Noncoherent ISAC over Block-Fading Channels: Asymptotic Performance Analysis

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.