Scaling Law Tradeoff Between Throughput and Sensing Distance in Large ISAC Networks

In this paper, we investigate the fundamental tradeoff between communication and sensing performance of \emph{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. Under the pure path loss channel gain model and the condition that the transmission power scales according to the communication distance, we fully characterize the optimal scaling law tradeoff between throughput and sensing distance by proposing an achievable scheme and proving its converse. Our results can be interpreted as follows: 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 prove that the same result also holds true for ISAC networks with random fading, despite the uncertainty on the connectivity and power level created by random fading. In addition, we show that the scaling law tradeoff cannot be improved by allowing the transmission power and communication distance to scale freely. To the best of our knowledge, this is the first work formally formulating and characterizing the communication and sensing performance scaling law tradeoff of \emph{ad hoc} ISAC networks.