On the potential of fixed arrays for hearing aids.

Microphone arrays with fixed (time-invariant) weights are directed at enhancing a desired signal from one direction (straight ahead) while attenuating spatially distributed interference and reverberation. Using the theory of sensitivity-constrained optimal beamforming [Cox et al., IEEE Trans. Acoust. Speech Sig. Process. ASSP-34, 393-398 (1986)], free-field arrays of head-sized extents were studied. The key parameters affecting array design and performance are the set of transfer functions from the target direction to each array microphone [H(f)] and the intermicrophone cross-spectral densities for isotropic noise [Szz(f)]. Design variables included the orientation of the array, the number, and [as motivated by Soede, Ph.D. thesis, Delft University of Technology (1990)] the directionality of the microphones within the array, and the complexity and robustness of the required processing. Performance was characterized by the broadband intelligibility-weighted directivity (gain against isotropic noise) and noise sensitivity (reflecting the array's sensitivity to uncorrelated noise, as well as device tolerances). For broadside orientation, a variety of arrays based on cardioid and hypercardioid microphones gave very similar performance. They can provide directivities of 7-8 dB with easily implemented weights (simple scalars). For endfire orientation, as Soede (1990) recognized, similar directivities result with weights based on analog gains and pure time delays. However, with weightings chosen independently for each frequency, directivities up to approximately 11 dB may be obtained, although the increased noise sensitivities of these arrays require practical evaluation. Because of sound diffraction, placement of arrays onto the head potentially impacts both their design and performance. In-situ measurements of H(f) and Szz(f) as well as simplified theoretical models are suggested to explore the optimization of head-mounted arrays.