Frequency-Invariant Beampattern Design for Circle-like Arrays

Traditional frequency-invariant beamforming methods typically rely on frequency-dependent characteristics and are associated with high computational complexity, especially when dealing with complex arrays. To address these issues, this communication proposes a simple frequency-invariant beamforming method for a class of centrally symmetric circular sensor arrays, termed circle-like arrays. Based on the minimum mean square error criterion, the proposed method first deduces the analytic relationship between the weighting vector and the desired value at different frequencies. Then, the required weighting vectors are derived by leveraging the geometric properties of circle-like arrays, ultimately synthesizing a broadband frequency-invariant beampattern. This method provides closed-form frequency-invariant solutions for some special arrays, including single-layer and multi-layer circular arrays, thereby improving computation efficiency. Simulation results demonstrated that the proposed method reduces the computation complexity while maintaining excellent frequency-invariance, and the beampattern performance is comparable to that of traditional numerical optimization methods.