Superdirective Robust Algorithms’ Comparison for Linear Arrays

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.

Keywords

• superdirective arrays
• broadband beamforming
• sequential quadratic programming
• frequency-invariant beam pattern
• robust beamforming