Privacy-preserving Channel Estimation in Cell-free Hybrid Massive MIMO Systems

TL;DR

This paper proposes privacy-preserving channel estimation methods for cell-free hybrid massive MIMO systems using differential privacy, balancing privacy guarantees with estimation accuracy through novel algorithms and theoretical analysis.

Contribution

It introduces two differentially private matrix completion algorithms for channel estimation, analyzing the privacy-error tradeoff and providing scaling laws for system performance.

Findings

Privacy-error tradeoff characterized mathematically

Estimation error can be reduced by increasing payload size

Simulation confirms the theoretical tradeoff analysis

Abstract

We consider a cell-free hybrid massive multiple-input multiple-output (MIMO) system with $K$ users and $M$ access points (APs), each with $N_a$ antennas and $N_r< N_a$ radio frequency (RF) chains. When $K\ll M{N_a}$, 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 APs, which may enable the CPU to infer the private information of user locations. We therefore develop and analyze privacy-preserving channel estimation schemes under the framework of differential privacy (DP). As the key ingredient of the channel estimator, two joint differentially private noisy matrix completion algorithms based respectively on Frank-Wolfe iteration and singular value decomposition are presented. We provide an analysis on the tradeoff between the privacy and the channel estimation error. In particular, we show that the estimation error can be mitigated while maintaining the same privacy level by increasing the payload size with fixed pilot size; and the scaling laws of both the privacy-induced and privacy-independent error components in terms of payload size are characterized. Simulation results are provided to further demonstrate the tradeoff between privacy and channel estimation performance.