The focal index as a singular metric for beamforming effectiveness

Abstract

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.

Simultaneous Passive Acoustic Mapping and Magnetic Resonance Thermometry for Monitoring of Cavitation-Enhanced Tumor Ablation in Rabbits Using Focused Ultrasound and Phase-Shift Nanoemulsions

“…At the opposite extreme, a map with a single high pixel has an area under the map equal to the area of one pixel; for example, a 0.5mm 2 pixel in a 500mm 2 mapping region gives a focal index value of 1000. A similar metric has been described before in the beamforming literature, using a ratio of areas of a beam pattern (Kelly et al 2014). Similarly, from the temperature maps we extracted the maximum pixel value as an indication of heating amplitude.…”

CABE: A Cloud-Based Acoustic Beamforming Emulator for FPGA-Based Sound Source Localization

“…A first metric described by Kelly et al [37] is the BeamWidth (BW) of the main lobe. The beamwidth of the main lobe is strongly related to the acoustic frequency and decreases with increasing frequency.…”

“…The Integrated Side Lobe Level (ISLL) is another metric proposed by Kelly et al [37] and allows to compute the ratio between the area outside the main lobe between α and β and the area of the response of the array over the complete area of interest for a 2D response. Here, this principle is extended to 3D by:ISLL=∫αβPα,β(ufalse→,S,z)dΩ∫abPa,b(ufalse→,S,z)dΩ×100%…”

“…E.g., it is possible that the PSLL returns a 0 dB value, while the main lobe and the second lobe share the same power value, but with optimal beam pattern in other steering orientations. Kelly et al [37] try to alleviate the shortcomings of these metrics by proposing the Focal Index (FI).…”