The influence of regularization on anechoic performance and robustness of sound zone methods

Recent attention to the problem of controlling multiple loudspeakers to create sound zones has been directed towards practical issues arising from system robustness concerns. In this study, the effects of regularization are analyzed for three representative sound zoning methods. Regularization governs the control effort required to drive the loudspeaker array, via a constraint in each optimization cost function. Simulations show that regularization has a significant effect on the sound zone performance, both under ideal anechoic conditions and when systematic errors are introduced between calculation of the source weights and their application to the system. Results are obtained for speed of sound variations and loudspeaker positioning errors with respect to the source weights calculated. Judicious selection of the regularization parameter is shown to be a primary concern for sound zone system designers - the acoustic contrast can be increased by up to 50dB with proper regularization in the presence of errors. A frequency-dependent minimum regularization parameter is determined based on the conditioning of the matrix inverse. The regularization parameter can be further increased to improve performance depending on the control effort constraints, expected magnitude of errors, and desired sound field properties of the system.