Constrained Maximum Directivity Beamformers Based on Uniform Linear Acoustic Vector Sensor Arrays

This paper studies the problem of beamforming with linear arrays consisting of acoustic vector sensors for speech signal acquisition. It presents a beamforming method, which maximizes the directivity factor (DF) in two steps. In the first step, the same weighting filter is applied to each vector sensor so that all the vector sensors in the lin-ear array have the same spatial response, which is steered to a look direction in the three-dimensional space. Then, a beamformer is de-signed in the second step to maximize the DF while constraining the gain of the beampattern to be maximum at the look direction. The resulting maximum DF (MDF) beamformer has many advantages over the traditional superdirective beamformer with linear arrays of omnidirectional sensors including, but not limited to: 1) it has better steering flexibility and its mainlobe can be steered to any direction in the three-dimensional space, while the traditional superdirective beamformer generally has its mainlobe placed in the endfire directions; 2) it is able to achieve a high DF with the same level of white noise gain. Simulations validate the theoretical study and demon-strate the properties of the presented method.