We study model-based end-to-end learning in the context of integrated sensing and communication (ISAC) under hardware impairments. A monostatic orthogonal frequencydivision multiplexing (OFDM) sensing and multiple-input singleoutput (MISO) communication scenario is considered, incorporating hardware imperfections at the ISAC transceiver antenna array. To enable end-to-end learning of the ISAC transmitter and sensing receiver, we propose a novel differentiable version of the orthogonal matching pursuit (OMP) algorithm that is suitable for multi-target sensing. Based on the differentiable OMP, we devise two model-based parameterization strategies to account for hardware impairments: (i) learning a dictionary of steering vectors for different angles, and (ii) learning the parameterized hardware impairments. For the single-target case, we carry out a comprehensive performance analysis of the proposed model-based learning approaches, a neural-networkbased learning approach and a strong baseline consisting of least-squares beamforming, conventional OMP, and maximumlikelihood symbol detection for communication. Results show that learning the parameterized hardware impairments offers higher detection probability, better angle and range estimation accuracy, lower communication symbol error rate (SER), and exhibits the lowest complexity among all learning methods. Lastly, we demonstrate that learning the parameterized hardware impairments is scalable also to multiple targets, revealing significant improvements in terms of ISAC performance over the baseline.Index Terms-Hardware impairments, integrated sensing and communication (ISAC), joint communication and sensing (JCAS), machine learning, model-based learning, orthogonal matching pursuit (OMP). I. INTRODUCTIONN EXT-generation wireless communication systems are expected to operate at higher carrier frequencies to meet the data rate requirements necessary for emerging use cases such as smart cities, e-health, and digital twins for manufacturing [1]-[4]. Higher carrier frequencies also enable new functionalities, such as integrated sensing and communication (ISAC).

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Integrated sensing and communication (ISAC) aims to unify radar and communication systems through a combination of joint hardware, joint waveforms, joint signal design, and joint signal processing. At high carrier frequencies, where ISAC is expected to play a major role, joint designs are challenging due to several hardware limitations. Model-based approaches, while powerful and flexible, are inherently limited by how well the models represent reality. Under model deficit, data-driven methods can provide robust ISAC performance. We present a novel approach for data-driven ISAC using an auto-encoder (AE) structure. The approach includes the proposal of the AE architecture, a novel ISAC loss function, and the training procedure. Numerical results demonstrate the power of the proposed AE, in particular under hardware impairments.