused to SAS by surface bounce path reverberation components decorrelated by the rough sea surface. Using at-sea gathered SACLANTCEN vertical array acoustic data, we characterize the reverberation vertical properties and investigate the separation of the direct and surface bounce path reverberation and target echo components. We propose two implementations of the PCI method of interference cancellation and demonstrate with actual data that they are effective in separating the reverberation in the vertical domain.