A maximum-achievable-directivity beamformer with white-noise-gain constraint for spherical microphone arrays

In microphone array beamforming, it is desirable to achieve a directive gain as high as possible for maximum acoustic noise rejection. The well-known superdirective beamformer was developed for this purpose; but it is sensitive to array imperfections such as sensors' self noise, sensor placement errors, mismatch among sensor responses, etc, which restrict its application in practical systems. To circumvent the robustness issue, we recently developed a flexible high directivity beamforming method that can achieve a flexible compromise between the directivity factor (DF) and the level of white noise gain (WNG) by adjusting the value of a control parameter. This principle is further extended in this work. We present a beamforming method with spherical microphone arrays. It first determines the maximum order (consequently the largest value of DF) that can be achieved in an analytical way based on a specified level of WNG that is tolerable by the array in the frequency band of interest. This order is then used to determine the value of a control parameter. The maximum-achievable-directivity beamformer is then designed. The advantage of this beamformer over the existing ones is that it is robust to implement and yet able to achieve the maximum possible DF.