Estimation of Covariance Matrix of Interference for Secure Spatial Modulation Against a Malicious Full-Duplex Attacker

Abstract

In secure spatial modulation with a malicious full-duplex attacker, how to obtain the interference subspace or channel state information (CSI) is very important for Bob to reduce or even completely cancel the interference from Mallory. In this paper, different from existing work with perfect CSI, the covariance matrix of malicious interference (CMMI) from Mallory is estimated to construct the interference subspace. To improve the estimation accuracy, a CMMI rank detector relying on the Akaike information criterion (AIC) is derived first. To achieve a high-precision CMMI estimation, two methods, principal component analysis-eigenvalue decomposition (PCA-EVD) and joint diagonalization (JD) are proposed. The proposed PCA-EVD is a rank deduction method whereas the JD method is a joint optimization method with improved performance in the low jamming-to-noise ratio (JNR) region at the expense of increased complexity. Simulation results show that the proposed PCA-EVD performs much better than existing methods like sample estimated covariance matrix (SCM) and EVD in terms of normalized mean square error (NMSE) and secrecy rate (SR). Additionally, the proposed JD has achieved a better NMSE performance than PCA-EVD in the low JNR region (JNR <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\leq$</tex-math></inline-formula> 0 dB) while the proposed PCA-EVD performs better than JD in the high JNR region.