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In a secure spatial modulation with a malicious full-duplex attacker, how toobtain the interference space or channel state information (CSI) is veryimportant for Bob to cancel or reduce the interference from Mallory. In thispaper, different from existing work with a perfect CSI, the covariance matrixof malicious interference (CMMI) from Mallory is estimated and is used toconstruct the null-space of interference (NSI). Finally, the receive beamformerat Bob is designed to remove the malicious interference using the NSI. Toimprove the estimation accuracy, a rank detector relying on Akaike informationcriterion (AIC) is derived. To achieve a high-precision CMMI estimation, twomethods are proposed as follows: principal component analysis-eigenvaluedecomposition (PCA-EVD), and joint diagonalization (JD). The proposed PCA-EVDis a rank deduction method whereas the JD method is a joint optimization methodwith improved performance in low signal to interference plus noise ratio (SINR)region at the expense of increased complexities. Simulation results show thatthe proposed PCA-EVD performs much better than the existing method like sampleestimated covariance matrix (SCM) and EVD in terms of normalized mean squareerror (NMSE) and secrecy rate (SR). Additionally, the proposed JD method has anexcellent 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.

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