  An important aspect of a humanoid robot is audition. Previous work has
presented robot systems capable of sound localization and source segregation
based on microphone arrays with various configurations. However, no theoretical
framework for the design of these arrays has been presented. In the current
paper, a design framework is proposed based on a novel array quality measure.
The measure is based on the effective rank of a matrix composed of the
generalized head related transfer functions (GHRTFs) that account for
microphone positions other than the ears. The measure is shown to be
theoretically related to standard array performance measures such as
beamforming robustness and DOA estimation accuracy. Then, the measure is
applied to produce sample designs of microphone arrays. Their performance is
investigated numerically, verifying the advantages of array design based on the
proposed theoretical framework.
