Theoretical Analysis and Robustness Optimization of FxLMS-Based Active Road Noise Control Under Non-Coherent Interference

Road noise has become a dominant interior noise source in electrified vehicles, especially at low and medium speeds. In practical active road noise control (ARNC) systems, the error microphones capture not only the road noise component correlated with the reference sensors but also non-coherent disturbances such as wind noise, engine harmonics, and heating, ventilation and air conditioning (HVAC) noise. These disturbances degrade the convergence stability and steady-state attenuation of the conventional filtered-x least mean square (FxLMS) algorithm. This study analyzes FxLMS under non-coherent interference and develops two robustness optimization methods. Under the small-step-size assumption, a statistical convergence model is derived for stationary random inputs, together with the corresponding convergence region and steady-state error expressions. Based on this analysis, a multichannel cascaded controller (MCC) and a bounded variable-step-size (VSS) FxLMS algorithm are proposed. Offline simulations and dSPACE-based experiments are conducted on a single-channel HVAC duct ANC test platform and a vehicle test bench. The vehicle-bench tests use controlled tonal excitations and should be interpreted as an intermediate validation step before real-driving broadband tests. Average noise reduction (ANR) and the norm of the adaptive-filter coefficients are used to evaluate robustness. Both MCC and VSS improve attenuation and reduce coefficient fluctuations under non-coherent interference. Relative to fixed-step FxLMS, the maximum ANR improvement reaches 15.8 dB in simulation and 14.2 dB in the real-time duct experiment. Within the controlled tonal and tonal-plus-white-noise conditions tested here, VSS achieves robustness improvements close to those of MCC with much lower computational cost; therefore, it is a practical candidate for further onboard ARNC evaluation rather than a completed validation under real-driving broadband road noise.