Joint Differentially Private Channel Estimation in Cell-free Hybrid Massive MIMO

This paper focuses on the channel estimation in cell-free hybrid massive multiple-input multiple-output (MIMO). Efficient uplink channel estimation and data detection with reduced number of pilots can be performed based on low-rank matrix completion. However, such a scheme requires the central processing unit (CPU) to collect received signals from all access points (APs), which may enable the CPU to infer the private information of user locations. We therefore develop privacy-preserving channel estimation schemes under the framework of differential privacy (DP). As the key ingredient of the channel estimator, a joint differentially private noisy matrix completion algorithm based on Frank-Wolfe iteration is presented. We provide an analysis on the tradeoff between the privacy and the channel estimation error. In particular, we characterize the scaling laws of the estimation error in terms of data payload size. Simulation results demonstrate the tradeoff between privacy and channel estimation performance, and show that the estimation error can be mitigated by increasing the payload size while keeping the pilot size fixed.