The paper characterizes the fundamental limits of integrated sensing and communication (ISAC) systems with a bi-static radar, where the radar receiver is located close to the transmitter and estimates or detects the state based on the transmitter's channel inputs and the backscattered signals. Two models are considered. In the first model, the memoryless state sequence is distributed according to a fixed distribution and the goal of the radar receiver is to reconstruct this state-sequence with smallest possible distortion. In the second model, the memoryless state is distributed either according to $P_S$ or to $Q_S$ and the radar's goal is to detect this underlying distribution so that the missed-detection error probability has maximum exponential decay-rate (maximum Stein exponent). Similarly to previous results, our fundamental limits show that the tradeoff between sensing and communication solely stems from the empirical statistics of the transmitted codewords which influences both performances. The main technical contribution are two strong converse proofs that hold for all probabilities of communication error $\epsilon$ and excess-distortion probability or false-alarm probability $\delta$ summing to less than 1, $\epsilon+\delta < 1$. These proofs are based on two parallel change-of-measure arguments on the sets of typical sequences, one change-of-measure to obtain the desired bound on the communication rate, and the second to bound the sensing performance.

翻译：本文刻画了双基地雷达集成感知与通信（ISAC）系统的基本极限，其中雷达接收机位于发射机附近，基于发射机的信道输入与反向散射信号进行状态估计或检测。论文考虑两种模型：第一种模型中，无记忆状态序列服从固定分布，雷达接收机的目标是以最小可能失真重构该状态序列；第二种模型中，无记忆状态分别服从$P_S$或$Q_S$分布，雷达的目标是检测该潜在分布，使得漏检错误概率具有最大指数衰减率（最大Stein指数）。与既有结论类似，本文的基本极限表明感知与通信之间的权衡完全源于传输码字的经验统计特性，该特性同时影响两项性能指标。主要技术贡献在于两个强逆定理的证明，其对满足$\epsilon+\delta < 1$的所有通信错误概率$\epsilon$与过度失真概率或虚警概率$\delta$均成立。这些证明基于典型序列集上的两组并行测度变换论证：第一组测度变换用于获得通信速率的期望界，第二组测度变换用于界定感知性能。