Adaptive Phase-Shifted Pilot Design for Uplink Multiple Access in ISAC Systems

In uplink integrated sensing and communication (ISAC) systems, pilot signal design is crucial for enabling accurate channel estimation and reliable radar sensing. In orthogonal frequency-division multiple access (OFDMA)-based frameworks, conventional pilot allocation schemes face a trade-off between spectral efficiency (SE) and sensing performance. Interleaved pilots improve user equipment (UE) multiplexing through sparse allocation but reduce the maximum unambiguous range. Conversely, orthogonal block-based pilots reduce range ambiguity but degrade sensing resolution due to limited delay granularity. To address this trade-off, the phase-shifted ISAC (PS-ISAC) scheme was recently proposed for uplink multiple access in ISAC systems. However, PS-ISAC suffers from spectral inefficiency due to the fixed cyclic prefix (CP) constraints. To overcome these limitations, we propose adaptive phase-shifted-ISAC (APS-ISAC), an enhanced pilot scheme that employs an overlapped block-pilot structure with UE-specific phase shifts determined by maximum excess delay of each UE. This design enables UEs to share the same time-frequency resources while preserving separable and contiguous channel impulse responses (CIRs) at the base station (BS). Simulation results show that APS-ISAC significantly outperforms conventional pilot allocation methods in terms of SE, approximately doubling the number of multiplexed UEs. It also achieves lower mean square error (MSE) under power constraints with reduced complexity. Furthermore, it yields maximum range resolution and unambiguous sensing performance. These results establish APS-ISAC as a scalable, spectrally efficient, ambiguity-resilient, and low-complexity pilot design paradigm for future uplink ISAC systems.