Explainable Deep Learning for Secrecy Energy-Efficiency Maximization in Ambient Backscatter Multi-User NOMA Systems

TL;DR

The paper tackles secrecy energy-efficiency ($SEE$) in a downlink multi-user NOMA system aided by ambient backscatter devices in the presence of a passive eavesdropper. It develops a triad of regimes: (i) single BD with closed-form reflection-coefficient and power-allocation solutions, (ii) two BDs with RCs on the Pareto boundary and closed-form allocation, and (iii) multiple BDs where grid-search and PSO address nonconvex optimization, complemented by a learning-based FNN predictor. An accompanying SHAP-based explainability framework interprets the learned power and reflection decisions, linking feature importance to dominant composite channels. Numerically, AmBC yields substantial $SEE$ gains (up to 615%) over conventional NOMA in high-noise scenarios, with the FNN achieving over 95% accuracy versus the optimal baseline and SHAP confirming model trustworthiness. The work demonstrates the feasibility and practical value of explainable AI in energy-efficient, secure AmBC–NOMA for next-generation IoT networks.

Abstract

In this paper, we investigate the secrecy energy-efficiency (SEE) of a multi-user downlink non-orthogonal multiple access (NOMA) system assisted by multiple ambient backscatter communications (AmBC) in the presence of a passive eavesdropper. We analyze both the trade-off and the ratio between the achievable secrecy sum-rate and total power consumption. In the special case of two backscatter devices (BDs), we derive closed-form solutions for the optimal reflection coefficients and power allocation by exploiting the structure of the SEE objective and the Pareto boundary of the feasible set. When more than two BDs are present, the problem becomes analytically intractable. To address this, we propose two efficient optimization techniques: (i) an exhaustive grid-based benchmark method, and (ii) a scalable particle swarm optimization algorithm. Furthermore, we design a deep learning-based predictor using a feedforward neural network (FNN), which closely approximates the optimal solutions. Numerical results show that the inclusion of AmBC significantly improves SEE, with gains up to 615% compared to conventional NOMA in high-noise regimes. Additionally, the FNN model achieves more than 95% accuracy compared to the optimal baseline, while reducing complexity. Finally, we employ SHAP (SHapley Additive exPlanations) to interpret the learned model, revealing that the most influential features correspond to the dominant composite channel components, in accordance with the theoretical system model. This demonstrates the potential of explainable artificial intelligence to build trust in energy-efficient and secure AmBC-NOMA systems for next-generation internet of things applications.

Figures (11)

• Figure 1: Downlink multi-user NOMA system assisted by ambient backscatter with an eavesdropper.
• Figure 2: Multi-user NOMA system with multiple ambient backscatter devices and a single eavesdropper.
• Figure 3: Secrecy energy-efficiency ratio $\zeta_{SEE}$ as a function of $P_{\max}$ for $K=2$ users and $R_{\min} = 1$ bit/s/Hz. An increase in the number of backscatter devices consistently improve the performance, regardless of $P_{\max}$.
• Figure 4: Secrecy energy-efficiency ratio $\zeta_{SEE}$ vs. $R_{\min}$ for $K=2$ users and $P_{\max} = 50$ dBm. The gain in $\zeta_{SEE}$ improves as the number of backscatter devices increases.
• Figure 5: Relative secrecy energy-efficiency gain of NOMA with one to four BDs and OMA with two BDs, compared to pure NOMA, as a function of the noise variance $\sigma_k^2$, for $K = 2$ users, $R_{\min} = 1$ bit/s/Hz, and $P_{\max} = 50$ dBm. The gain increases with the number of BDs and becomes more significant in high-noise scenarios. For high values of $\sigma_k^2$, OMA with two BDs outperforms NOMA with a single BD.

Theorems & Definitions (3)

• Theorem 1
• Theorem 2
• Remark 1