Robustness Analysis Of The Linear Wideband Beamformers In The Presence Of Microphone Mismatches

Wideband beamforming is one of the key technologies in signal processing, which has foundwide applications in radar, sonar, video conference, hearing aid and speech recording in carenvironment, etc. In practical applications, there usually exist microphone mismatches, i.e.,microphone gain and phase errors and microphone position errors. Therefore, it is important to designrobust beamformers. Amount of robust wideband beamformers appear, but there is still a lack of thesystematical and theoretical analysis on the effects of microphone mismatches on widebandmicrophone array beamformers. This paper studies the effects of microphone mismatches on thefarfield and nearfield linear wideband beamformers with statistical analysis. The main work is brieflysummarized as follows:1. The different effects of microphone gain and phase errors and microphone position errorson the performance of the bias and variance of the array response on the farfield widebandbeamformer. Meanwhile, we get the formulas of bias and variance of array response in the presence ofdifferent microphone mismatches and point out the effects of microphone mismatches, direction ofarrival and sound speech on the performance of array response. The difference between microphonegain and phase errors and microphone position errors is studied. Some numerical examples arepresented to further confirm the theoretical results.2. The study of the different effects of microphone position errors and microphone gain andphase errors on the performance of array response bias and variance has been proposed on nearfieldwideband beamforming. Some insightful properties have been derived through the analysis of theformulas of array response bias and response to gain insights into the robustness characteristics ofnearfield wideband beamformers on microphone mismatch, source location and sound speed, etc. Thedifference of the effects of different microphone mismatches is performed. Several numericalsimulations have been presented to further verify the theoretical analysis.The main effort of this paper is to analyze the robustness of wideband beamforming, so as togain a deep understanding of the robustness characteristics of microphone arrays in the presence ofmicrophone mismatches, which is meaningful in practical application.