Computational Analysis of Secrecy Outage in Energy-Harvesting Multi-Backscatter IoT Networks

This paper studies the secrecy outage performance (SOP) of an energy-harvesting multi-backscatter-device (BD) network in the presence of a passive eavesdropper. A dedicated radio-frequency source illuminates multiple BDs employing power splitting (PS), and the BD with the strongest source-to-BD channel is opportunistically selected for confidential backscatter transmission. Unlike conventional secure backscatter communication models that assume an always-active BD, we explicitly impose a practical circuit-activation constraint requiring the selected BD to harvest sufficient energy before transmission. Consequently, the selected source-to-BD channel jointly determines circuit availability and the strengths of the legitimate and wiretap cascaded links. A tractable analytical framework for the SOP is developed by accounting for activation failure, secrecy-rate outage, opportunistic selection, PS, and Rayleigh fading. Since the activation constraint yields a non-zero lower integration bound, we derive a finite-sum approximation using the binomial expansion and Gaussian -Chebyshev quadrature. We further obtain a high-signal-to-noise-ratio expression that reveals a non-zero secrecy outage floor caused by the proportional scaling of the legitimate and eavesdropping links. Monte Carlo simulations validate the analysis and show that increasing the number of candidate BDs improves secrecy performance, particularly in energy-limited regimes, but with diminishing returns. The results also reveal the trade-off between circuit activation and backscattered-signal strength and quantify the effects of the activation threshold, PS coefficient, and channel conditions on secrecy performance.