Noncoherent ISAC over Block-Fading Channels: Asymptotic Performance Analysis

2026-06-12

AI Summary

This work addresses the fundamental trade-off between sensing and communication performance in integrated sensing and communication (ISAC) systems under non-coherent conditions where channel state information is unavailable at both transmitter and receiver. By jointly designing sensing-aware beamforming and communication modulation through optimized spatial power allocation, the study conducts asymptotic performance analysis across high and low signal-to-noise ratio (SNR) regimes. Leveraging a lower bound on non-coherent mutual information, a sensing-induced rate loss metric, and a projected gradient algorithm, the paper quantifies the communication rate penalty due to sensing at high SNR and optimizes beamforming accordingly. Notably, it proves that at low SNR, sensing and communication objectives can be perfectly aligned, achieving zero first-order communication performance loss—thereby revealing a fundamental dichotomy and synergistic potential between the two functions across different SNR regimes.

Abstract

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.

Problem

• Integrated Sensing and Communication
• Noncoherent
• Block-Fading Channels
• Performance Tradeoff
• Channel State Information

Innovation

• Noncoherent ISAC
• Block-fading channels
• Sensing-induced rate loss
• Asymptotic analysis
• Spatial power allocation