Noise Reduction in Differential Phase Shift Keying Modulator Using Recursive Least Square Filter

Abstract

This study investigates the performance enhancement of Differential Phase Shift Keying (DPSK) commu‐ nication systems under noisy channel conditions using an adaptive filtering method, specifically the Recursive Least Squares (RLS) approach. The primary objective is to mitigate interference and improve signal integrity in real‐time applications where additive white Gaussian noise (AWGN) degrades performance. DPSK signals were mathematically modelled, considering phase shifts of 0° and 180° for binary encoding, and transmitted through simulated noisy channels with input SNRs ranging from 0 to 20 dB. A model‐based design framework in MATLAB was employed to implement the RLS filter, which recursively updates its coefficients to minimise the mean square error between the received and estimated signals. Performance was quantitatively evaluated using Bit Error Rate (BER), Signal‐to‐Noise Ratio (SNR), and spectral efficiency metrics. Results indicate that the RLS filter achieved a maximum noise reduction of 8 dB at 0 dB input SNR and consistently outperformed conventional Butterworth filters. At a critical SNR of 10 dB, the DPSK‐RLS system reduced noise by 75%, compared to 25.2% and 41.2% reported by Ofeogbu et al. (2022) and Liang et al. (2023), respectively, and increased spectral efficiency from 1.15 to 3.45 bps/Hz. Stability and convergence analyses using Lyapunov functions confirmed reliable real‐time adaptation. The proposed method demonstrates a robust and adaptive solution for high‐reliability communication systems, ensuring superior error mitigation, improved SNR, and enhanced bandwidth utilisation, providing practical guidance for deploying adaptive filtering in modern digital communication networks. Also adaptive recursive least square filter reduces mean squared errors from 0.25v 2 to 0.01v 2 significantly outperforming traditional fixed filters like Butter‐ work.