A compact sensor array for blind separation of sources

In this work, the authors are interested in the separation of N source signals recorded simultaneously by M (M greater than or equal to N) receivers. To solve this cocktail-party problem, the authors propose to collect a set of microphones making up an array with a few centimeters in diameter. On each sensor, signals are received with different time delays. The linear memoryless conventional model for source separation is then no more suitable. However, when time delays are small in comparison to the coherence time of each source, the authors show that this problem can be simplified building up a particular set of instantaneous mixtures involving derivatives of sources with respect to time. Sources can then be extracted using an adapted second-order method. When more microphones than sources are available, it is shown how to deal with noisy mixtures. The validity of the proposed approach is confirmed by computer simulations. Finally, the method is applied to an experiment where two-source signals are extracted from their mixtures observed with two omnidirectional microphones in a normal room. A general view of second-order methods is also presented in this work.