Superdirective Robust Algorithms’ Comparison for Linear Arrays

Danilo Greco,Andrea Trucco

doi:10.3390/acoustics2030038

Abstract

Frequency-invariant beam patterns are often required by systems using an array of sensors to process broadband signals. In some experimental conditions (small devices for underwater acoustic communication), the array spatial aperture is shorter than the involved wavelengths. In these conditions, superdirective beamforming is essential for an efficient system. We present a comparison between two methods that deal with a data-independent beamformer based on a filter-and-sum structure. Both methods (the first one numerical, the second one analytic) formulate a mathematical convex minimization problem, in which the variables to be optimized are the filters coefficients or frequency responses. The goal of the optimization is to obtain a frequency invariant superdirective beamforming with a tunable tradeoff between directivity and frequency-invariance. We compare pros and cons of both methods measured through quantitative metrics to wrap up conclusions and further proposed investigations.

Highlights

A beamformer is an important data processing method in different fields to elaborate the signals coming from an array of sensors to get a versatile spatial filtering [1]
The results shown confirm that the Robust Least-Squares Frequency-Invariant Beamformer Design (RLSFIB) design is capable of controlling the robustness of the resulting beamformer, which underlines the flexibility of this design procedure
With the parameters’ choice, directivity and W NG are comparable for the two methods at the higher frequencies, but at lower frequencies W NG has an oscillating behavior for Frequency-Invariant Beam Pattern Design (FIBP) method, avoided by definition for the RLSFIB design

Summary

Introduction

A beamformer is an important data processing method in different fields (radar, sonar, biomedical imaging, and audio processing) to elaborate the signals coming from an array of sensors to get a versatile spatial filtering [1]. In filter-and-sum beamforming, each array sensor (microphones in our case) of the array feeds a transversal finite impulse response (FIR) filter (Figure 1) [2,3,4] and the filter outputs are summed-up by a convolution in the time-domain with an impulse response wn,l (N is the total number of sensors and L is the FIR filter’s length) to produce the desired beam signal. The beam pattern (BP) (Equation (2)) represents the beamformer spatial response in the far-field region and is a function of the direction of arrival θ (DOA) and the frequency ω/2π. S(ω) is the input source (plane wave) and Z(ω, θ) (Equation (1)) is the final output (Figure 1)

Methods

Results

Discussion

Conclusion