Spherical microphone arrays (SMAs) are widely used for spatial sound field analysis due to their geometric symmetry and compatibility with spherical harmonic (SH) processing. However, the spatial resolution achievable by SMAs is fundamentally limited by their maximum SH order. At low frequencies, the contributions of higher-order modes are suppressed by spherical Bessel functions, resulting in degraded resolution. To address these limitations, we propose augmenting the SMA with multiple linear microphone arrays (LMAs) positioned around it to provide complementary spatial information. A unified set of spatial modes is derived via singular value decomposition (SVD) of the combined transfer matrix of the SMA–LMA system. The resulting data-driven modal basis adapts to the joint array geometry and frequency, capturing spatial patterns beyond the SH subspace. Subspace analysis shows that the unified modes approximate SH modes near the SMA’s aliasing frequency but diverge elsewhere, enabling representation of spatial content inaccessible to SH-based processing. Simulation results demonstrate that the proposed modal solution improves sparse recovery accuracy, enhances numerical stability through better conditioning, and extends the operational bandwidth of the array. This approach provides a physically consistent and scalable framework for wideband sound field reconstruction using combined SMA–LMA configurations.
Xu et al. (Wed,) studied this question.
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