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

TL;DR

This paper studies power allocation in OFDM wire-tap channels with practical discrete inputs, revealing non-concavity of secrecy rate and proposing an efficient asymptotically optimal algorithm.

Contribution

It introduces a novel power allocation algorithm for discrete inputs in OFDM secrecy systems, addressing non-concavity issues unhandled by traditional methods.

Findings

Secrecy rate is non-concave with discrete inputs.

The proposed algorithm's gap from optimality diminishes as O(1/√N).

Algorithm complexity is linear in the number of sub-carriers.

Abstract

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.