Array configuration optimization of first-order steerable differential arrays with minimum number of microphones

The first-order steerable differential arrays (FOSDAs), which have found a variety of applications in speech and audio processing, are usually designed by construction of two orthogonal dipoles using four microphones. Actually, however, three microphones are enough to construct a FOSDA by forming two dipoles with a shared microphone, which is the scheme with the minimum number of microphones and, hence, the most cost-effective. This paper studies the design and analysis of such three-element FOSDAs by using a least-squares method. In particular, the effect of the array configuration on the three-element FOSDA is studied, and optimum array configurations under different steering angle ranges are derived in terms of both beampattern fitting quality and white noise gain. It also reveals that care should be taken to avoid a conservative setting of the steering angle range in order to achieve superior design of the three-element FOSDA.