  In secure spatial modulation (SM) networks, power allocation (PA) strategies
are investigated in this paper under the total power constraint. Considering
that there is no closed-form expression for secrecy rate (SR), an approximate
closed-form expression of SR is presented, which is used as an efficient metric
to optimize PA factor and can greatly reduce the computation complexity. Based
on this expression, a convex optimization (CO) method of maximizing SR (Max-SR)
is proposed accordingly. Furthermore, a method of maximizing the product of
signal-to-leakage and noise ratio (SLNR) and artificial noise-to-leakage-and
noise ratio (ANLNR) (Max-P-SAN) is proposed to provide an analytic solution to
PA with extremely low-complexity. Simulation results demonstrate that the SR
performance of the proposed CO method is close to that of the optimal PA
strategy of Max-SR with exhaustive search and better than that of Max-P-SAN in
the high signal-to-noise ratio (SNR) region. However, in the low and medium SNR
regions, the SR performance of the proposed Max-P-SAN slightly exceeds that of
the proposed CO.
