[Paper Review] QoS-Based Source and Relay Secure Optimization Design with Presence of Channel Uncertainty

Meng Zhang, Jian Huang+3 more|arXiv (Cornell University)|Mar 25, 2020

Cooperative Communication and Network Coding11 references13 citations

TL;DR

This paper proposes a robust QoS-aware beamforming design for secure relay-aided networks under channel uncertainty, minimizing total source and relay power while ensuring the legitimate user's quality of service and constraining the eavesdropper's SNR below a threshold. Using a norm-bounded error model for the relay-eavesdropper channel and a randomization-based optimization, the scheme achieves reliable secrecy performance even with imperfect CSI, outperforming non-robust designs in maintaining eavesdropper SNR constraints.

ABSTRACT

In this letter, we study relay-aided networks with presence of single eavesdropper. We provide joint beamforming design of the source and relay that can minimize the overall power consumption while satisfying our predefined quality-of-service (QoS) requirements. Additionally, we investigate the case that the channel between relay and eavesdropper suffers from channel uncertainty. Finally, simulation results are provided to verify the effectiveness of our algorithm.

Motivation & Objective

• Address the challenge of secure communication in relay-aided networks where the eavesdropper's channel state information (CSI) is imperfect due to passive eavesdropping.
• Minimize the total transmit power at the source and relay while satisfying the legitimate user’s quality-of-service (QoS) requirements.
• Ensure that the eavesdropper’s signal-to-noise ratio (SNR) remains below a predefined threshold despite channel uncertainty.
• Develop a robust optimization framework that accounts for norm-bounded channel errors in the relay-eavesdropper link.

Proposed method

• Formulate a joint source and relay beamforming design as a semi-definite program (SDP) under QoS and secrecy constraints.
• Model the relay-eavesdropper channel uncertainty using a norm-bounded error model, where the true channel lies within a ball around the estimated channel.
• Transform the non-convex robust optimization problem into a tractable form using the S-lemma and Schur complement, enabling convex relaxation.
• Apply a randomization technique to generate candidate beamforming vectors from the dual solution, followed by scaling via α and β to satisfy constraints.
• Use the scaled beamformers as quasi-optimal solutions, with the best among K randomizations selected as the final output.
• Leverage vectorization and Kronecker product operations to express the robustness constraints in a compact, computationally manageable form.

Experimental results

Research questions

• RQ1 How can joint source and relay beamforming be optimized to minimize total power consumption while maintaining QoS for the legitimate user under channel uncertainty?
• RQ2 What is the impact of imperfect CSI on the eavesdropper’s SNR, and how can it be bounded to ensure secrecy in relay-aided networks?
• RQ3 How does the proposed robust beamforming scheme compare to non-robust designs in terms of power efficiency and eavesdropper SNR control?
• RQ4 Can a randomization-based approach effectively recover a feasible and near-optimal beamforming solution from the relaxed SDP dual problem?

Key findings

• The robust precoding scheme consumes more power than the non-robust scheme due to worst-case channel error considerations, but this is necessary for reliability under uncertainty.
• For fixed QoS thresholds, increasing the secrecy threshold (i.e., tightening the eavesdropper’s SNR constraint) leads to higher power consumption, as expected.
• The non-robust scheme fails to meet the eavesdropper SNR constraint in nearly half of the channel realizations, while the robust scheme keeps the majority of eavesdropper SNRs below the threshold.
• Despite robustness to worst-case errors, some eavesdropper SNRs still exceed the threshold due to the conservative nature of worst-case design, indicating room for improvement in trade-offs.
• Simulation results confirm that the proposed algorithm effectively maintains secrecy and QoS under channel uncertainty, validating its robustness and practicality.