Low-Complexity Uncertainty-Set-Based Robust Adaptive Beamforming for Passive Sonar

Abstract

Recent work has highlighted the potential benefits of exploiting ellipsoidal uncertainty set based robust Capon beamformer (RCB) techniques in passive sonar. Regrettably, the computational complexity of forming RCB weights is cubic in the number of adaptive degrees of freedom, which is often prohibitive in practice. For this reason, several low-complexity techniques for computing RCB weights, or equivalent worst-case robust adaptive beamformer (WC-RAB) weights, have recently been developed, whose complexities are only quadratic in the number of adaptive degrees of freedom. In this work, we review several such techniques for passive sonar, evaluating them initially on simulated data. The best performing methods are then evaluated on in-water recorded passive sonar data. Index TermsEfficient robust adaptive beamforming, robust Capon beamforming, worst-case robust adaptive beamforming, robust adaptive beamforming, underwater acoustics. I. INTRODUCTIONIn this work, we are interested in examining techniques for efficiently computing ellipsoidal uncertainty set based robust Capon beamformer (RCB) weights, or equivalent worst-case robust adaptive beamformer (WC-RAB) weights, for the purposes of implementing recent RCB-based passive sonar beamformers with low computational complexity.As is well known, an adaptive beamformer can outperform a conventional delay-and-sum beamformer providing that it a) is robust to array steering vector errors, b) can converge sufficiently on the, often limited, data available, and c) is low enough complexity to be implementable on the, typically limited, computational resources that are available [1], [2]. The model of the signal-of-interest spatial signature, or array steering vector, that is used by a beamformer is usually derived under plane-wave assumptions, as a set of complex phase delays, and is subject to several sources of error. These include calibration errors, due to sensor gain/phase errors, mutual coupling effects and sensor position errors, pointing errors, caused by differences in the assumed angle-of-arrival and the true one, and deviations from plane wave assumptions, e.g., caused by inhomogeneity in the ocean and/or multipath propagation. If not properly dealt with, these errors lead to cancellation of the desired signal and a consequent loss of array output signal to noise ratio [3] [14]. The main practical drawback with many robust adaptive algorithms is that the user is a required to select a parameter that is not directly related to the steering vector uncertainty, making the parameter choice difficult and often ad hoc. For instance, it is unclear how to choose a white noise gain constraint, which is a constraint on the norm of the weights, based on the array steering vector uncertainty [15]. The main benefit of the

Robust Capon Beamforming against Steering Vector Error Dominated by Large Direction-of-Arrival Mismatch for Passive Sonar

“…Therefore, the strong targets are considered as interferences for the weak targets. Capon beamforming [1,2], as an important pre-processing technique in array signal processing, is often applied in passive sonar arrays for improving the detectability of weak underwater targets [3][4][5]. By extracting the signal of weak targets and suppressing the strong interferences and noise at the beamformer output simultaneously, Capon beamformer can obtain the optimal output signal-to-interference-plus-noise ratio (SINR) and prevent the weak sources from submerging in strong interferences.…”

Air Ultrasonic Signal Localization with a Beamforming Microphone Array

“…While beamforming with passive acoustic arrays is often used in sonar [9] and seismology [10], there are fewer applications in ultrasonic nondestructive testing. It was shown that beamforming techniques can be used to improve the performance of sensor arrays for acoustic emission monitoring of large concrete structures [11].…”

A Decision Support System to Ease Operator Overload in Multibeam Passive Sonar

“…However, some of these beamforming techniques suffer from reliability issues [1]. More recently, adaptive beamforming techniques have been shown to improve the output signal-to-noise ratio (SNR) of passive sonar arrays (see, for example, [2] and the references therein). Extensions of adaptive beamforming beyond the standard linear array structure have been implemented in [3].…”

“…Extensions of adaptive beamforming beyond the standard linear array structure have been implemented in [3]. Issues of the complexity cost of implementing robust adaptive beamformers can be reduced from cubic to quadratic in the number of parameters, as discussed in [2], and have been made manageable in [4] through implementation using graphical processing units.…”