Robust Superdirective Beampattern Synthesis via Eigenbeam Optimization for Arbitrary Small-Aperture Arrays

Small-aperture arrays with element spacing smaller than the signal wavelength are widely used in acoustic detection, wireless communication, and intelligent sensing. By fully exploiting the inter-element correlation in small-aperture arrays, superdirective beamforming methods can achieve superior performance over conventional approaches. However, this technology faces two core challenges in practical applications: (1) robust control is required to mitigate its high sensitivity to array errors and interferences; and (2) precise tuning of critical beampattern parameters is necessary to synthesize frequency-invariant or low-sidelobes beampatterns to accommodate diverse scenario-specific requirements. To address these challenges, this paper proposes a robust superdirective beampattern synthesis via eigenbeam optimization, applicable to arbitrary small-aperture arrays. The method first decomposes the optimal superdirective beam into eigenbeams with different directivity and robustness. Then, based on the desired mainlobe width, sidelobe level, and null distributions, virtual interference sources are introduced to iteratively optimize each eigenbeam, generating a new set of eigenbeams with distinct properties compared to the original ones. By selecting appropriate eigenbeams, the synthesized beampattern satisfies multiple requirements, including directivity, robustness, mainlobe width, sidelobe level, and null distributions. Simulations and experiments show the proposed method exhibits superior performance while maintaining low computational complexity, requiring only simple parameter tuning and remaining compatible with arbitrary small-aperture arrays.