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.

MIMO Detection via Gaussian Mixture Expectation Propagation: A Bayesian Machine Learning Approach for High-Order High-Dimensional MIMO Systems

MIMO systems can simultaneously transmit multiple data streams within the same frequency band, thus exploiting the spatial dimension to enhance performance. MIMO detection poses considerable challenges due to the interference and noise introduced by the concurrent transmission of multiple streams. Efficient Uplink (UL) MIMO detection algorithms are crucial for decoding these signals accurately and ensuring robust communication. In this paper a MIMO detection algorithm is proposed which improves over the Expectation Propagation (EP) algorithm. The proposed algorithm is based on a Gaussian Mixture Model (GMM) approximation for Belief Propagation (BP) and EP messages. The GMM messages better approximate the data prior when EP fails to do so and thus improve detection. This algorithm outperforms state of the art detection algorithms while maintaining low computational complexity.