Quartic Perturbation-based Outage-constrained Robust Design in Two-hop One-way Relay Networks

TL;DR

This paper develops a robust design framework for two-hop relay networks with channel uncertainties, using quartic perturbation models and convex safe approximations to ensure outage constraints are met efficiently.

Contribution

It introduces a novel outage-constrained robust design approach based on quartic perturbations and compares the tightness of moment and Bernstein-type inequalities for the first time.

Findings

Bernstein-type inequality is less conservative than moment inequality in certain regimes.

The proposed design effectively minimizes relay power while satisfying outage constraints.

Numerical results confirm the robustness and tightness of the proposed methods.

Abstract

In this work, we study a classic robust design problem in two-hop one-way relay system. We are particularly interested in the scenario where channel uncertainty exists in both the transmitter-to-relay and relay-to-receiver links. By considering the problem design that minimizes the average amplify-and-forward power budget at the relay side while satisfying SNR outage requirements, an outage-constrained robust design problem involving quartic perturbations is formulated to guarantee the robustness during transmission. This problem is in general difficult as it involves constraints on the tail probability of a high-order polynomial. Herein, we resort to moment inequality and Bernstein-type inequality to tackle this problem, which provide convex restrictions, or safe approximations, of the original design. We also analyze the relative tightness of the two safe approximations for a quadratic perturbation-based outage constrained problem. Our analysis shows that the Bernstein-type inequality approach is less conservative than the moment inequality approach when the outage rate is within some prescribed regime. To our best knowledge, this is the first provable tightness result for these two safe approximations. Our numerical simulations verify the superiority of the robust design and corroborate the tightness results.