The focal index as a singular metric for beamforming effectiveness.

Hearing-impaired individuals frequently cite intelligibility problems in multi-talker environments. Microphone arrays performing time-delay beamforming address conditions of poor signal-to-noise ratio by spatially filtering incoming sound. Existing beam pattern metrics including peak side lobe level, integrated side lobe level, beamwidth, and planar directivity index fail to quantitatively capture all elements essential for improving speech intelligibility in multi-talker situations. The focal index (FI) was developed to address these deficiencies. Simulations were performed to exemplify the robust nature of the FI and to demonstrate the utility of this metric for driving array parameter selection. Beam patterns were generated and the metrics were calculated and evaluated against the strict unidirectional requirements for the array. Array performance was assessed by human subjects in a speech recognition task that incorporated competing speech from multiple locations. Simulations of array output were presented under conditions differing in array sparsity. The resulting human subject data were used to demonstrate the linear relationship (R(2) > 0.975) between speech-intelligibility-weighted FI (SII-FI) and the signal-to-noise ratio thresholds for 20% and 80% correct responses. Data indicate that the FI and SII-FI are robust singular metrics for determining the effectiveness of the array.