Cascade algorithms for combined acoustic feedback cancelation and noise reduction

Abstract This paper presents three cascade algorithms for combined acoustic feedback cancelation (AFC) and noise reduction (NR) in speech applications. A prediction error method (PEM)-based adaptive feedback cancelation (PEM-based AFC) algorithm is used for the AFC stage, while a multichannel Wiener filter (MWF) is applied for the NR stage. A scenario with M microphones and 1 loudspeaker is considered, without loss of generality. The first algorithm is the baseline algorithm, namely the cascade M -channel rank-1 MWF and PEM-AFC, where a NR stage is performed first using a rank-1 MWF followed by a single-channel AFC stage using a PEM-based AFC algorithm. The second algorithm is the cascade $$(M+1)$$ ( M + 1 ) -channel rank-2 MWF and PEM-AFC, where again a NR stage is applied first followed by a single-channel AFC stage. The novelty of this algorithm is to consider an ( $$M+1$$ M + 1 )-channel data model in the MWF formulation with two different desired signals, i.e., the speech component in the reference microphone signal and in the loudspeaker signal, both defined by the speech source signal but not equal to each other. The two desired signal estimates are later used in a single-channel PEM-based AFC stage. The third algorithm is the cascade M -channel PEM-AFC and rank-1 MWF where an M -channel AFC stage is performed first followed by an M -channel NR stage. Although in cascade algorithms where NR is performed first and then AFC the estimation of the feedback path is usually affected by the NR stage, it is shown here that by performing a rank-2 approximation of the speech correlation matrix this issue can be avoided and the feedback path can be correctly estimated. The performance of the algorithms is assessed by means of closed-loop simulations where it is shown that for the considered input signal-to-noise ratios (iSNRs) the cascade $$(M+1)$$ ( M + 1 ) -channel rank-2 MWF and PEM-AFC and the cascade M -channel PEM-AFC and rank-1 MWF algorithms outperform the cascade M -channel rank-1 MWF and PEM-AFC algorithm in terms of the added stable gain (ASG) and misadjustment (Mis) as well as in terms of perceptual metrics such as the short-time objective intelligibility (STOI), perceptual evaluation of speech quality (PESQ), and signal distortion (SD).