Channel Estimation for Massive MIMO Uplink Under Active Jamming Attack

Abstract

We consider channel estimation (CE) against jamming attack (JA) in a single cell massive multiple-input–multiple-output (MIMO) system, wherein malicious users (MUs) want to beguile the base station (BS) into obtaining false channel state information. The MUs perform JA in uplink by sending jamming symbols to the BS through pilot and data transmission of the legitimate users (LUs). Especially, its employed active JA strategies include 1) sending the jamming symbols according to arbitrary distributions that are unknown to the BS; and 2) sending the jamming symbols that are correlative to those of the LUs. We analyze the empirical distribution of the uplink received signals (ED-RS), and prove that its characteristic function (CF) asymptotically approaches to the product of the CFs of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">desired signal</i> (DS) and the noise, where the DS is the product of the channel matrix and the signal sequences sent by the LUs/MUs. Motivated by the proof, our proposed extractor first estimates the CF of DS from the ED-RS and then extracts the alphabet of the DS. The extracted alphabet includes linear combinations of channel vectors of LUs and MUs, which leads to CE from the alphabet decomposition. Both analysis and simulation confirm that the proposed CE achieves good performance.