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On the Discreteness of the Worst Jamming Distribution for SP-OFDM
IEEE Transactions on Information Forensics and Security ( IF 6.8 ) Pub Date : 2020-03-05 , DOI: 10.1109/tifs.2020.2978616 Yuan Liang , Tongtong Li
IEEE Transactions on Information Forensics and Security ( IF 6.8 ) Pub Date : 2020-03-05 , DOI: 10.1109/tifs.2020.2978616 Yuan Liang , Tongtong Li
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.
中文翻译:
SP-OFDM的最坏干扰分布的离散性
安全预编码OFDM(SP-OFDM)是一种新近提出的安全有效的抗干扰方案,旨在增强在恶劣环境下基于OFDM的4G和5G系统的物理层安全性。在本文中,通过利用约束功能优化中的工具,我们探索了最坏的干扰分布,该分布在实际假设下将SP-OFDM的信道容量最小化,其中传输符号均匀分布在有限字母上,并且干扰会受到干扰平均功率约束,但可能具有或没有峰值功率约束。首先,我们证明了最严重的干扰分布的存在和唯一性。其次,通过分析最严重干扰的Kuhn-Tucker条件,我们证明了最严重干扰分布的振幅是离散的,具有有限数量的质量点,有或没有峰值功率限制。数值结果提供了在伪装干扰下最差的干扰分布和最小信道容量。结果表明,在最严重的伪装干扰下,SP-OFDM的最小信道容量被保证为正,而在伪装干扰下,传统OFDM的最小信道容量为零。我们的理论和数值结果都证明了SP-OFDM的鲁棒性,并且还揭示了其在伪装干扰下的性能下限。而传统的OFDM在伪装干扰下的最小容量为零。我们的理论和数值结果都证明了SP-OFDM的鲁棒性,并且还揭示了其在伪装干扰下的性能下限。而传统OFDM在伪装干扰下的最小容量为零。我们的理论和数值结果都证明了SP-OFDM的鲁棒性,并且还揭示了其在伪装干扰下的性能下限。
更新日期:2020-04-22
中文翻译:
SP-OFDM的最坏干扰分布的离散性
安全预编码OFDM(SP-OFDM)是一种新近提出的安全有效的抗干扰方案,旨在增强在恶劣环境下基于OFDM的4G和5G系统的物理层安全性。在本文中,通过利用约束功能优化中的工具,我们探索了最坏的干扰分布,该分布在实际假设下将SP-OFDM的信道容量最小化,其中传输符号均匀分布在有限字母上,并且干扰会受到干扰平均功率约束,但可能具有或没有峰值功率约束。首先,我们证明了最严重的干扰分布的存在和唯一性。其次,通过分析最严重干扰的Kuhn-Tucker条件,我们证明了最严重干扰分布的振幅是离散的,具有有限数量的质量点,有或没有峰值功率限制。数值结果提供了在伪装干扰下最差的干扰分布和最小信道容量。结果表明,在最严重的伪装干扰下,SP-OFDM的最小信道容量被保证为正,而在伪装干扰下,传统OFDM的最小信道容量为零。我们的理论和数值结果都证明了SP-OFDM的鲁棒性,并且还揭示了其在伪装干扰下的性能下限。而传统的OFDM在伪装干扰下的最小容量为零。我们的理论和数值结果都证明了SP-OFDM的鲁棒性,并且还揭示了其在伪装干扰下的性能下限。而传统OFDM在伪装干扰下的最小容量为零。我们的理论和数值结果都证明了SP-OFDM的鲁棒性,并且还揭示了其在伪装干扰下的性能下限。