Adaptive Microphone Beamforming

Frequency-invariant beamforming (FIB) holds significant importance in distortion-free acquisition and processing of speech signals for microphone arrays. Classical FIB design methods are typically proposed under far-field plane wave models. This paper, however, presents an enhanced approach based on the near-field spherical wave model for microphone arrays. Specifically, we incorporate the spatial response variation (SRV) function to improve the near-field Linear Constrained Minimum Variance (LCMV) broadband beamforming algorithm. In this methodology, the spatial response function serves as an optimization constraint, and a closed-form solution is derived through Lagrange multipliers to obtain frequency-invariant weight vectors. Key implementation aspects include: 1) constructing near-field steering vectors using spherical wave propagation formulas, 2) formulating LCMV constraints with SRV requirements through diagonal loading techniques, and 3) solving the optimization problem via matrix inversion operations. Compared to classical FIB design methods, this approach demonstrates superior resistance to environmental interference and noise, resulting in more stable weight distribution. Simulation results validate both the effectiveness of the proposed method and the correctness of theoretical analysis, providing new insights for advancing FIB technology. The algorithm's practical implementation would involve MATLAB functions like `pinv()` for matrix pseudoinversion and `fft()` for frequency-domain processing, with careful attention to regularization parameters for numerical stability.