Random Signal Design for Joint Communication and SAR Imaging Towards Low-Altitude Economy

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 trade-off between the communication and SAR imaging tasks. Numerical results are provided to validate the effectiveness of the proposed ISAC waveform designs for JCASAR systems.