  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.
