Practical and mathematical aspects of pairing microphones for hearing aid directional arrays

Directional microphone arrays in hearing aids are short baseline, end-fire arrays, which require tight matching of response characteristics between the microphones, as previously reported [J. Acoust. Soc. Am. 113(4,) 2219 (2003)]. Pairing tolerances for good directional performance are much tighter than normal manufacturing tolerances on individual microphones, so it is infeasible to produce entire production lots within these tolerances. Instead, microphones are selected in pairs based on their measured performance. In some cases, the pairing tolerance is on par with the measurement uncertainty of even a well-designed manufacturing test system. Standard gauge analysis is not well suited to this pairing measurement. An analysis of acoustical measurement error as it relates to the pairing problem, the statistics of successful pairing from a large quantity of microphones, and the underlying graph theory of optimum pairing will be discussed in this paper.