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.

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