Criteria for positioning of sensors for a microphone array

Sensor positioning has an important influence on the performance of array processing. The main contributions of this paper are criteria to evaluate and to optimize the performance of an array of sensors through its geometric configuration-the number and the positions of sensors. The distance between the observed and the desired directivity patterns has been used as a criterion. We propose a generalization of this criterion. We obtain a second criterion by an orthogonality measurement between two subspaces, respectively, containing the noise and the desired signals. This measurement is obtained by an integration of the variance of the signal estimated by an unbiased linear estimator. The output power of a minimum variance distortionless response (MVDR) filter is considered as another criterion. Considering the channels between the desired sources and the array as a multidimensional communication channel, we obtain as a criterion the channel information capacity, which shows the maximum information that we may transfer by this channel. The simulation results confirm that the criteria are related and properly characterize the array configuration. For a linear equally spaced array and narrowband plane-wave signals, the classical results regarding the sensor spacing are confirmed