Estimation of Covariance Matrix of Interference for Secure Spatial Modulation against a Malicious Full-duplex Attacker

Abstract: In a secure spatial modulation with a malicious full-duplex attacker, how to obtain the interference space or channel state information (CSI) is very important for Bob to cancel or reduce the interference from Mallory. In this paper, different from existing work with a perfect CSI, the covariance matrix of malicious interference (CMMI) from Mallory is estimated and is used to construct the null-space of interference (NSI). Finally, the receive beamformer at Bob is designed to remove the malicious interference using the NSI. To improve the estimation accuracy, a rank detector relying on Akaike information criterion (AIC) is derived. To achieve a high-precision CMMI estimation, two methods are proposed as follows: principal component analysis-eigenvalue decomposition (PCA-EVD), and joint diagonalization (JD). The proposed PCA-EVD is a rank deduction method whereas the JD method is a joint optimization method with improved performance in low signal to interference plus noise ratio (SINR) region at the expense of increased complexities. Simulation results show that the proposed PCA-EVD performs much better than the existing method like sample estimated covariance matrix (SCM) and EVD in terms of normalized mean square error (NMSE) and secrecy rate (SR). Additionally, the proposed JD method has an excellent NMSE performance better than PCA-EVD in the low SINR region (SINR < 0dB) while in the high SINR region PCA-EVD performs better than JD.