Sensor array optimization for sources separation and detection in the at-worst determined case

Most of the number of sources estimation techniques use the well-known signal-subspace approach in which the number of dominant sources is deduced regarding the multiplicity of the lowest eigenvalues of the correlation matrix. In the at-worst determined case (number of microphones just equals the maximal number of possible radiating sources) such methods are inoperative because the noise subspace could be inexistant. However, a well chosen sensor array geometry permits to achieve source detection using eigenvalues above conditions to some a priori knowledge on the sources. This paper explores some relation between geometry and eigenvalues in order to achieve optimal sources detection and separation. This study yields analytical formulations of both optimisation problem by working on the simple case of two uncorrelated harmonic sources. Theoretical and experimental measurements are presented and discussed.