We discuss the frequency-domain blind source separation (BSS) of convolutive mixtures when the number of source signals is large, and the potential source locations are omnidirectional. The most critical problem related to the frequency-domain BSS is the permutation problem, and geometric information is helpful as regards solving it. In this paper, we propose a method for obtaining proper geometric information with which to solve the permutation problem when the number of source signals is large and some of the signals come from the same or a similar direction. First, we describe a method for estimating the absolute DOA by using relative DOAs obtained by the solution provided by independent component analysis (ICA) and the far-field model. Next, we propose a method for estimating the spheres on which source signals exist by using ICA solution and the near-field model. We also address another problem with regard to frequency-domain BSS that arises from the circularity of discrete-frequency representation. We discuss the characteristics of the problem and present a solution for solving it. Experimental results using eight microphones in a room show that the proposed method can separate a mixture of six speech signals arriving from various directions, even when two of them come from the same direction.
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