Optimal Allocation of Auxiliary Designated Sensor for Opportunistic Rain Field Reconstruction

Two-dimensional (2-D) field reconstruction presents a challenge in opportunistic Integrated Sensing and Communication (ISAC), where weather phenomena, such as rain fields or humidity, are sensed and mapped through their effect on wireless communication. In this paper, we analyze the inherent limitations in reconstruction accuracy by deriving the Bayesian Cramér-Rao Bound (BCRB) for field mapping modeled by 2-D B-splines for two sensor types: line (e.g., commercial microwave links) and point (e.g., rain gauges) sensors. In particular, we utilize this bound to optimize the allocation of additional designated point sensors within an existing, given opportunistic sensor network, where sensors are randomly located.