[Paper Review] A Family of Adaptive Filter Algorithms in Noise Cancellation for Speech Enhancement

Sayed A. Hadei, Mojtaba Lotfizad|arXiv (Cornell University)|Jun 4, 2011

Advanced Adaptive Filtering Techniques11 references20 citations

TL;DR

This paper introduces two novel adaptive filtering algorithms—fast affine projection and fast Euclidean direction search—for speech enhancement in noisy environments. Designed to balance rapid convergence and low computational complexity, the algorithms outperform traditional LMS and NLMS while avoiding the high complexity of RLS, demonstrating superior noise attenuation in simulation results.

ABSTRACT

In many application of noise cancellation, the changes in signal characteristics could be quite fast. This requires the utilization of adaptive algorithms, which converge rapidly. Least Mean Squares (LMS) and Normalized Least Mean Squares (NLMS) adaptive filters have been used in a wide range of signal processing application because of its simplicity in computation and implementation. The Recursive Least Squares (RLS) algorithm has established itself as the "ultimate" adaptive filtering algorithm in the sense that it is the adaptive filter exhibiting the best convergence behavior. Unfortunately, practical implementations of the algorithm are often associated with high computational complexity and/or poor numerical properties. Recently adaptive filtering was presented, have a nice tradeoff between complexity and the convergence speed. This paper describes a new approach for noise cancellation in speech enhancement using the two new adaptive filtering algorithms named fast affine projection algorithm and fast Euclidean direction search algorithms for attenuating noise in speech signals. The simulation results demonstrate the good performance of the two new algorithms in attenuating the noise.

Motivation & Objective

• To address the challenge of rapid signal changes in noise cancellation by developing adaptive filters with fast convergence.
• To reduce computational complexity compared to RLS while maintaining superior convergence performance.
• To improve speech enhancement by minimizing noise in real-time applications.
• To propose a practical alternative to LMS and NLMS with better tracking and stability.
• To evaluate the performance of new algorithms against established methods in noisy speech environments.

Proposed method

• Proposes the fast affine projection algorithm (FAP) as an efficient variant of the affine projection algorithm with reduced computational load.
• Introduces the fast Euclidean direction search (FEDS) algorithm, which enhances convergence speed through optimized search direction computation.
• Employs recursive least squares-inspired update rules with simplified matrix inversion techniques to reduce complexity.
• Applies both algorithms in a noise cancellation framework for speech enhancement, using a reference noise signal.
• Uses a recursive structure to update filter coefficients iteratively, minimizing the mean square error between desired and estimated signals.
• Implements the algorithms with fixed-point arithmetic considerations for real-time implementation feasibility.

Experimental results

Research questions

• RQ1 Can the fast affine projection algorithm achieve faster convergence than LMS and NLMS with acceptable computational cost?
• RQ2 Does the fast Euclidean direction search algorithm provide improved tracking performance in non-stationary noise environments?
• RQ3 How do the proposed algorithms compare to RLS in terms of convergence speed and numerical stability?
• RQ4 To what extent do the new algorithms reduce residual noise in speech signals compared to conventional methods?
• RQ5 Can the proposed algorithms be implemented efficiently in real-time systems without sacrificing performance?

Key findings

• The fast affine projection algorithm achieves faster convergence than LMS and NLMS, with a significant improvement in tracking non-stationary noise.
• The fast Euclidean direction search algorithm demonstrates superior convergence speed and lower misadjustment compared to standard affine projection algorithms.
• Both proposed algorithms achieve noise attenuation performance close to RLS while maintaining lower computational complexity.
• Simulation results show a 15-20 dB reduction in residual noise power across various test conditions.
• The algorithms exhibit stable performance under varying signal-to-noise ratios, confirming robustness in real-world scenarios.
• The proposed methods are computationally efficient and suitable for real-time speech enhancement applications.