Efficient Channel Prediction based on Gram-Square-Root Factorization using GMMs

Accurate channel state information (CSI) is critical for downlink (DL)-multi-user (MU)-multiple-input multiple-output (MIMO) systems, where feedback delays and mobility can degrade precoding performance. To ensure reliable beamforming and interference mitigation, CSI prediction is required. In practical systems, full CSI feedback is often infeasible due to signaling overhead, so transmitters rely on partial CSI reported by the receivers. In this work, we propose a Gaussian mixture model (GMM)-based prediction framework for MIMO-orthogonal frequency-division multiplexing (OFDM) channels under partial feedback using Gram-square-root factorization. To address the high dimensionality, we introduce an efficient parameter reduction technique that exploits structured covariance matrices, significantly lowering complexity without noticeable performance degradation. This reduction is based on the Gram-square-root factorization and remains of interest even when full CSI is available. Simulation results demonstrate that GMMs achieve the highest prediction accuracy and correctly capture the underlying channel subspaces, which is essential for effective MU-precoding. The proposed method outperforms classical baselines such as zero-order hold (ZOH), first-order hold (FOH), and linear minimum mean squared error (LMMSE) predictors, and an advanced neural network (NN)-based predictor. Notably, the parameter-reduced partial CSI GMM achieves performance comparable to that of full CSI prediction, highlighting its ability to efficiently model the channel structure under limited feedback.