On the Scaling Law Tradeoff of Integrated Sensing and Communication Networks

In this paper, we investigate the communication and sensing performance tradeoff of ad hoc integrated sensing and communication (ISAC) wireless networks. Specifically, we consider that $n$ nodes are randomly located in an extended network with area $n$ and transmit ISAC signals. Our goal is to answer the following questions: what is the tradeoff between the throughput and sensing range of an ISAC network and how does it scale with the network size or node numbers? Under the condition that the transmission power scales according to the communication distance, we fully characterize the scaling law tradeoff between throughput and sensing distance by proposing an achievable scheme and proving its converse. Interestingly, our results reveal that by reducing the throughput by a factor of a function of $n$, the sensing range order improves according to the same function of $n$, raised to the power of the ratio between the path loss factors in communication and sensing. We also show that the scaling law tradeoff cannot be improved by allowing the transmission power and communication distance to scale differently. To the best of our knowledge, this is the first work formally formulating and characterizing the communication and sensing performance scaling law tradeoff of ad hoc ISAC networks.