The problem of bistatic integrated sensing and communications over memoryless relay channels is considered, where destination concurrently decodes the message sent by the source and estimates unknown parameters from received signals with the help of a relay. A state-dependent discrete memoryless relay channel is considered to model this setup, and the fundamental limits of the communication-sensing performance tradeoff are characterized by the capacity-distortion function. An upper bound on the capacity-distortion function is derived, extending the cut-set bound results to address the sensing operation at the destination. A hybrid-partial-decode-and-compress-forward coding scheme is also proposed to facilitate source-relay cooperation for both message transmission and sensing, establishing a lower bound on the capacity-distortion function. It is found that the hybrid-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 three specific classes of relay channels. Numerical examples are provided to illustrate the communication-sensing tradeoff and demonstrate the benefits of integrated design.

翻译：本文研究了双工记忆中继信道下的集成感知与通信问题，其中目的节点在协助下同时解码源节点发送的信息并从接收信号中估计未知参数。采用状态相关的离散无记忆中继信道对该场景进行建模，并通过容量-失真函数刻画通信-感知性能权衡的基本极限。本文推导了容量-失真函数的上界，将割集界结果扩展至目的节点的感知操作。同时提出了一种混合部分解码压缩转发编码方案，以促进源-中继在信息传输与感知两方面的协作，从而建立了容量-失真函数的下界。研究发现，当忽略通信任务时，混合部分解码压缩转发方案可实现最优感知性能。此外，针对三类特定中继信道，证明了所提上下界是重合的。数值算例展示了通信-感知权衡关系，并验证了集成设计的优势。