Infinite impulse response echo canceller in STFT domain for reverberant environments

Acoustic echo cancellation and system identification in reverberant environments have been thoroughly studied in the literature. Theoretically, in a reverberant environment the Acoustic Impulse Response (AIR) relating the loudspeaker signal, denoted reference, with the corresponding signal component at the microphone, denoted echo, is of an infinite length and can be modeled as an Infinite Impulse Response (IIR) filter. Correspondingly, the echo signal can be modeled as an Auto Regressive Moving Average (ARMA) process. Yet, most methods for this problem adopt a Finite Impulse Response (FIR) system model or equivalently a Moving Average (MA) echo signal model due to their favorable simplicity and stability. Latter methods, denoted FIR-Acoustic Echo Canceller (AEC), employ an Adaptive Filter (AF) for tracking a possibly time-varying system and cancelling echo. Some contributions adopt an IIR system model and utilize it to derive a time-domain AEC and accurately analyze the room behaviour. An IIR system model has also been successfully applied in the Short Time Fourier Transform (STFT) domain for the dereverberation problem. In this contribution we consider an IIR model in the STFT domain and propose a novel online AEC algorithm, denoted IIR-AEC, which tracks the model parameters and cancels echo. The order of the feed-back filter, equivalent to the order of the Auto Regressive (AR) part of the echo signal model, can be designed to fit the acoustic model and the order of the feed-forward filter, equivalent to the order of the MA part of the echo signal model, is limited to a single tap, thereby requiring that the STFT window is longer than the early part of the AIR. The computational complexity of proposed IIR-AEC is comparable to a Recursive Least Squares (RLS) implementation of FIR-AEC. These methods are evaluated using real measured AIRs drawn from a recording campaign and the IIR-AEC is shown to outperform the FIR-AEC.