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Nonlinear acoustic echo cancellation (AEC) is a highly challenging task in a single-microphone; hence, the AEC technique with a microphone array has also been considered to more effectively reduce the residual echo. However, these algorithms track only a linear acoustic path between the loudspeaker and the microphone array. This study proposes a microphone array form of the single-microphone nonlinear AEC (NAEC) algorithm in the reverberant condition. We extend a single-microphone-based model of the nonlinear acoustic echo to the microphone array case and propose the modeling of the acoustic transfer function (ATF) vector extended with a power series using a state-space equation. The Kalman filter is also adapted to optimally and recursively estimate the ATF vector. Furthermore, low-rank approximation and multi-microphone Wiener filtering are applied to estimate the multi-microphone near-end speech covariance, which results in the microphone array NAEC algorithm showing a consistently outstanding performance under severe signal-to-echo ratio (SER) and highly reverberant conditions. Consequently, our approach outperforms conventional methods regarding echo reduction and near-end speech quality for a wide range of SER and reverberation conditions.
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