For each hearing aid, we consider one of the microphones to be the reference microphone, i.e., disregarding equalization effects the receiver signal would optimally be equal to the reference microphone signal in the absence of noise.
For spatially distributed microphones, the selection of the reference microphone may have a large influence on the performance of the MWF depending on the positions of the speech/noise sources and the microphones [5 7, 17].
Given the estimated source positions and the signal measured at a real reference microphone, a virtual microphone signal is obtained by applying suitable gains to a reference signal.
The transfer function represents the primary path from the reference microphone to the error microphone, and is the secondary-path transfer function between the output of adaptive filter and the output of error microphone.
The desired signal of the standard MWF (S-MWF) is usually the speech component in one of the microphone signals, referred to as the reference microphone signal.
It is shown that a 6dB reduction in sound pressure level is obtainable by adding reference microphones, error microphones, a speaker, and some acoustical foam into the system even though the length of the noise cancelation system is small, approx. 6", compared to the fundamental wavelength of the noise, approx 23".
Therefore, it is sufficient to estimate the phase differences to a reference microphone, for example, to the first microphone for all.
where g 1(k) is the RTF vector of the desired source with the first microphone as a reference, and (phi _{S_{1}} t,k) = operatorname {E}left [|S_{1} t,k)|^{2}right ]) is the PSD of the desired signal at the first microphone.
Using a reference microphone, the phase difference information at point of microphone pairs is stored in the vector (9).
A reference microphone may be placed outside of the usable source microphone area to capture a signal representative of the undesired ambient and interference noise.
