This paper investigates the fundamental limits of integrated sensing and communication (ISAC) systems with 1-bit receiver quantization. We analyze a Gaussian fading ISAC channel with separate communication and monostatic sensing links, where both communication and sensing receivers are equipped with 1-bit quantizers. When the communication channel state information (CSI) is available at the receiver, we characterize the communication-sensing capacity region of 1-bit ISAC channel and show that no trade-off exists between communication and sensing performance. In particular, both communication and sensing capacities can be simultaneously achieved by a constant-amplitude input distribution with a specific rotational symmetry. For the scenario where communication CSI is also available at the transmitter, we formulate a weighted optimization problem that balances communication and sensing rates in 1-bit ISAC channel under an average power constraint and then derive the corresponding optimal power control policy. The results demonstrate how the optimal power control policy evolves with the weighting parameter, transitioning from a communication-centric water-filling structure to a more uniform allocation as sensing becomes increasingly prioritized.

翻译：本文研究了具有1比特接收机量化的集成感知与通信（ISAC）系统的基本极限。我们分析了一个包含独立通信链路和单站感知链路的高斯衰落ISAC信道，其中通信和感知接收机均配备1比特量化器。当接收端已知通信信道状态信息（CSI）时，我们刻画了1比特ISAC信道的通信-感知容量区域，并表明通信与感知性能之间不存在折中关系。特别地，通过采用具有特定旋转对称性的恒幅输入分布，通信和感知容量可以同时达到。针对发射端也已知通信CSI的场景，我们构建了一个在平均功率约束下权衡1比特ISAC信道中通信速率与感知速率的加权优化问题，并推导了相应的最优功率控制策略。结果表明，随着感知优先级的提升，最优功率控制策略会从以通信为中心的水注填充结构逐渐演变为更均匀的功率分配。