Robustness and efficiency of an acoustically coupled two-source superdirective array

In a number of applications it is desirable to reproduce sound in a specific region whilst minimising it elsewhere. This can, in theory, be achieved using loudspeaker arrays and optimal, or superdirective beamforming techniques. However, these superdirective methods generally require a large electrical power at low frequencies, where the wavelength is large compared to the array, and are generally sensitive to practical uncertainties that may occur in the electroacoustic response of the loudspeaker array. In order to overcome these limitations, regularisation is often used to constrain the electrical power requirements of these arrays and improve their robustness to response uncertainties. However, in the context of a two-source line array an alternative method of reducing the required electrical power by coupling the two loudspeakers together via a common acoustic enclosure has been proposed. This paper investigates the performance of the coupled two-source loudspeaker array, and compares its performance to the standard uncoupled two-source array in terms of the acoustic contrast, electrical power requirement and robustness to uncertainties in the system’s responses. It is firstly shown through a series of simulations that when there is no uncertainty in the responses, although the two arrays achieve the same acoustic contrast performance, the electrical power required by the coupled array is about 100 times lower than that required by the uncoupled array at low frequencies. It is then shown that the coupled array is significantly more robust to response uncertainties than the uncoupled array and, even when the electrical power required by the uncoupled array is limited to be equal to that required by the coupled array, it achieves a higher level of acoustic contrast performance.