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The Worst Jamming Distribution for Securely Precoded OFDM

In this paper, we address the problem of finding the worst jamming distribution in terms of channel capacity for the securely precoded OFDM (SP-OFDM) system, so as to evaluate the performance of SP- OFDM under destructive hostile jamming. We consider a practical communication scenario, where the transmitting symbols are uniformly distributed over a discrete and finite alphabet, and the jamming interference is subject to both average and peak power constraints. Using tools in functional analysis and complex analysis, first, we show the existence and uniqueness of the worst jamming distribution; then we further prove that the worst jamming distribution is discrete in amplitude with a finite number of mass points. Numerical examples are provided under different scenarios to demonstrate our theoretical results.