EURASIP Journal on Applied Signal Processing 
Volume 2003 (2003), Issue 11, Pages 1157-1166
doi:10.1155/S1110865703305074

Equivalence between Frequency-Domain Blind Source Separation and Frequency-Domain Adaptive Beamforming for Convolutive Mixtures

Shoko Araki,1 Shoji Makino,1 Yoichi Hinamoto,2 Ryo Mukai,1 Tsuyoki Nishikawa,2 and Hiroshi Saruwatari2

 1NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japan
2Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara 630-0192, Japan
Received 2 December 2002; Revised 16 March 2003

Abstract

Frequency-domain blind source separation (BSS) is shown to be equivalent to two sets of frequency-domain adaptive beamformers (ABFs) under certain conditions. The zero search of the off-diagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the ABFs. The unmixing matrix of the BSS and the filter coefficients of the ABFs converge to the same solution if the two source signals are ideally independent. If they are dependent, this results in a bias for the correct unmixing filter coefficients. Therefore, the performance of the BSS is limited to that of the ABF if the ABF can use exact geometric information. This understanding gives an interpretation of BSS from a physical point of view.