[Paper Review] Robust Max-Min Fairness Energy Harvesting in Secure MISO Cognitive Radio With SWIPT

Fuhui Zhou, Zan Li+3 more|arXiv (Cornell University)|Feb 26, 2016

Energy Harvesting in Wireless Networks16 references3 citations

TL;DR

This paper proposes a robust max-min fairness beamforming and power splitting design for secure MISO cognitive radio networks with simultaneous wireless information and power transfer (SWIPT), under imperfect channel state information. By leveraging S-Procedure and semidefinite relaxation, it achieves optimal artificial noise-aided beamforming that maximizes the minimum harvested energy while ensuring secrecy rate and interference constraints, demonstrating a tradeoff between secrecy rate and energy harvesting fairness.

ABSTRACT

A multiple-input single-output cognitive radio downlink network is studied with simultaneous wireless information and power transfer. In this network, a secondary user coexists with multiple primary users and multiple energy harvesting receivers. In order to guarantee secure communication and energy harvesting, the problem of robust secure artificial noise-aided beamforming and power splitting design is investigated under imperfect channel state information. Specifically, the max-min fairness energy harvesting problem is formulated under the bounded channel state information error model. A one-dimensional search algorithm based on ${\cal S} ext{-Procedure} $ is proposed to solve the problem. It is shown that the optimal robust secure beamforming can be achieved. A tradeoff is elucidated between the secrecy rate of the secondary user receiver and the energy harvested by the energy harvesting receivers under a max-min fairness criterion.

Motivation & Objective

• To address the energy scarcity and security challenges in spectrum-sharing cognitive radio networks with energy-harvesting receivers.
• To design a robust beamforming scheme that ensures secure communication and efficient energy harvesting under imperfect channel state information (CSI).
• To optimize the minimum harvested energy among all energy harvesting receivers under max-min fairness, while maintaining secrecy rate and primary user interference constraints.
• To jointly design artificial noise-aided beamforming and power splitting ratios to balance secrecy rate and energy harvesting fairness.

Proposed method

• Formulates a non-convex optimization problem under bounded CSI error models to maximize the minimum harvested energy across all energy harvesting receivers.
• Applies semidefinite relaxation (SDR) and the S-Procedure to transform the non-convex problem into a tractable form.
• Derives necessary conditions using Karush-Kuhn-Tucker (KKT) optimality, proving that the optimal artificial noise covariance matrix has rank one.
• Employs a one-dimensional search algorithm over a single variable to efficiently solve the relaxed problem and recover the optimal beamforming solution.
• Integrates constraints on secrecy rate, interference to primary users, and power splitting ratios at the secondary user receiver.
• Uses matrix decomposition and inequality relaxation techniques to handle uncertainty in channel estimates.

Experimental results

Research questions

• RQ1 How can robust beamforming be designed in a MISO cognitive radio system with SWIPT under imperfect CSI to ensure both secure communication and energy harvesting?
• RQ2 What is the optimal tradeoff between the secrecy rate of the secondary user and the minimum harvested energy among energy harvesting receivers under max-min fairness?
• RQ3 Can the optimal artificial noise-aided beamforming be achieved even with channel estimation errors, and what is the rank of the optimal artificial noise covariance matrix?
• RQ4 How does the proposed one-dimensional search algorithm based on S-Procedure and SDR achieve the optimal solution efficiently?

Key findings

• The optimal robust secure beamforming solution is always achievable, and the rank of the optimal artificial noise covariance matrix is proven to be one.
• The proposed one-dimensional search algorithm based on S-Procedure and SDR efficiently converges to the global optimum of the non-convex problem.
• A fundamental tradeoff is revealed between the secrecy rate of the secondary user and the minimum harvested energy across all energy harvesting receivers under max-min fairness.
• The system achieves secure communication with guaranteed secrecy rate while ensuring fairness in energy harvesting, even under bounded CSI errors.
• Simulation results confirm that the proposed scheme outperforms conventional beamforming designs in terms of fairness and robustness under channel uncertainty.