On the influence of transfer function noise on sound zone control in a room

Sound zones are valuable in scenarios where multiple people are present in the same room but want to listen to individual audio content without wearing headphones. The purpose of sound zone methods is to minimize the acoustic leakage between the zones by controlling multiple loudspeakers. This requires knowledge of how the loudspeakers interact with the room and radiate sound to the zones. That interaction is characterized by the transfer functions between the loudspeakers and microphones sampling the sound field in the zones. In this paper, the effect on the acoustic separation due to inherent noise in in situ transfer function measurements is investigated. The attainable separation is analyzed in the frequency range 20-300 Hz by means of the eigenfunctions of a rectangular room. The concept of observable degrees of freedom is introduced to indicate the number of active eigenfunctions, which are different within the zones at a given frequency. Likewise, controllable degrees of freedom indicate whether each source can excite the active eigenfunctions independently. It is argued that high separation can be achieved when the observable degrees of freedom are fewer than the controllable, and the target sound field can be described by the observable degrees of freedom. However, to attain this high separation it is a requirement that the details in the transfer functions associated with these degrees of freedom can be resolved in the presence of the measurement noise. For both simulated and experimental conditions the transfer functions are estimated using Bayesian inference and the uncertainty in the estimates is used to automatically regularize the sound field control. This regularization is seen to improve the performance when the measurement noise is correlated between the microphones and have little effect when the noise is uncorrelated.