This paper investigates the fundamental limits and optimal signal distribution design for Integrated Sensing and Communication (ISAC) systems operating under strictly noncoherent conditions. Unlike conventional coherent frameworks that rely on perfect channel state information, we consider a block-fading MIMO channel where the channel realizations are unknown to both the transmitter and the receiver. We adopt a realization-wise perspective to characterize the noncoherent performance tradeoff across different signal-to-noise ratio (SNR) regimes. In the high-SNR regime, we derive a lower bound for the noncoherent mutual information and define a metric, termed sensing-induced rate loss, to quantify the communication penalty incurred by sensing-oriented beamforming. We then employ a projected gradient algorithm to optimize the spatial power allocation, balancing the conflict between the unitary space-time modulation-based structure for communication and the task-oriented spatial power allocation for sensing. Conversely, in the low-SNR regime, we perform a first-order asymptotic analysis of the ergodic minimum mean squared error (EMMSE). Our theoretical derivation reveals a fundamental synergy: the sensing-optimal strategy collapses to a rank-one transmission along the dominant eigenvector of the target response, which incurs no first-order communication loss in the low-SNR regime. This result demonstrates that the conflicting tradeoff observed at high SNR vanishes asymptotically at low SNR, enabling perfect alignment between sensing and communication objectives.

翻译：本文研究了在严格非相干条件下工作的集成感知与通信系统的基本极限及最优信号分布设计。与依赖完美信道状态信息的传统相干框架不同，我们考虑发射机和接收机均未知信道实现的块衰落MIMO信道，并从实现角度刻画不同信噪比区间下的非相干性能权衡。在高信噪比区间，我们推导了非相干互信息的下界，并定义了一个名为"感知诱导速率损失"的度量，以量化面向感知的波束赋形带来的通信代价。随后采用投影梯度算法优化空间功率分配，平衡基于酉空时调制的通信结构与面向感知的任务导向空间功率分配之间的冲突。相反，在低信噪比区间，我们对遍历最小均方误差（EMMSE）进行了一阶渐近分析。理论推导揭示了一个基本协同效应：感知最优策略退化为沿目标响应主特征向量的秩-1传输，这在低信噪比区间不会引起一阶通信损失。该结果表明，在高信噪比下观察到的冲突权衡在低信噪比下渐近消失，使得感知与通信目标能够完美对齐。