Beam-forming for Secure Communication in Amplify-and-Forward Networks: An SNR based approach

TL;DR

This paper develops SNR-based optimization methods for secure communication in amplify-and-forward relay networks, balancing rate maximization and power minimization while ensuring eavesdropper SNR remains below thresholds.

Contribution

It introduces convex and semi-definite relaxation techniques for optimizing relay scaling factors to enhance security in AF networks with multiple eavesdroppers.

Findings

Efficient solutions for maximizing legitimate rate under eavesdropper constraints.

Power minimization strategies maintaining secure SNR levels.

Analytical bounds for the proposed optimization problems.

Abstract

The problem of secure communication in Amplify-and-Forward (AF) relay networks with multiple eavesdroppers is considered. Assuming that a receiver (destination or eavesdropper) can decode a message only if the received SNR is above a predefined threshold, we introduce SNR based optimization formulations to calculate optimal scaling factors for relay nodes in two scenarios. In the first scenario, we maximize the achievable rate at the legitimate destination, subject to the condition that the received SNR at each eavesdropper is below the target threshold. Due to the non-convex nature of the objective function and eavesdroppers' constraints, we transform variables and obtain a Quadratically Constrained Quadratic Program (QCQP) with convex constraints, which can be solved efficiently. When the constraints are not convex, we consider a Semi-definite relaxation (SDR). In the second scenario, we minimize the total power consumed by all relay nodes, subject to the condition that the received SNR at the legitimate destination is above the threshold and at every eavesdropper, it is below the corresponding threshold. We propose a semi-definite relaxation of the problem in this scenario and also provide an analytical lower bound.