  Movable antenna (MA) technology is highly promising for improving
communication performance, due to its advantage of flexibly adjusting positions
of antennas to reconfigure channel conditions. In this paper, we investigate
MAs-assisted secure transmission under a legitimate transmitter Alice, a
legitimate receiver Bob and multiple eavesdroppers. Specifically, we consider a
practical scenario where Alice has no any knowledge about the instantaneous
non-line-of-sight component of the wiretap channel. Under this setup, we
evaluate the secrecy performance by adopting the secrecy outage probability
metric, the tight approximation of which is first derived by interpreting the
Rician fading as a special case of Nakagami fading and concurrently exploiting
the Laguerre series approximation. Then, we minimize the secrecy outage
probability by jointly optimizing the transmit beamforming and positions of
antennas at Alice. However, the problem is highly non-convex because the
objective includes the complex incomplete gamma function. To tackle this
challenge, we, for the first time, effectively approximate the inverse of the
incomplete gamma function as a simple linear model. Based on this
approximation, we arrive at a simplified problem with a clear structure, which
can be solved via the developed alternating projected gradient ascent (APGA)
algorithm. Considering the high complexity of the APGA, we further design
another scheme where the zero-forcing based beamforming is adopted by Alice,
and then we transform the problem into minimizing a simple function which is
only related to positions of antennas at Alice.As demonstrated by simulations,
our proposed schemes achieve significant performance gains compared to
conventional schemes based on fixed-position antennas.
