Integrated Minimum Mean Squared Error Algorithms for Combined Acoustic Echo Cancellation and Noise Reduction

In many speech recording applications, noise and acoustic echo corrupt the desired speech. Consequently, combined noise reduction (NR) and acoustic echo cancellation (AEC) is required. Generally, a cascade approach is followed, i.e., the AEC and NR are designed in isolation by selecting a separate signal model, formulating a separate cost function, and using a separate solution strategy. The AEC and NR are then cascaded one after the other, not accounting for their interaction. In this paper, however, an integrated approach is proposed to consider this interaction in a general multi-microphone/multi-loudspeaker setup. Therefore, a single signal model of either the microphone signal vector or the extended signal vector, obtained by stacking microphone and loudspeaker signals, is selected, a single mean squared error cost function is formulated, and a common solution strategy is used. Using this microphone signal model, a multi channel Wiener filter (MWF) is derived. Using the extended signal model, an extended MWF (MWFext) is derived, and several equivalent expressions are found, which nevertheless are interpretable as cascade algorithms. Specifically, the MWFext is shown to be equivalent to algorithms where the AEC precedes the NR (AEC NR), the NR precedes the AEC (NR-AEC), and the extended NR (NRext) precedes the AEC and post-filter (PF) (NRext-AECPF). Under rank-deficiency conditions the MWFext is non-unique, such that this equivalence amounts to the expressions being specific, not necessarily minimum-norm solutions for this MWFext. The practical performances nonetheless differ due to non-stationarities and imperfect correlation matrix estimation, resulting in the AEC-NR and NRext-AEC-PF attaining best overall performance.

Cascaded noise reduction and acoustic echo cancellation based on an extended noise reduction

In many speech recording applications, the recorded desired speech is corrupted by both noise and acoustic echo, such that combined noise reduction (NR) and acoustic echo cancellation (AEC) is called for. A common cascaded design corresponds to NR filters preceding AEC filters. These NR filters aim at reducing the near-end room noise (and possibly partially the echo) and operate on the microphones only, consequently requiring the AEC filters to model both the echo paths and the NR filters. In this paper, however, we propose a design with extended NR (NRext) filters preceding AEC filters under the assumption of the echo paths being additive maps, thus preserving the addition operation. Here, the NRext filters aim at reducing both the near-end room noise and the far-end room noise component in the echo, and operate on both the microphones and loudspeakers. We show that the succeeding AEC filters remarkably become independent of the NRext filters, such that the AEC filters are only required to model the echo paths, improving the AEC performance. Further, the degrees of freedom in the NRext filters scale with the number of loudspeakers, which is not the case for the NR filters, resulting in an improved NR performance.