  We in this paper introduce an advanced eavesdropper that aims to paralyze the
artificial-noise-aided secure communications. We consider the M-1-2 Gaussian
MISO wiretap channel, which consists of a M-antenna transmitter, a
single-antenna receiver, and a two-antenna eavesdropper. This type of
eavesdropper, by adopting an optimal Grassmann manifold (OGM) filtering
structure, can reduce the maximum achievable secrecy rate (MASR) to be zero by
using only two receive antennas, regardless of the number of antennas at the
transmitter. Specifically, the eavesdropper exploits linear filters to serially
recover the legitimate information symbols and intends to find the optimal
filter that minimizes the meansquare error (MSE) in estimating the symbols.
During the process, a convex semidefinite programming (SDP) problem with
constraints on the filter matrix can be formulated and solved. Interestingly,
the resulted optimal filters constitute a complex Grassmann manifold on the
matrix space. Based on the filters, a novel expression of MASR is derived and
further verified to be zero under the noiseless environment. Besides this, an
achievable variable region (AVR) that induces zero MASR is presented
analytically in the noisy case. Numerical results are provided to illustrate
the huge disaster in the respect of secrecy rate.
