A computationally efficient multichannel feedforward time–frequency-domain adjoint least mean square algorithm for active road noise control

•A multichannel TFD-ALMS algorithm for ARNC is proposed with enhanced convergence speed and low computational load.•The TFD-ALMS algorithm is compared with conventional FxLMS and ALMS across various noise sources.•The effect of delay in reference signals on the convergence performance of the TFD-ALMS algorithm is analyzed.•Enhanced performance of the proposed algorithm is demonstrated in real vehicle ARNC tests under varying conditions. Active road noise control (ARNC) emerges as a promising solution for reducing vehicle interior road noise, owing to its efficacy in controlling low-frequency noise. However, the feedforward ARNC system demands numerous reference signals to achieve notable control, leading to a significant computational burden. To address this, the adjoint least mean square (ALMS) algorithm might be a viable alternative due to its lower computational intensity, especially in multichannel scenarios. Nevertheless, factors such as the spectral distribution of reference signals and complex acoustic paths with multi-modal responses may impact its convergence performance. This paper introduces a time–frequency-domain ALMS (TFD-ALMS) algorithm, where weight vectors are updated in the frequency domain, allowing for individualized step size settings for each frequency point, thereby enhancing convergence performance. Additionally, the time-reversed estimated secondary paths with magnitude equalization are constructed to mitigate the adverse impact of the magnitude-frequency response of the acoustic paths. Simulations are conducted to assess the performance of the TFD-ALMS algorithm, accompanied by discussions on the potential for the algorithm to converge to a biased solution due to the proposed step size setting. Moreover, the influence of the reference signal delay on the convergence speed is examined in a broader context. Consequently, a strategy for determining the fastest convergence step size, based on the Fibonacci search method, is proposed to aid in studying the convergence performance of the algorithm when dealing with narrowband and broadband noises of varying frequencies or bandwidths. Finally, the proposed algorithm is validated through ARNC tests under steady-state and unsteady-state working conditions. Results illustrate its capability to achieve superior control performance with reduced computational complexity compared to conventional methods.