  In this paper, we investigate power allocation that maximizes the secrecy
rate of orthogonal frequency division multiplexing (OFDM) systems under
arbitrarily distributed inputs. Considering commonly assumed Gaussian inputs
are unrealistic, we focus on secrecy systems with more practical discrete
distributed inputs, such as PSK, QAM, etc. While the secrecy rate achieved by
Gaussian distributed inputs is concave with respect to the transmit power, we
have found and rigorously proved that the secrecy rate is non-concave under any
discrete inputs. Hence, traditional convex optimization methods are not
applicable any more. To address this non-concave power allocation problem, we
propose an efficient algorithm. Its gap from optimality vanishes asymptotically
at the rate of $O(1/\sqrt{N})$, and its complexity grows in the order of O(N),
where $N$ is the number of sub-carriers. Numerical results are provided to
illustrate the efficacy of the proposed algorithm.
