On the Discreteness of the Worst Jamming Distribution for SP-OFDM

• Published in: IEEE transactions on information forensics and security Vol. 15; p. 1
• Main Authors: Liang, Yuan, Li, Tongtong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel capacity; Codes; Constraints; functional optimization; hostile jamming; Interference; Jamming; Kuhn-Tucker method; Lower bounds; OFDM; Optimization; Precoding; Receivers; Robustness (mathematics); secure precoding; Synchronization
• ISSN: 1556-6013; 1556-6021
• DOI: 10.1109/TIFS.2020.2978616

Securely precoded OFDM (SP-OFDM) is a newly proposed secure and efficient anti-jamming scheme designed to enhance the physical layer security of OFDM based 4G and 5G systems under hostile environments. In this paper, by exploiting tools in constrained functional optimization, we explore the worst jamming distribution that minimizes the channel capacity of SP-OFDM under practical assumptions, where the transmitted symbols are uniformly distributed over a finite alphabet, and the jamming interference is subject to an average power constraint, but may or may not have a peak power constraint. First, we prove the existence and uniqueness of the worst jamming distribution. Second, by analyzing the Kuhn-Tucker conditions for the worst jamming, we prove that the worst jamming distribution is discrete in amplitude with a finite number of mass points, either with or without peak power constraints. Numerical results are provided on the worst jamming distribution and the minimum channel capacity under disguised jamming. It is shown that the minimum channel capacity of SP-OFDM is guaranteed to be positive under the worst disguised jamming, while the minimum capacity of the traditional OFDM under disguised jamming is zero. Both our theoretical and numerical results demonstrate the robustness of SP-OFDM and also reveal its performance lower bound under disguised jamming.