  In this paper, we propose a novel directional modulation (DM) scheme based on
random frequency diverse arrays with artificial noise (RFDA-DM-AN) to enhance
physical layer security of wireless communications. Specifically, we first
design the RFDA-DM-AN scheme by randomly allocating frequencies to transmit
antennas, thereby achieving two-dimensionally (i.e., angle and range) secure
transmissions, and outperforming the state-of-the-art one-dimensional (i.e.,
angle) phase array (PA) based DM scheme. Then we develop the closed-form
expression of a lower bound on the ergodic secrecy capacity (ESC) of our
RFDA-DM-AN scheme. Based on the theoretical lower bound derived, we further
optimize the transmission power allocation between the useful signal and
artificial noise (AN) in order to enhance the ESC. Simulation results show that
1) our RFDA-DM-AN scheme achieves a higher secrecy capacity than that of the PA
based DM scheme, 2) the lower bound derived is shown to approach the ESC as the
number of transmit antennas N increases and precisely matches the ESC when N is
sufficiently large, and 3) the proposed optimum power allocation achieves the
highest ESC compared with other power allocations in the RFDA-DM-AN.
