An Approach for Solving Signal Cancellation Problem in Spherical Microphone Array

Abstract

Background and Objectives: One major problem in the minimum power distortionless response (MPDR) beamformer is the signal cancellation problem, i.e., the desired signal is canceled by the reflected signal, even though the distortionless response constraint is satisfied. Solving this problem is the objective of this paper. Methods: It is well known that the signal cancellation problem can be avoided by minimizing the cross-spectrum matrix of noise, i.e., using the minimum variance distortionless response (MVDR) beamformer. But, in the case of disturbance signals which have correlation with the desired signal, estimation of this matrix is a challenging problem. In this paper we propose an approach for estimating the cross-spectrum matrix of noise signal from which we can solve the signal cancellation problem. Results: Simulation examples show that using the proposed method we can bypass the signal cancellation problem completely. Conclusion: A common belief is that in the case of a disturbance that is a reflected version of the desired signal, due to cohesive appearance and disappearance of both the disturbance and the desired signal, the estimation of cross-spectrum matrix of noise signal is typically not possible in practice. So, based on this common belief, we can’t use the MVDR beamformer in this case. In this paper, we show that this common belief is a fault. We propose a general approach for estimating the cross-spectrum matrix of noise signal that is applicable even in the case of correlated disturbances.