Cross-spectral matrix denoising for beamforming in wind tunnels

Microphone-array based beamforming measurements in wind tunnels exhibit reduced dynamic range due to flow-induced noise in the individual microphones. Even in open wind tunnels with the arrays outside the flow region, air turbulence will induce such flow noise. Assuming stationary signals and performing long-time averaging of a cross-spectral matrix (CSM), the noise contamination will be concentrated on the CSM diagonal. When the CSM is used for traditional frequency-domain beamforming, Diagonal Removal (DR) will avoid use of the contaminated diagonal. DR is effective at suppressing the noise, but it also often underestimates source strengths and removes weak sources. Other array processing methods must use the diagonal. Several algorithms that attempt to reconstruct the CSM diagonal have been published. It has been shown that remaining off-diagonal noise contributions will limit the performance of methods that operate only on the diagonal. A few algorithms exist that can overcome this limitation by performing modifications also on the off-diagonal elements of the matrix. The paper describes a few of these methods and describes their respective limitations and advantages. Results from simulated and real measurements are presented.