Acoustic feedback is a problem in hearing aids that contain a substantial amount of gain, hearing aids that are used in conjunction with vented or open molds, and in-the-ear hearing aids. Acoustic feedback is both annoying and reduces the maximum usable gain of hearing-aid devices. This paper studies analytically the steady-state convergence behavior of LMS-based adaptive algorithms when used in continuous adaptation to reduce acoustic feedback. A bias is found in the adaptive filter's estimate of the hearing-aid acoustic feedback path. Methods for reducing this bias and producing an improved estimate of the acoustic feedback path are analyzed and compared. It is shown that by the use of a delay in the forward or cancellation paths of the hearing aid plant, and for representative feedback paths, it is possible to reduce this bias by more than 15 dB.

This paper studies analytically the steady-state convergence behavior of adaptive algorithms that approximate the Wiener solution when operating in continuous adaptation to reduce acoustic feedback in hearing aids. A bias is found in the adaptive filter's estimate of the hearing-aid feedback path when the input signal is not white. Delays in the forward and cancellation paths are shown to reduce the magnitude of the bias. Equations for the bias transfer function are obtained. A discussion about properties of the bias when delays are placed in the forward and cancellation paths follows.

The recursive least squares (RLS) algorithms for FIR adaptive filtering are particularly attractive due to their fast convergence, especially for correlated input signals. A detailed analysis of the QR-RLS algorithm in finite and infinite precision implementations is presented, emphasizing the case where the input signal samples are correlated. The expressions for the mean square values of all internal variables in a steady state are first derived. These expressions are the key used to determine the dynamic range of the internal signals, and to derive the analytical expressions for the mean square values of the deviations in the output variables of the algorithm in finite wordlength implementations. Previous works address this problem considering the input signal a white noise, a situation not so often encountered in practice. The accuracy of all analytical results are verified through a number of computer simulations.

Developing high-quality echo cancelers is an important area of research and is becoming increasingly so with the wide use of hands-free telephones. Although LS algorithms have a faster convergence rate than the more widely-used LMS algorithms, the LS algorithms have not been popular in echo cancelers either because of their bad numerical properties and/or because of large complexity overhead. The authors investigate the performance of a fast RLS algorithm (FQRD-RLS) in the context of speech echo cancellation. The FQRD algorithm is not computationally complex and appears to possess good numerical properties. The computer simulations involve both direct and subband-filtering implementations. The results indicate that the FQRD-RLS is a powerful option for speech echo cancellation.>

This work develops relations for the mean squared value of internal variables in the fast QRD-RLS. The objective is to derive relations based on known characteristics of input signals that predict the behavior of the internal quantities of the algorithm. It is shown that the fast and conventional QRD-RLS algorithms have some variables in common, and thus previous results of the infinite precision analysis of the conventional algorithm remain valid for the fast version. Conditions for avoiding over flow in fixed-point implementations are presented. Simulation results are also shown.>