[Paper Review] Simulation and Performance Analysis of Adaptive Filtering Algorithms in Noise Cancellation

Lilatul Ferdouse, Nasrin Akhter+2 more|arXiv (Cornell University)|Apr 11, 2011

Advanced Adaptive Filtering TechniquesEngineering9 references22 citations

TL;DR

This paper proposes a comparative simulation study of three adaptive filtering algorithms—Recursive Least Square (RLS), Fast Transversal RLS (FTRLS), and Gradient Adaptive Lattice (GAL)—for noise cancellation in communication systems. It demonstrates that GAL outperforms RLS and FTRLS in convergence speed, signal-to-noise ratio (SNR), and correlation coefficient, establishing GAL as the most effective algorithm under the evaluated performance criteria.

ABSTRACT

Noise problems in signals have gained huge attention due to the need of noise-free output signal in numerous communication systems. The principal of adaptive noise cancellation is to acquire an estimation of the unwanted interfering signal and subtract it from the corrupted signal. Noise cancellation operation is controlled adaptively with the target of achieving improved signal to noise ratio. This paper concentrates upon the analysis of adaptive noise canceller using Recursive Least Square (RLS), Fast Transversal Recursive Least Square (FTRLS) and Gradient Adaptive Lattice (GAL) algorithms. The performance analysis of the algorithms is done based on convergence behavior, convergence time, correlation coefficients and signal to noise ratio. After comparing all the simulated results we observed that GAL performs the best in noise cancellation in terms of Correlation Coefficient, SNR and Convergence Time. RLS, FTRLS and GAL were never evaluated and compared before on their performance in noise cancellation in terms of the criteria we considered here.

Motivation & Objective

• To evaluate and compare the performance of adaptive filtering algorithms in real-time noise cancellation applications.
• To analyze convergence behavior, convergence time, correlation coefficients, and signal-to-noise ratio (SNR) across different algorithms.
• To identify the most effective algorithm for noise cancellation based on quantitative performance metrics.
• To provide a novel comparative analysis of RLS, FTRLS, and GAL—previously untested together—under identical simulation conditions.

Proposed method

• The study employs a standard adaptive noise cancellation framework where the primary input contains the desired signal corrupted by noise, and the reference input captures the noise component.
• Three adaptive filtering algorithms—RLS, FTRLS, and GAL—are implemented and simulated using MATLAB for consistent performance evaluation.
• The algorithms iteratively update filter coefficients to minimize the error between the estimated and actual noise, using recursive least squares and lattice-based gradient adaptation.
• Performance is evaluated using four key metrics: convergence time, SNR improvement, correlation coefficient between original and estimated signals, and mean square error (MSE) reduction.
• All simulations are conducted under identical signal and noise conditions to ensure fair comparison across algorithms.
• The results are analyzed and compared quantitatively to determine the best-performing algorithm in terms of speed, accuracy, and noise suppression.

Experimental results

Research questions

• RQ1 Which adaptive filtering algorithm—RLS, FTRLS, or GAL—achieves the fastest convergence in noise cancellation?
• RQ2 How do RLS, FTRLS, and GAL compare in terms of signal-to-noise ratio (SNR) improvement?
• RQ3 What is the correlation coefficient between the original clean signal and the output of each algorithm, and which performs best?
• RQ4 How does the computational complexity of each algorithm influence its performance in real-time applications?

Key findings

• The Gradient Adaptive Lattice (GAL) algorithm achieved the highest correlation coefficient between the original and estimated signals, indicating superior signal reconstruction.
• GAL demonstrated the fastest convergence time among the three algorithms, reducing the error to near-minimum levels more quickly than RLS and FTRLS.
• GAL provided the highest signal-to-noise ratio (SNR) improvement, confirming its effectiveness in enhancing signal quality.
• RLS and FTRLS showed slower convergence and lower SNR gains compared to GAL, despite their established performance in other contexts.
• The study confirms that GAL outperforms RLS and FTRLS in noise cancellation when evaluated on convergence speed, SNR, and correlation coefficient.
• This is the first comparative evaluation of RLS, FTRLS, and GAL using these specific performance criteria, revealing GAL as the optimal choice under the tested conditions.