  In this paper, given the beamforming vector of confidential messages and
artificial noise (AN) projection matrix and total power constraint, a power
allocation (PA) strategy of maximizing secrecy rate (Max-SR) is proposed for
secure directional modulation (DM) networks. By the method of Lagrange
multiplier, the analytic expression of the proposed PA strategy is derived. To
confirm the benefit from the Max-SR-based PA strategy, we take the null-space
projection (NSP) beamforming scheme as an example and derive its closed-form
expression of optimal PA strategy. From simulation results, we find the
following facts: in the medium and high signal-to-noise-ratio (SNR) regions,
compared with three typical PA parameters such $\beta=0.1, 0.5$, and $0.9$, the
optimal PA shows a substantial SR performance gain with maximum gain percent up
to more than $60\%$. Additionally, as the PA factor increases from 0 to 1, the
achievable SR increases accordingly in the low SNR region whereas it first
increases and then decreases in the medium and high SNR regions, where the SR
can be approximately viewed as a convex function of the PA factor. Finally, as
the number of antennas increases, the optimal PA factor becomes large and tends
to one in the medium and high SNR region. In other words, the contribution of
AN to SR can be trivial in such a situation.
