Samuel D. Somasundaram

Linearly Constrained Robust Capon Beamforming

In this paper, a novel linearly constrained robust Capon beamformer (LCRCB) framework is proposed. In the LCRCB, linear constraints can be used, e.g., for beampattern control and ellipsoidal array steering vector sets can be exploited, using robust Capon beamforming techniques, e.g., to allow for arbitrary array steering vector errors, such as those arising from calibration errors. The LCRCB is applicable to arbitrary array geometries and can be computed efficiently. For the limiting case that the ellipsoid is a point, we show that the LCRCB coincides with a linearly constrained minimum variance beamformer. To show the utility of the LCRCB, mainbeam and null-pattern control examples are included.

Wideband Robust Capon Beamforming for Passive Sonar

In passive sonar, narrowband adaptive beamforming techniques can be exploited to increase the signal-to-interference-plus-noise ratio (SINR), providing that array steering vector (ASV) errors and cross-spectral density matrix (CSDM) estimation errors can be controlled. When beamforming large aperture, many-element arrays in dynamic scenarios, the number of stationary snapshots available for CSDM estimation can be small compared to the number of array elements, leading to the problem of snapshot deficiency. Furthermore, common narrowband approaches become computationally prohibitive for large bandwidths. Here, we exploit the wideband nature of passive sonar signals to alleviate snapshot deficiency and reduce computational complexity. Narrowband robust Capon beamformers (RCBs), which exploit ellipsoidal ASV uncertainty sets to maintain high SINR, are extended to the wideband problem via the steered covariance matrix (STCM) method, yielding wideband RCBs (WBRCBs). To further reduce computational complexity and speed up algorithm convergence, subarray techniques are also incorporated, yielding wideband subarray RCBs (WBSARCBs). These algorithms, which are applicable to arbitrary array geometries, are evaluated using simulated and experimental passive sonar data.

Evaluation of Robust Capon Beamforming for Passive Sonar

Adaptive beamforming is often used in passive sonar, e.g., to improve the detectability of weak sources. The recently proposed robust Capon beamformer (RCB) exploits array steering vector uncertainty sets, eliminating the need for the ad hoc parameter choices often required when implementing robust adaptive beamforming algorithms. Here, we evaluate the performance of the RCB using experimental and simulated underwater acoustics data.

Robust and Automatic Data-Adaptive Beamforming for Multidimensional Arrays

The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, for example, by calibration and/or angle-of-arrival (AOA) errors, which would, otherwise, seriously degrade the performance of an adaptive beamformer. Here, we examine robust Capon beamforming of multidimensional arrays, where robustness to AOA errors is needed in both azimuth and elevation. It is shown that the commonly used spherical uncertainty sets are unable to control robustness in each of these directions independently. Here, we instead propose the use of flat ellipsoidal sets to control the AOA uncertainty. To also allow for other errors, such as calibration errors, we combine these flat ellipsoids with a higher dimension error ellipsoid. Computationally efficient automatic techniques for estimating the necessary uncertainty sets are derived, and the proposed methods are evaluated using both simulated data and experimental underwater acoustic measurements, clearly showing the benefits of the technique.

Data-adaptive reduced-dimension robust Capon beamforming

We present low complexity, quickly converging robust adaptive beamformers that combine robust Capon beamformer (RCB) methods and data-adaptive Krylov subspace dimensionality reduction techniques. We extend a recently proposed reduced-dimension RCB framework, which ensures proper combination of RCBs with any form of dimensionality reduction that can be expressed using a full-rank dimension reducing transform, providing new results useful for data-adaptive dimensionality reduction. We consider Krylov subspace methods computed with the Powers-of-R (PoR) and Conjugate Gradient (CG) techniques, illustrating how a fast CG-based algorithm can be formed by beneficially exploiting that the CG-algorithm yields a diagonal reduced-dimension covariance matrix. Our simulations show the benefits of the proposed approaches.

Robust fundamental frequency estimation in the presence of inharmonicities

We develop a general robust fundamental frequency estimator that allows for non-parametric inharmonicities in the observed signal. To this end, we incorporate the recently developed multi-dimensional covariance fitting approach by allowing the Fourier vector corresponding to each perturbed harmonic to lie within a small uncertainty hypersphere centered around its strictly harmonic counterpart. Within these hyperspheres, we find the best perturbed vectors fitting the covariance of the observed data. The proposed approach provides the estimate of the fundamental frequency in two steps, and, unlike other recentmethods, involves only a single 1-D search over a range of candidate fundamental frequencies. The proposed algorithm is numerically shown to outperform the current competitors under a variety of practical conditions, including various degrees of inharmonicity and different levels of noise.

A framework for reduced dimension robust Capon beamforming

Recent robust Capon beamformers (RCBs) systematically allow for array steering vector (ASV) errors by exploiting ASV uncertainty ellipsoids, which are typically characterized in element space (ES). Reduced dimension (RD) techniques are often used to reduce computational complexity and speed up algorithm convergence. Here, a general framework is proposed for combining RD and RCB techniques, producing RD-RCBs. The key to this framework is a complex propagation theorem, which propagates the ES ellipsoid through the dimension reducing transform, so that the appropriate ASV uncertainty information is exploited in the RD space.

Using robust Capon beamforming to minimise the impact of angle of arrival errors in 2-D arrays

When sampling only a coarse set of azimuth and elevation angles for a 2-D array, the resulting angle of arrival errors often lead to target nulling in adaptive beamformers. Methods currently used to alleviate these errors often prevent target nulling at the expense of source localisation. In this paper, we show how the robust Capon beamformer, exploiting a flat ellipsoidal uncertainty set of the array steering vector, can be used to prevent target nulling at far less cost to source localisation. Furthermore, we present a new, computationally efficient technique for estimating the ellipsoids associated with angle of arrival uncertainty.

Degradation of covariance reconstruction-based robust adaptive beamformers

We show that recent robust adaptive beamformers, based on reconstructing either the noise-plus-interference or the data covariance matrices, are sensitive to the noise-plus-interference structure and degrade in the typical case when interferer steering vector mismatch exists, often performing much worse than common diagonally loaded sample covariance matrix based approaches, even when signal-of-interest steering vector mismatch is absent.

Robust Capon beamforming with additional linear constraints

The robust Capon beamformer (RCB) allows for errors in the look direction array steering vector (ASV) by exploiting ASV uncertainty ellipsoids. Here, we allow for extra linear constraints, which can be used, e.g., to exploit additional prior knowledge, yielding the linearly constrained RCB (LCRCB). We show that the RCB and a modified version of the coherent RCB (CRCB), which we term MCRCB, are both special cases of the LCRCB.