Multichannel room response equalization with a broadened control region using a linearly constrained approach and sensor interpolation

Abstract

This paper describes a room response equalization technique based on an underdetermined multichannel inverse filtering (UMIF) and linearly constrained minimum variance (LCMV) approach. Not limited to the local control at the neighborhood of the measured control points, the proposed UMIF-LCMV system is capable of widening the effective equalization area of the reproduced sound field, with a large number of interpolated control points. Specifically, a constrained optimization problem is formulated to minimize the matching error at the interpolated control points while seeking precise matching at the measured control points. In practical implementation, only the frequency responses (FRs) associated with a limited number of control points need to be measured, whereas the FRs for the interpolated points are established by using a plane wave decomposition-based sensor interpolation technique. A two-stage procedure is developed to trim down plane wave components by using the least absolute shrinkage and selection operator (LASSO) algorithm and to obtain the complex amplitudes of the principal components. Simulations and objective and subjective experiments are conducted for a system comprising a linear loudspeaker array and a linear microphone array. The results have confirmed the efficacy of the proposed system in widening the effective listening area with only limited discrete measurements.