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In this paper, we investigate power allocation that maximizes the secrecyrate of orthogonal frequency division multiplexing (OFDM) systems underarbitrarily distributed inputs. Considering commonly assumed Gaussian inputsare unrealistic, we focus on secrecy systems with more practical discretedistributed inputs, such as PSK, QAM, etc. While the secrecy rate achieved byGaussian distributed inputs is concave with respect to the transmit power, wehave found and rigorously proved that the secrecy rate is non-concave under anydiscrete inputs. Hence, traditional convex optimization methods are notapplicable any more. To address this non-concave power allocation problem, wepropose an efficient algorithm. Its gap from optimality vanishes asymptoticallyat 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 toillustrate the efficacy of the proposed algorithm.

Optimal Power Allocation for OFDM-Based Wire-Tap Channels with Arbitrarily Distributed Inputs