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, opportunistic transmission 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。我们分析了一个高斯衰落ISAC信道，其中包含独立的通信链路和单站感知链路，且两条链路的接收机均配备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，并证明了通信与感知性能之间不存在权衡关系。特别地，通过一种具有特定旋转对称性的恒幅输入分布，通信容量与感知容量可同时达到。针对发射端亦已知通信CSI的情形，我们在平均功率约束下构建了一个加权优化问题以平衡1比特ISAC信道中的通信与感知速率，并推导出相应的最优功率控制策略。结果表明，最优功率控制策略随权重参数变化而演进：从以通信为中心的机遇式传输，逐步过渡到随感知优先级提升而趋于均匀分配的传输模式。