Movable Antenna-Aided Cooperative ISAC Network With Time Synchronization Error and Imperfect CSI

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Abstract
Cooperative-integrated sensing and communication (C-ISAC) networks have emerged as promising solutions for communication and target sensing. However, imperfect channel state information (CSI) estimation and time synchronization (TS) errors degrade performance, affecting communication and sensing accuracy. This paper addresses these challenges by employing movable antennas (MAs) to enhance C-ISAC robustness. We analyze the impact of CSI errors on achievable rates and introduce a hybrid Cramer-Rao lower bound (HCRLB) to evaluate the effect of TS errors on target localization accuracy. Based on these models, we derive the worst-case achievable rate and sensing precision under such errors. We optimize cooperative beamforming, base station (BS) selection factor and MA position to minimize power consumption while ensuring accuracy. We then propose a constrained deep reinforcement learning (C-DRL) approach to solve this non-convex optimization problem, using a modified deep deterministic policy gradient (DDPG) algorithm with a Wolpertinger architecture for efficient training under complex constraints. To the best of our knowledge, this is the first work that jointly integrates TS errors and imperfect CSI into a unified MA-aided cooperative ISAC framework, providing a physically consistent model for both communication and sensing under dual uncertainties. Simulation results show that the proposed method significantly improves system robustness against CSI and TS errors, where robustness mean reliable data transmission under poor channel conditions. These findings demonstrate the potential of MA technology to reduce power consumption in imperfect CSI and TS environments.
Funding Information
  • National Natural Science Foundation of China (61871070)
  • National Natural Science Foundation of China (61831004)
  • National Natural Science Foundation of China (62203451)
  • National Natural Science Foundation of China (91938202)
  • National Science and Technology Major Project of China (2025ZD1302000)

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