Equivalence between frequency domain blind source separation and frequency domain adaptive null beamformers

Frequency domain Blind Source Separation (BSS) is shown to be equivalent to two sets of frequency domain adaptive microphone arrays, i.e., Adaptive Null Beamformers (ANB). The minimization of the off-diagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the ANB. The unmixing matrix of the BSS and the filter coefficients of the ANB converge to the same solution in the mean square error sense if the two source signals are ideally independent. Therefore, we can conclude that the performance of the BSS is upper bounded by that of the ANB. This understanding clearly explains the poor performance of the BSS in a real room with long reverberation. The fundamental difference exists in the adaptation period when they should adapt. That is, the ANB can adapt in the presence of a jammer but the absence of a target, whereas the BSS can adapt in the presence of a target and jammer, and also in the presence of only a target.