  In this paper, we investigate the design of statistically robust detectors
for multi-input multi-output (MIMO) systems subject to imperfect channel state
information (CSI). A robust maximum likelihood (ML) detection problem is
formulated by taking into consideration the CSI uncertainties caused by both
the channel estimation error and the channel variation. To address the
challenging discrete optimization problem, we propose an efficient alternating
direction method of multipliers (ADMM)-based algorithm, which only requires
calculating closed-form solutions in each iteration. Furthermore, a robust
detection network RADMMNet is constructed by unfolding the ADMM iterations and
employing both model-driven and data-driven philosophies. Moreover, in order to
relieve the computational burden, a low-complexity ADMM-based robust detector
is developed using the Gaussian approximation, and the corresponding deep
unfolding network LCRADMMNet is further established. On the other hand, we also
provide a novel robust data-aided Kalman filter (RDAKF)-based channel tracking
method, which can effectively refine the CSI accuracy and improve the
performance of the proposed robust detectors. Simulation results validate the
significant performance advantages of the proposed robust detection networks
over the non-robust detectors with different CSI acquisition methods.
