  In this paper, we investigate the anti-jamming problem of a directional
modulation (DM) system with the aid of intelligent reflecting surface (IRS). As
an efficient tool to combat malicious jamming, receive beamforming (RBF) is
usually designed to be on null-space of jamming channel or covariance matrix
from Mallory to Bob. Thus, it is very necessary to estimate the receive jamming
covariance matrix (JCM) at Bob. To achieve a precise JCM estimate, three JCM
estimation methods, including eigenvalue decomposition (EVD), parametric
estimation method by gradient descend (PEM-GD) and parametric estimation method
by alternating optimization (PEM-AO), are proposed. Here, the proposed EVD is
under rank-2 constraint of JCM. The PEM-GD method fully explores the structure
features of JCM and the PEM-AO is to decrease the computational complexity of
the former via dimensionality reduction. The simulation results show that in
low and medium jamming-noise ratio (JNR) regions, the proposed three methods
perform better than the existing sample covariance matrix method. The proposed
PEM-GD and PEM-AO outperform EVD method and existing clutter and disturbance
covariance estimator RCML.
