Simulation-Based Asymptotic Study of Multi-channel Filtered-x Least Mean Square (MC-FxLMS) Algorithm for Active Noise Control

Background Noise reduction across spatial regions of limited size in large enclosures is a practically useful application of global active noise control (ANC). ANC systems based on Multi-channel filtered-x least mean square (MC-FxLMS) algorithm are employed to spatially extend the quiet zone beyond cancellation points. Purpose Analytical expressions are available that give the maximum achievable reduction in acoustic potential energy across an enclosure and the minimum mean square residual noise achievable at error microphone locations using MC-FxLMS algorithm. However, such expressions are not available to determine the maximum achievable average noise reduction across a quiet zone in an arbitrary region situated within the enclosure. The present study performs numerical simulations to estimate maximum achievable global noise reduction across the chosen quiet zone using MC-FxLMS algorithm. Methods Simulation of a room environment having reverberation in three-dimensional space is done. Noise reduction performance is evaluated at uniformly placed grid points across a two-dimensional square zone of quiet having an area of 1 m 2 . This paper reports a systematic simulation study of MC-FxLMS algorithm in which the numbers of control sources and residue sensors are progressively increased and analysis of asymptotic performance of the ANC system is done. Results and Conclusions The study shows that after a certain point, further increase in the number of components does not yield appreciable improvement in global noise reduction across the chosen quiet zone, and the performance of MC-FxLMS algorithm saturates. The number of components so obtained is significantly less than that required as per modal analysis.