Performance analysis of beamforming for circular array with rigid cylindrical baffle

The influence of a rigid cylindrical baffle on a uniform circular microphone array（UCA） response is analyzed based on the array model of a UCA mounted on a rigid cylindrical baffle.In the phase mode space derived from the decomposed sound field,expressions of white noise gain（WNG） and directivity index（DI） for phase mode and delayand -sum beamforming array are derived after some algebraic manipulations.The relationship between WNG and DI with frequencies is analyzed.The WNG and DI of phase mode beamforming array are compared with those of delayand -sum beamforming array using UCA with and without the rigid cylindrical baffle respectively.The influence of offset between UCA and cylinder on the array received signals and array performance is studied.Computer simulations demonstrate that under two conditions the phase mode beamforming array has frequency-independent directivity,which is achieved at the cost of reduced robustness at low frequency,and the delay-and-sum beamforming array has constant WNG throughout the whole frequency range,while the DI is reduced at low frequency until it becomes an omidirectional array.Both of the WNG of two kinds of array are improved when there is a rigid cylindrical baffle and the former’s DI is unchanged while the latter’s DI is increased with a certain extent.The offset between the UCA and the cylinder can reduce the robustness of the array at high frequency.