Beamforming with noise minimization

Optimal beamformer design, as presented in Chap. 6, may be very useful, but does not take into account the properties of the specific sound field producing the signals at the microphones. In this chapter, beamforming in which the beam pattern is tailored to the actual sound field is presented. This beamforming distinguishes between the desired signal and the noise and, therefore, potentially achieves improved performance in real, noisy sound fields. The measured sound field is characterized by spatial cross-spectrum matrices, typically divided into matrices representing the desired signals and matrices representing the unwanted noise. Therefore, the first part of this chapter extends the array equations, in both the space and the spherical harmonics domains (as presented in Chap. 5) to include noise. In particular, explicit expressions are developed for designs that consider noise fields that are spatially white and noise fields that are acoustically diffuse. The second part of the chapter employs the new models in the development of popular beamformers, such as the minimum variance distortionless response (MVDR) and the linearly constrained minimum variance (LCMV). These beamformers are developed for spherical arrays with explicit formulations in the spherical-harmonics domain, emphasizing their advantages when formulated in this domain. The chapter concludes with design examples to illustrate the performance of the beamformers under various conditions.