Resolving FD-BSS permutation for arbitrary array in presence of spatial aliasing

This paper presents a novel method for solving the permutation problem inherent to frequency domain blind signal separation of multiple simultaneous speakers. As conventional methods, the proposed method exploits the direction of arrival (DOA) of the different speakers to resolve the permutation. But it is designed to exploit the information from pairs of microphones that are usually discarded because of the spatial aliasing. The proposed method is based on an explicit expression of the spatial aliasing effect on the DOA estimation. By introducing a vector of integer values in the equation used to estimate the DOA, it becomes possible to compensate the spatial aliasing by solving the equation relatively to that vector. The proposed method operates sequentially along the frequency bins. First the spatial aliasing is compensated by an iterative procedure that also detects the permutations. Then the detected permutation are suppressed and the DOA are estimated using all available pairs of microphones. Some simulation results demonstrate the effectiveness of the method.