Bistatic Integrated Sensing and Communication over Memoryless Relay Channels

A relay-aided bistatic integrated sensing and communication (ISAC) system is considered, where the destination concurrently decodes a message and estimates unknown state parameters from its received signals. This system is modeled by a generalized state-dependent relay channel. Its fundamental limits of the communication-sensing performance tradeoff, characterized by the capacity-distortion function, are established. Specifically, an upper bound on the capacity-distortion function extending the cutset bound for relay channels to address the state estimation at the destination is developed. Additionally, a hybrid partial-decode-and-compress-forward coding scheme is proposed to facilitate source-relay cooperation for both message transmission and state estimation, establishing a lower bound on the capacity-distortion function. It is found that partial-decode-and-compress-forward scheme achieves optimal sensing performance when the communication task is ignored. Furthermore, the upper and lower bounds are shown to coincide for some special classes of channels. Two numerical examples are provided to illustrate the communication-sensing tradeoff in the considered ISAC system.