Steerable Invariant Beamformer Using a Differential Line Array of Omnidirectional and Directional Microphones with Null Constraints

Line differential microphone arrays have attracted attention for their ability to achieve frequency-invariant beampatterns and high directivity. Recently, the Jacobi-Anger expansion-based approach has enabled the design of fully steerable-invariant differential beamformers for line arrays combining omnidirectional and directional microphones. However, this approach relies on the analytical expression of the ideal beam pattern and the proper selection of truncation order, which is not always practical. This paper introduces a null-constraint-based method for designing frequency- and steerable-invariant differential beamformers using a line array of omnidirectional and directional microphones. The approach employs a multi-constraint optimisation framework, where the reference filter and ideal beam pattern are first determined based on specified nulls and desired direction. Subsequently, the white noise gain constraint is derived from the reference filter, and the beampattern constraint is from the ideal beam pattern. The optimal filter is then obtained by considering constraints related to the beampattern, nulls, and white noise gain. This method achieves a balance between white noise gain and mean square error, allowing robust, frequency- and steerableinvariant differential beamforming performance. It addresses limitations in beam pattern flexibility and truncation errors, offering greater design freedom and improved practical applicability. Simulations and experiments demonstrate that this method outperforms the Jacobi-Anger expansion-based approach in three key aspects: an extended effective range, improved main lobe and null alignment, and greater flexibility in microphone array configuration and beam pattern design, requiring only steering direction and nulls instead of an analytic beam pattern expression.