This paper proposes a parametric network for the joint compensation of multiple linear impairments in coherent optical communication systems. The considered linear impairments include both static and time-variant effects such as in-phase/quadrature (IQ) imbalance, laser phase noise (PN), chromatic dispersion (CD), polarization mode dispersion (PMD), and carrier frequency offset (CFO). To jointly compensate for these considered impairments, the proposed network is composed of parametric layers that exploit the particular signal model of each impairment. The layers’ parameters are jointly learned during a training stage. This stage uses a supervised step that exploits the knowledge of some transmitted data (preamble and/or pilots) and a self-labeling step that uses the knowledge of the symbol constellation. In addition, a new validation technique that does not require a different dataset is developed to avoid overfitting. The parametric network performance is compared to classical digital signal processing (DSP), and Deep Learning (DL) approaches using simulated data. Simulation results show that the proposed network outperforms the competing approaches in terms of Bit Error Rate (BER) while maintaining a relatively reduced computational complexity. In the scenarios considered, compared to the parametric network, the DSP approach introduces an OSNR penalty between 0.2 dB and 1.7 dB at a BER of 4×10^−3 . Furthermore, simulation results demonstrate that the proposed network is way more flexible than other approaches since it can easily be adapted to a different scenario and coupled with other techniques.