Matrix-free mode composition beamforming with CLEAN-SC for broadband rotating sound source localization

High-resolution localization of broadband rotating sound sources is attractive for practical aeroacoustic measurements, but Mode Composition Beamforming (MCB) with CLEAN-SC becomes computationally prohibitive for one-third-octave processing, large mode numbers, and dense scanning grids. This paper presents an exact matrix-free implementation of the MCB+CLEAN-SC workflow that avoids explicit formation and storage of the mode-composed cross-spectral matrix and its residuals. The method combines matrix-free evaluation of the MCB quadratic form, exact operator-form CLEAN-SC updates, and frequency-parametric steering reuse. Simulations show machine-precision agreement with the baseline workflow, one-third-octave speedup ranges of 7.59–30.29 × for MCB and 17.14–71.28 × for CLEAN-SC over the tested regimes, and substantial memory reduction. In a larger tested mode-number case, the proposed workflow remains feasible whereas the baseline runs out of memory. Measured propeller data further confirm that the localization outcome is preserved, while consistent reductions in runtime and peak memory usage are observed across the tested one-third-octave bands under the available operating condition. The proposed workflow improves the practical applicability of broadband rotating sound source localization without changing the underlying MCB and CLEAN-SC definitions.