Efficient Continuous Beam Steering for Planar Arrays of Differential Microphones

Performing continuous beam steering, from planar arrays of high-order differential microphones, is not trivial. The main problem is that shape-preserving beams can be steered only in a finite set of privileged directions, which depend on the position and the number of physical microphones. In this letter, we propose a simple and computationally inexpensive method for alleviating this problem using planar microphone arrays. Given two identical reference beams pointing in two different directions, we show how to build a beam of nearly constant shape, which can be continuously steered between such two directions. The proposed method, unlike the diffused steering approaches based on linear combinations of eigenbeams (spherical harmonics), is applicable to planar arrays also if we deal with beams characterized by high-order polar patterns. Using the coefficients of the Fourier series of the polar patterns, we also show how to find a tradeoff between shape invariance of the steered beam, and maximum angular displacement between the two reference beams. We show the effectiveness of the proposed method through the analysis of models based on first-, second-, and third-order differential microphones.