Cochlear implants (CI) are implantable electronic prostheses that aim to restore communication in people with severe to profound hearing loss. This is achieved by transforming the acoustic signals into electrical stimuli and applying them directly to the cochlea through a set of electrodes. Despite its effectiveness under optimal environmental conditions, its performance is severely degraded in the presence of noise. This work proposes an envelope-based minimum-variance distortionless response (MVDR) approach for multichannel noise reduction in CI applications. The original constraint in the conventional time-domain MVDR beamformer is modified to ensure that the second-order statistical moments of the processed and original speech-only envelopes are equivalent. Assuming strict computational limitations, as those found in commercial multielectrode systems, a low computational-cost particular case of the proposed method results in a power-based MVDR that has a semianalytical solution. The resulting algorithm provides a fast calculation method for its optimal coefficients without losing significant performance compared to its general form. Results obtained from computational simulations and objective criteria indicate higher intelligibility levels achieved by the proposed methods compared to the conventional time-domain MVDR beamformer. This evidence is corroborated by psychoacoustic experiments with ten normal-hearing volunteers listening to vocoded speech, and one CI user employing a research interface.

This article presents a multichannel Wiener filter (MWF) based noise reduction method with preservation of the interaural level difference (ILD). It minimizes the MWF cost function subject to two constraints for ILD preservation. Under this approach, the weighting coefficient that establishes the trade-off between noise reduction and binaural cue preservation takes a physical interpretation, facilitating its design. The proposed approach results in a convex optimization problem that admits a computationally efficient semi-analytical closed-form solution. Simulation experiments in hearing aid applications were performed considering practical acoustic scenarios. Considering an appropriate set of control parameters, the average performance of the proposed method preserves the ILD of a single interfering source in the same way as the conventional MWF-ILD, keeping the same level of noise reduction as the classic MWF, with approximately the same amount of speech ILD distortion. The proposed method is particularly interesting for implementing real-time noise reduction methods in binaural hearing aids.

Cochlear implants (CI) are surgically implanted auditory prostheses for partially compensating severe to profound sensorineural hearing losses. Despite providing significant intelligibility levels under silent conditions, their performance is highly affected by additive noise. Time-frequency masks, such as the binary mask, the Wiener filter (WF) and their variations, have been widely employed for noise reduction. However, they were not originally designed for CI applications, which have very particular characteristics. In this work, we propose a new method for noise reduction, especially designed for CI. It is based on the minimization of the mean square error between the squared envelopes of the estimated and target speech. The theoretical derivation of the proposed time-frequency mask is presented and a closed-form for the one-coefficient optimal solution is obtained. Numerical simulations with objective criteria indicate that the proposed method results in higher intelligibility scores as compared to the time-domain implementation of the WF time-frequency mask. Psychoacoustic experiments with normal hearing volunteers and vocoded signals, as well as CI users, corroborate simulation results, showing significant increases in intelligibility, especially for SNR <; -5 dB. The proposed method may result in an intelligibility increase of up to 70%, for SNR = -25 dB, as compared to the WF. These findings were obtained considering an ideal signal-to-noise ratio estimator.

This paper presents a robust beamformer for stereo noise reduction in hearing aid applications. The worst-case optimization method was applied to the binaural minimum-variance distortionless-response (BMVDR) beamformer, for providing robustness against parameter estimation inaccuracies. This property is essential in real-world applications, since it is well known that steering-vector and noise-correlation estimation errors may significantly degrade the BMVDR performance. It is shown that its control parameters can be designed as a function of the noisy-speech interaural-level-difference estimate. Simulation experiments for synthetic and real-world noise, as well as for a range of signal to interference ratios (SIR) were performed. For a particular set of fixed control parameters, it is shown that the mean performance of the conventional BMVDR may be improved by 0.76 wideband perceptual evaluation of speech quality (WPESQ). The proposed method is especially effective for input SIRs higher than 10 dB, which is a crucial range for hearing aid users.

This paper presents a noise reduction method with perceptually relevant preservation of the interaural time difference (ITD) of the residual noise in binaural hearing aids. The interaural coherence (IC) concept, previously applied to the multichannel Wiener filter (MWF) for preservation of the spatial subjective sensation of diffuse noise fields, is proposed here to both preserve and emphasize the ITD binaural cues of a directional acoustic noise source. It is demonstrated that the previously developed MWF-ITD technique may decrease the original IC magnitude of the processed noise, consequently increasing the variance of the interaural phase difference (IPD) of the output signals. It is shown that the MWF-IC technique simultaneously minimizes a nonlinear function of the difference between input and output IPD, which is strictly related to ITD, and preserves the natural coherence of directional noise captured by the reference microphones. Objective measures and psychoacoustic experiments corroborate the theoretical findings, showing that the MWF-IC technique provides relevant noise reduction, while preserving the original ITD subjective perception and original lateralization for a directional noise source. These results are especially relevant for hearing aid designers, since they indicate MWF-IC as a noise reduction technique that provides residual noise spatial preservation for both diffuse and directional noise sources in frequencies below 1.5 kHz.

This work presents a modified version of the variable step size Kwong and Johnston's algorithm (VSS) for LMS adaptive filtering. The new proposal, called robust variable step size (RVSS), presents less sensitivity to the power of the measurement noise with only a very small increase in the computational complexity. A theoretical analysis demonstrates the main properties of the new algorithm. For white Gaussian input signals the RVSS presents the same performance than the original VSS in a noise free environment. Simulation results are provided, showing the better performance of the new algorithm. The RVSS should find application, for example, in telephony applications when double talking interferences are significant

This paper presents a new analytical model for the normalized least mean square (NLMS) adaptive algorithm. The new model is derived using a stochastic differential equation (SDE) approach. An accurate estimate of the steady-state weight-error correlations is also derived, which leads to an improved model performance for medium and large step sizes. Numerical simulations compare the new model with existing models and show better agreement with Monte Carlo simulations.

The paper presents an analytical model for predicting the stochastic behavior of the affine projection (AP) algorithm. The model is derived for autoregressive (AR) Gaussian inputs and for unity step size (fastest convergence). Deterministic recursive equations are presented for the mean weight and mean square error for a large number of adaptive taps, N, as compared to the algorithm order, P. The model predictions show better agreement between theory and simulations in transient and steady-state than previous models described in the literature. The learning behavior of the AP algorithm is of great interest in applications such as acoustic echo cancellation.

This work studies the Minimum Output Variance Least Mean Square Estimator (MOV-LMS) when the output of the adaptive filter is constrained by a saturation-type nonlinearity. This situation is typical in several adaptive modeling and control systems where the associated hardware and transducers have a finite power handling capability. Analytical expressions are obtained for the behaviors of the mean weight vector and for mean square error for Gaussian inputs and slow learning. The optimum leakage factor is determined, which provides an unbiased solution to the associated nonlinear mean square estimation. problem. Monte Carlo simulations show excellent agreement between model and simulations for transient and steady-state conditions. The results in this paper demonstrate that the MOV-LMS algorithm with the optimized leakage factor has a superior steady-state performance than the LMS algorithm in the studied nonlinear environment.

This work presents a new analytical model for the Normalized Least Mean Square (NLMS) algorithm for Gaussian signals and large number of coefficients. These characteristics are of special interest in applications such as echo canceling and active noise control. The new results are compared to previous models described in the literature, showing a better agreement with Monte Carlo simulations even for unit step-size (maximum convergence speed). The new results contribute to an ongoing discussion about the relative performances of the NLMS and LMS algorithms. The new model shows that both algorithms have similar performances for a large number of coefficients and properly chosen step-sizes.

This work considers the practical situation where adaptive systems are subject to a saturation nonlinearity at the output of the adaptive filter. Such is the case in active control of noise and vibration. A new adaptive algorithm is proposed which implements the true stochastic gradient approach to the nonlinear problem. Deterministic nonlinear recursions are derived which model the mean weight and mean square error behaviors. The steady-state behavior is also studied. The practical aspects of nonlinearity estimation and hardware implementation are addressed. It is shown that the new algorithm outperforms the LMS algorithm even for considerable errors in estimating the nonlinearity parameters.

This paper investigates the properties of the performance surface for a problem of nonlinear mean-square estimation of a random sequence. The problem studied has direct application to the study of active noise control (ANC) systems when the transducers are driven into nonlinear behavior. A deterministic expression is derived for the mean-square error (MSE) surface as a function of the system's degree of nonlinearity. It is shown how the presence of the nonlinearity deforms the MSE surface. It is demonstrated that the surface is unimodal, and the expression for the optimum weight vector is determined. The new results are then used to quantify the behavior of ANC systems employing the LMS adaptive algorithm. Important algorithm properties are derived from this study. Examples are presented to verify the analytical models derived.

This paper presents a statistical analysis of the multiple-error Filtered-X Least Mean Square algorithm with nonlinearities in the secondary paths. Each nonlinearity is modelled by a scaled error function that can represent the saturation behavior of the transducers and associated hardware in active noise control applications. Deterministic recursions are derived for the mean weight and mean square error behavior for white Gaussian inputs and slow adaptation. The independence theory is not used in the derivations. Monte Carlo simulations show excellent agreement with the behavior predicted by the theoretical models. The new results predict the behavior of the algorithm for different amounts of nonlinear distortion.

This paper presents a statistical analysis of the least mean square (LMS) algorithm when a zero-memory nonlinearity appears at the adaptive filter output. The nonlinearity is modelled by a scaled error function. Deterministic nonlinear recursions are derived for the mean weight and mean square error (MSE) behavior for white Gaussian inputs and slow adaptation. Monte Carlo simulations show excellent agreement with the behavior predicted by the theoretical models. The analytical results show that a small nonlinear effect has a significant impact on the converged MSE.