This paper proposes a parametric-based network architecture for joint channel estimation and data detection in communications systems with hardware impairments. This architecture is composed of a data-augmented layer, a custom soft thresholding function, and several linear layers modeling the effect of channel effects and hardware impairments. In the proposed network, the soft thresholding function softly constrains the detected data to be within the considered constellation. The latter depends only on one one parameter that is optimized during training. The benefit of the proposed approach is illustrated through a communications chain corrupted by multiple impairments and noises.