Gradient flow adaptive beamforming and signal separation in a miniature microphone array

Gradient flow converts the problem of separating unknown delayed mixtures of sources, from traveling waves impinging on an array of sensors, into a simpler problem of separating unknown instantaneous mixtures of the time-differentiated sources, obtained by acquiring or computing spatial and temporal derivatives on the array. The linear coefficients in the instantaneous mixture directly represent the delays, which in turn determine the direction angles of the sources. This formulation is attractive, since it allows to separate and localize waves on broadband signals using standard tools of independent component analysis (ICA), yielding the sources along with their direction angles. The technique is suited for arrays of small aperture, with dimensions shorter than the coherence length of the waves. We present gradient flow experiments on an array of four hearing aid microphones placed within a 5 mm radius, yielding 20 dB separation of joint speech in outdoors acoustic environments, and 10 dB separation indoors under mild reverberant conditions. These results suggest applications of gradient flow miniature microphone arrays to intelligent hearing aids with adaptive suppression of interfering signals and nonstationary noise.