  This paper considers a data detection problem in multiple-input
multiple-output (MIMO) communication systems with hardware impairments. To
address challenges posed by nonlinear and unknown distortion in received
signals, two learning-based detection methods, referred to as model-driven and
data-driven, are presented. The model-driven method employs a generalized
Gaussian distortion model to approximate the conditional distribution of the
distorted received signal. By using the outputs of coarse data detection as
noisy training data, the model-driven method avoids the need for additional
training overhead beyond traditional pilot overhead for channel estimation. An
expectation-maximization algorithm is devised to accurately learn the
parameters of the distortion model from noisy training data. To resolve a model
mismatch problem in the model-driven method, the data-driven method employs a
deep neural network (DNN) for approximating a-posteriori probabilities for each
received signal. This method uses the outputs of the model-driven method as
noisy labels and therefore does not require extra training overhead. To avoid
the overfitting problem caused by noisy labels, a robust DNN training algorithm
is devised, which involves a warm-up period, sample selection, and loss
correction. Simulation results demonstrate that the two proposed methods
outperform existing solutions with the same overhead under various hardware
impairment scenarios.
