Technology Category
Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Distributed SearchPlanning, Routing, and Scheduling: Scheduling under Uncertainty
On the Optimum Secrecy Outage Probability and Ergodic Secrecy Rate over Wireless Channels
🤖 AI Summary
This study addresses the problem of determining the optimal input distribution for physical-layer security in a stochastic wireless channel with only statistical channel state information available and in the presence of an eavesdropper. Focusing on secrecy metrics including secrecy outage probability (SOP), ergodic secrecy rate (ESR), and positive ergodic secrecy rate (EPSR), the work introduces two stochastic channel ordering relations—uniformly less noisy ordering and average less noisy ordering—and leverages information-theoretic tools together with fading channel modeling to derive closed-form expressions for secrecy performance under Rayleigh fading. The main contributions are twofold: first, it proves the optimality of non-precoded Gaussian inputs for the aforementioned secrecy metrics when the legitimate channel satisfies the proposed ordering conditions; second, in single-antenna systems, it establishes the optimal input distribution without requiring any channel ordering assumptions.
Technology Category
Application Category
📝 Abstract
We study the secrecy of wireless channels in the presence of an eavesdropper, where the channels are random and the transmitter only has knowledge of the channel statistics. We investigate the optimal input distribution with respect to several secrecy metrics: the Secrecy Outage Probability (SOP), defined as the probability that the coding rate $r$ exceeds the instantaneous secrecy rate; the Ergodic Secrecy Rate (ESR), defined as the expected secrecy rate over channel realizations; and the Ergodic Positive Secrecy Rate (EPSR), defined as the expected value of the positive part of the secrecy rate. We introduce two partial orderings for random channels: the uniformly less noisy order and the less noisy on average order. We show that when the main channel is uniformly less noisy than the eavesdropper channel, the optimal input distribution is a non-precoded Gaussian input for both the SOP and the EPSR. Furthermore, we show that the same input distribution is optimal for the ESR when the less noisy on average order holds. In addition, similar optimality results for the SOP and the EPSR are obtained for single-transmit-antenna channels without requiring any channel ordering assumptions. Closed-form expressions of the secrecy metrics are derived for special cases of Rayleigh fading channels.
Problem
Research questions and friction points this paper is trying to address.
Secrecy Outage Probability
Ergodic Secrecy Rate
Wireless Channels
Eavesdropper
Input Distribution
Innovation
Methods, ideas, or system contributions that make the work stand out.
optimal input distribution
secrecy outage probability
ergodic secrecy rate
channel ordering
physical-layer security
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