Design of 3D Steerable Frequency-Invariant Beamformers With Concentric Circular Superarrays

Superarrays refer to microphone arrays that combine both omnidirectional and directional sensors, enabling higher array gain or additional functionalities that traditional arrays with the same geometry cannot achieve. In our previous work, we demonstrated that concentric circular superarrays (CCSAs) can achieve directivity and three-dimensional (3D) steering capabilities comparable to volumetric arrays, but with a more compact, two-dimensional geometry. This makes CCSAs particularly promising for high-fidelity speech signal in compact devices. However, prior CCSA designs have been limited to omnidirectional and bidirectional sensors, restricting their flexibility and broader applicability. Additionally, the theoretical conditions required for effective array configuration remain unclear. This paper introduces a generalized framework for designing CCSAs and their corresponding fully steerable, frequency-invariant beamformers in 3D space. The contributions are twofold: 1) a method is proposed for designing 3D steerable, frequency-invariant beamformers using CCSAs equipped with directional microphones of arbitrary types; and 2) the necessary and sufficient conditions for array configurations are derived to enable effective design of first-, second-, and third-order frequency-invariant beamformers. We further summarize the construction of first-, second-, and third-order beamformers. Extensive simulations and real experiments validate the proposed method and demonstrate the practical efficacy and theoretical novelty of our approach.