Abstract
This work presents, using the least squares estimation theory, a theoretical and experimental analysis on the performance of the standard adaptive filtering algorithms when applied to acoustic feedback cancellation. Expressions for the bias and covariance matrix of the acoustic feedback path estimate provided by these algorithms are derived as a function of the signals statistics as well as derivatives of the cost function. It is demonstrated that, in general, the estimate is biased and presents a large covariance because the closed-loop nature of the system makes the cross-correlation between the loudspeaker and system input signals non-zero. Simulations are carried out to exemplify the results using speech signals, a long acoustic feedback path and the recursive least squares algorithm. The results illustrate that these algorithms converge very slowly to a solution that is not the true acoustic feedback path. The relationship between the performance of the adaptive filtering algorithms and the aforementioned cross-correlation is proven by varying the signal-to-noise ratio and the delay introduced by the forward path.
Highlights
A sound reinforcement (SR) system essentially comprises microphones, amplifiers and loudspeakers
This work has two goals: first, using the least squares (LS) estimation theory, to present a theoretical analysis on the poor performance of the standard adaptive filtering algorithms when applied to acoustic feedback cancellation (AFC), compiling in detail the results available in the literature; second, to exemplify the conclusions drawn from the theoretical analysis using speech signals, a long acoustic feedback path of a public address (PA) system and the recursive LS (RLS) algorithm
Expressions for the bias and covariance matrix of the acoustic feedback path estimate provided by these algorithms were derived as functions of the signals statistics as well as derivatives of the cost function
Summary
A sound reinforcement (SR) system essentially comprises microphones, amplifiers and loudspeakers. Another possible solution is to not utilize the standard gradient or least-squares based adaptive filtering algorithms to update the adaptive filter Following this approach, the works in [2], [20] have demonstrated that the cepstra of the microphone and error signals can be defined as a function of the impulse responses of the feedback path, forward path and adaptive filter. This work has two goals: first, using the LS estimation theory, to present a theoretical analysis on the poor performance of the standard adaptive filtering algorithms when applied to AFC, compiling in detail the results available in the literature; second, to exemplify the conclusions drawn from the theoretical analysis using speech signals, a long acoustic feedback path of a PA system and the recursive LS (RLS) algorithm. This paper is organized as follows: Section II presents the modelling of both acoustic feedback problem and acoustic feedback cancellation; Section III presents the theoretical analysis and compiles in detail the results available in the literature; Section IV describes the configuration of the simulated experiments; in Section V, the experimental results are presented and discussed based on the statistical properties of the desired sound signal, ambient noise and closed-loop system impulse response; Section VI concludes the paper, emphasizing its main contributions
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