Coherence-based performance analysis on noise reduction in multichannel active noise control systems

Active noise control (ANC) over an extended spatial region using multiple microphones and multiple loudspeakers has become an important problem. The maximum noise reduction (NR) potential over the control area is a critical evaluation variable as it indicates the fundamental limitation of a given ANC system. In this paper, a method to mathematically formulate the NR potential for any given multichannel ANC systems is developed. First, the residual error in the multichannel feedforward ANC system is formulated, and then the multiple-input-multiple-output problem is decomposed into the parallel-channel problem. The total energy of the residual error is further decomposed into three different terms representing (i) the signal coherence between the reference signals and error signals, (ii) the filter, and (iii) the system null space. The experimental results validate the proposed evaluation method and illustrate the effectiveness on the maximum NR performance evaluation for given systems. Using the proposed analyzing method more insight into the contribution of each component to the NR potential can be achieved.