  Conventional synthetic aperture radar (SAR) imaging systems typically employ
deterministic signal designs, which lack the capability to convey communication
information and are thus not suitable for integrated sensing and communication
(ISAC) scenarios. In this letter, we propose a joint communication and SAR
imaging (JCASAR) system based on orthogonal frequency-division multiplexing
(OFDM) signal with cyclic prefix (CP), which is capable of reconstructing the
target profile while serving a communication user. In contrast to traditional
matched filters, we propose a least squares (LS) estimator for range profiling.
Then the SAR image is obtained followed by range cell migration correction
(RCMC) and azimuth processing. By minimizing the mean squared error (MSE) of
the proposed LS estimator, we investigate the optimal waveform design for SAR
imaging, and JCASAR under random signaling, where power allocation strategies
are conceived for Gaussian-distributed ISAC signals, in an effort to strike a
flexible performance tradeoff between the communication and SAR imaging tasks.
Numerical results are provided to validate the effectiveness of the proposed
ISAC waveform design for JCASAR systems.
