Abstract
This paper develops and applies a numerical optimization procedure to compute broadband noise-adaptive weights for delay and sum beamforming that are conditioned to maximize the deflection coefficient at the output of a square law detector for a given set of underwater pressure measurements. The resulting optimal weights mitigate the effects of noise and interferers and maximize signal detection. Comparison of the optimal weights with minimum variance distortionless response weights show that the presented algorithm provides higher attenuation of interferers. We also use the noise-adaptive algorithm to find the optimal sparse array geometry for a given number of sensors and aperture. Comparison of the resulting optimal array with coprime, nested, and semi-coprime arrays shows that the proposed sparse array suppresses interferers more than the other sparse arrays.
Highlights
Delay-and-sum beamforming (DSB) is the oldest beamforming algorithm and it persists as a preferable and powerful approach today because of its simplicity and robustness—other approaches are very sensitive [1]
In this paper we applied the noise adaptive beamforming algorithm, noise-adaptive delay-and-sum beamforming (NADSB), to an underwater dataset obtained from a linear array and obtained the optimal shading for conventional beamforming (CBF)
Our results showed that the NADSB provides greater attenuation of interferers when there are sufficient number of snapshots
Summary
Delay-and-sum beamforming (DSB) is the oldest beamforming algorithm and it persists as a preferable and powerful approach today because of its simplicity and robustness—other approaches are very sensitive [1]. An additional category of beamformers, known as adaptive beamformers, calculate shading weights based on the characteristics of the observations. Wettergren et al developed noise-adaptive delay-and-sum beamforming (NADSB) that preserves the simplicity of classical DSB but adapts its parameters to observations without having to invert an SCM [3]–[5]. We formulated the NADSB algorithm to find the optimal sensor locations for sparse arrays with a given aperture and number of sensors. 3) Formulation of the NADSB algorithm to find the optimal sparse array for a given aperture and number of sensors. E{a} denotes the expected value of a and V{a} denotes the variance of a. a ∼ NL (μ, R) means a is an L-by-1 random vector with normal distribution with mean μ and covariance matrix R
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