A novel joint Gaussian and impulse noise denoising method for very low-frequency communication over atmospheric channel

Abstract

Very low-frequency (VLF) communication systems are significantly degraded by the non-Gaussian noise (impulsive noise+Gaussian background noise) over the atmospheric channel. Conventional noise reduction methods, which rely on Gaussian assumptions, demonstrate limited efficacy in scenarios with mixed noise distributions. Therefore, a novel noise model that applies symmetric $\alpha$-Stable (S$\alpha$S) distribution to characterize VLF noise statistics is introduced in this paper. Subsequently, to address this noisy environment, we propose a novel joint denoising algorithm named AADMF+IWTFE. The algorithm consists of two complementary stages: (1) the received signal is denoised by adaptive absolute differences median filter (AADMF) to suppress impulsive noise, which can identify the noised samples and adaptively adjust the length of sliding window, by taking advantages of the absolute differences between the filtered sample and its neighbors, then (2) the filtered received signal is further denoised by Gaussian background noise reduction based on improved wavelet threshold function with exponential factors (IWTFE), of which the optimal parameters are obtained by the recent swarm intelligence algorithm, namely population quality improvement golden jackal optimization (PQI-GJO) algorithm. In order to evaluate the performance of the proposed method on denoising VLF communication signals, minimum shift keying (MSK) signals and continuous phase modulation with prolate spheroidal wave function (CPM-PSWF) signals are used in the simulation experiments. Numerical experiments indicate that the proposed AADMF+IWTFE outperforms conventional and state-of-the-art denoising approaches with higher signal-to-noise ratio (SNR), normalized correlation coefficient (NCC), and lower mean square error (MSE).