Large random matrix-based channel estimation for massive MIMO-OFDM uplink

This study investigates the benefits offered by random matrix theory (RMT) towards the design of reliable channel estimation algorithms for a multi-user massive multiple-input multiple-out (MIMO)-orthogonal frequency-division multiplexing uplink. Assuming no a priori knowledge of channel statistics (KCS) at the massive base station, the authors propose RMT-aided minimum mean square estimation (MMSE) and RMT-aided sparse Bayesian learning (SBL) approaches for massive channel estimation. These approaches render efficient channel estimates, as illustrated through mean square error (MSE) performance, extracted via Monte-Carlo simulations. The results also show that with increasing antennas at the base station, MSE from the RMT-aided MMSE approach decreases, suggesting its aptness to massive MIMO systems. To further enhance the MSE performance, the MMSE and SBL estimated channel impulse responses are pruned using threshold computed from RMT analysis. The authors characterise MSE degradation due to the randomness in the threshold, with the help of the Marcenko-Pastur law-based non-asymptotic framework and concentration inequalities. Analysis results show that, for channels with approximate sparse common support, this MSE degradation is quite insignificant. Altogether, the study demonstrates that RMT analysis is competent in improving channel estimation at a massive MIMO system, when a priori KCS is completely unavailable.