Approximate MVDR Beamformer With Automatic Null Steering and Free of Noise Covariance Matrix Estimation

The traditional minimum variance distortionless response (MVDR) beamformer requires the estimation of the noise covariance matrix, which poses significant challenges in complex acoustic environments. Recently, model-based approaches have been introduced to address this issue, showing promising results. However, a major drawback of these methods is their high computational complexity, particularly in estimating model parameters, such as the direction of interference. To address this challenge, we propose a low-complexity, model-based beamforming technique tailored for small-spacing linear microphone arrays, commonly found in consumer devices. Drawing inspiration from a useful decomposition, we derive an approximate MVDR beamformer that combines a regularized superdirective beamformer with a first-order adaptive differential beamformer. This approach eliminates the need for explicit estimation of noise statistics and interference direction. Instead, the method relies on two key parameters: one related to the spectral characteristics of the noise, and the other to the direction of the noise source. An alternating iterative optimization process is introduced to determine the optimal values of these parameters by minimizing the variance of the array output. Simulation results show that the proposed beamformer significantly reduces computational complexity compared to two leading model-based MVDR beamformers, while also outperforming other baseline algorithms in terms of speech enhancement performance.