Infinite-dimensional SVD for analyzing microphone array

Information Measures for Microphone Arrays

“…The analogy between the free-space propagation model in (13) and the general SIMO model in ( 6) is obvious. Hence, the channel capacity results from the previous section could be straightforwardly applied to the narrowband free-space propagation model to compute C(f, θ) as…”

“…• Device Scattering: The channel capacity is related to the incidence angle only through the steering vector d of the corresponding plane-wave in (13). This corresponds to the total wavefield observed at the microphone array, which has the general form…”

“…In a practical setting, it is computed either using simulation, e.g., through finiteelement analysis of the acoustic wave equation, or using physical anechoic measurement. In either case, the resulting response becomes steering vector in (13), and the remaining analysis is the same.…”

“…A notably different approach for microphone array analysis that is physics-based was proposed in [13], where the singular vectors of the infinite-dimensional singular value decomposition (SVD) of the steering vectors matrix is computed. This metric is independent of the beamforming algorithm but does not resolve the other issues.…”