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

TL;DR

This paper introduces methods to accurately estimate the covariance matrix of malicious interference in secure spatial modulation, enabling better interference cancellation and improving secrecy performance against a full-duplex attacker.

Contribution

It proposes PCA-EVD and joint diagonalization techniques for high-precision interference covariance estimation, outperforming existing methods especially in low SINR scenarios.

Findings

PCA-EVD outperforms SCM and EVD in NMSE and secrecy rate.

JD method excels in low SINR regions with better NMSE.

PCA-EVD performs better than JD in high SINR scenarios.

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.