Integrated sensing and communication (ISAC) has the advantages of efficient spectrum utilization and low hardware cost. It is promising to be implemented in the fifth-generation-advanced (5G-A) and sixth-generation (6G) mobile communication systems, having the potential to be applied in intelligent applications requiring both communication and high-accurate sensing capabilities. As the fundamental technology of ISAC, ISAC signal directly impacts the performance of sensing and communication. This article systematically reviews the literature on ISAC signals from the perspective of mobile communication systems, including ISAC signal design, ISAC signal processing algorithms and ISAC signal optimization. We first review the ISAC signal design based on 5G, 5G-A and 6G mobile communication systems. Then, radar signal processing methods are reviewed for ISAC signals, mainly including the channel information matrix method, spectrum lines estimator method and super resolution method. In terms of signal optimization, we summarize peak-to-average power ratio (PAPR) optimization, interference management, and adaptive signal optimization for ISAC signals. This article may provide the guidelines for the research of ISAC signals in 5G-A and 6G mobile communication systems.

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