  This paper aims to devise a generalized maximum likelihood (ML) estimator to
robustly detect signals with unknown noise statistics in multiple-input
multiple-output (MIMO) systems. In practice, there is little or even no
statistical knowledge on the system noise, which in many cases is non-Gaussian,
impulsive and not analyzable. Existing detection methods have mainly focused on
specific noise models, which are not robust enough with unknown noise
statistics. To tackle this issue, we propose a novel ML detection framework to
effectively recover the desired signal. Our framework is a fully probabilistic
one that can efficiently approximate the unknown noise distribution through a
normalizing flow. Importantly, this framework is driven by an unsupervised
learning approach, where only the noise samples are required. To reduce the
computational complexity, we further present a low-complexity version of the
framework, by utilizing an initial estimation to reduce the search space.
Simulation results show that our framework outperforms other existing
algorithms in terms of bit error rate (BER) in non-analytical noise
environments, while it can reach the ML performance bound in analytical noise
environments. The code of this paper is available at
https://github.com/skypitcher/manfe.
