Deep Learning Based Channel Estimator for Non-gaussian Channel Statistics

This study addresses MMSE channel estimation in OFDM systems where Maximal Ratio Transmitter (MRT) beamforming induces non-Gaussian, Square-Root Gamma (SR-Gamma) channel statistics, making the conventional LMMSE sub-optimal. Since the multivariate SR-Gamma prior is analytically intractable, we develop a neural network (NN)-based estimator which outperforms LMMSE in the practical, correlated setting. Our core contribution is the analytical treatment of the one-dimensional MMSE estimator under the SR-Gamma prior. This includes the derivations of prior distribution, the general n-th order raw moment formula, an exact, non-asymptotic expression for the scalar MMSE estimator, a recurrence relation for one-sided Gaussian integrals for efficient computation, and the Bayesian Cramér–Rao Lower Bound (Van Trees). We also characterize the estimator’s low- and high-SNR asymptotic behavior. Simulation results confirm the estimator’s MSE tightly matches the theoretical Van Trees bound, validating our analytical framework.