Linear Regression-Based Channel Estimation for Non-Gaussian Noise

This work presents a novel mathematical framework of a machine learning algorithm for linear regression under non-Gaussian estimation noise. The Laplacian noise is selected as a contender for the non-Gaussian noise, as it is found in many real-world scenarios, like the differential privacy of users and as impulsive noise in wireless communication channels. In particular, we show the use-case of our analytical work in the regression-based application of wireless communication systems, specifically channel estimation. We exhibit the fundamental technique of linear regression to evaluate the wireless channel coefficients over additive Laplacian noise. In order to establish the need for the proposed framework, we illustrate a comparison between the behaviour of Gaussian and non-Gaussian noises. Furthermore, we investigate the maximum-likelihood estimator using gradient descent, the maximum a posteriori estimator, and the mean square error performances for the considered system scenario; to observe that the estimators derived under the actual non-Gaussian noise assumption yield better results as compared to those found under mathematically tractable simplified Gaussian assumption.