Coordinated Transmit Beamforming for Networked ISAC With Imperfect CSI and Time Synchronization

This paper studies a networked integrated sensing and communication (ISAC) system, where distributed base stations (BSs) implement coordinated transmit beamforming to communicate with their respective user and cooperatively perform multi-static target sensing. To fully reap the performance gains provided by the networked ISAC system, accurate channel state information (CSI) and time synchronization (TS) among distributed BSs are crucial. However, CSI errors and TS errors are inevitable in practice due to the imperfect channel training and the inaccurate synchronization. To reveal the effect of CSI errors on communication, a Gaussian distributed CSI error model is formulated based on the channel estimation process, and accordingly, the users’ achievable rates with CSI errors are derived. To characterize the effect of TS errors on multi-static sensing, the Cramér-Rao lower bound (CRLB) for estimating target position in the presence of TS errors is derived. It is shown that due to the existence of CSI errors and TS errors, additional terms are introduced in the achievable rate and CRLB formulas, degrading the communication and sensing performance, respectively. Based on the above derivations, we aim at maximizing the sum-rate of users by designing the coordinated transmit beamforming at the BSs, while guaranteeing the CRLB requirements for target sensing. In particular, we consider two cases with and without TS errors, for which the corresponding non-convex optimization problems are solved via a penalty-based algorithm and an alternating optimization algorithm, respectively. Simulation results show that the proposed algorithms significantly outperform benchmark schemes for both cases with and without CSI/TS errors, thus validating the robustness in ISAC performance optimization.