Joint Channel Estimation and User Activity Detection for mmWave Grant-Free Massive MTC Networks under Pilot Contamination Attack

Due to the lack of authentication, millimeter-wave (mmWave) grant-free massive machine-type communication (GFmMTC) networks are vulnerable to the pilot contamination attack (PCA), which will cause serious performance degradation of channel estimation (CE) and active user detection (AUD). However, the existing works towards the PCA detection in the mmWave GFmMTC networks perform the CE, AUD, and PCA detection through two separated phases, which will limit the system performance. To solve the problem, in this paper, we establish a three-dimensional transmission model with time-correlated two-dimensional sparsity for both legitimate users (LUs) and attackers in mmWave GFmMTC networks, where the LU and attacker activity sparsity, the virtual angular channel sparsity, and the temporal correlation of L U activity are jointly considered. Based on the established transmission model, a three-dimensional multiple measurement vector-compressive sensing (MMV-CS) based joint CE and AUD scheme against PCA is proposed. Specifically, we first formulate the joint CE and AUD under PCA as a three-dimensional MMV-CS problem. Then, by utilizing the sparsity of user activity and angular virtual channel, we develop a parallel expectation-maximization vector approximate message passing with MMV (Parallel EM- VAMP-MMV) algorithm to efficiently solve the formulated problem. Simulation results show that the proposed scheme can achieve a substantial performance gain over comparison methods.