Channel Estimation Using Linear Regression with Bernoulli–Gaussian Noise

This study introduces a novel mathematical framework for a machine learning algorithm tailored to address linear regression problems in the presence of non-Gaussian estimation noise. In particular, we focus on Bernoulli–Gaussian noise, which frequently occurs in practical scenarios such as wireless communication channels and signal processing systems. We apply our framework within the context of wireless systems, particularly emphasizing its utility in channel estimation tasks. This article demonstrates the efficacy of linear regression in estimating wireless channel fading coefficients under the influence of additive Bernoulli–Gaussian noise. Through comparative analysis with Gaussian noise scenarios, we underscore the indispensability of the proposed framework. Additionally, we evaluate the performance of the maximum-likelihood estimator using gradient descent, highlighting the superiority of estimators tailored to non-Gaussian noise assumptions over those relying solely on simplified Gaussian models.