  We study model-based end-to-end learning in the context of integrated sensing
and communication (ISAC) under hardware impairments. A monostatic orthogonal
frequency-division multiplexing (OFDM) sensing and multiple-input single-output
(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-network-based learning
approach and a strong baseline consisting of least-squares beamforming,
conventional OMP, and maximum-likelihood 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.
