Geometric Machine Learning for Channel Covariance Estimation in Vehicular Networks

Learning the covariance matrices of spatially-correlated wireless channels, in millimeter-wave (mmWave) vehicular communication, can be utilized in designing environmen-taware beamforming codebooks. Such channel covariance matrices can be represented on non-Euclidean Riemannian manifolds, thanks to their symmetric positive definite (SPD) characteristics. Consequently in this paper, we propose a Riemannian-Geometric machine learning (G-ML) approach for estimating the channel covariance matrices based on unsupervised K-Means model. The proposed K-means algorithm utilizes Log-Euclidean metric (LEM) as the distance measure among channel covariance matrices over the Riemannian manifolds. We show that our proposed K-Means G-ML model can achieve up to 80% less error compared to Euclidean-based K-Means algorithm, which applies clustering on the channel vectors themselves.