[Paper Review] Optimal Amplify-and-Forward Schemes for Relay Channels with Correlated Relay Noise

Binyue Liu, Ye Yang+1 more|arXiv (Cornell University)|Jan 24, 2013

Cooperative Communication and Network Coding10 references3 citations

TL;DR

This paper proposes a unified second-order cone programming (SOCP)-based framework to optimize amplify-and-forward (AF) relay schemes in one- and two-way relay channels with correlated relay noise, a scenario often overlooked in prior work. It shows that noise correlation can be beneficial on average, even without perfect knowledge of the noise covariance, and derives closed-form suboptimal schemes that are approximately optimal under individual relay power constraints.

ABSTRACT

This paper investigates amplify-and-forward (AF) schemes for both one and two-way relay channels. Unlike most existing works assuming independent noise at the relays, we consider a more general scenario with correlated relay noise. We first propose an approach to efficiently solve a class of quadratically constrained fractional problems via second-order cone programming (SOCP). Then it is shown that the AF relay optimization problems studied in this paper can be incorporated into such quadratically constrained fractional problems. As a consequence, the proposed approach can be used as a unified framework to solve the optimal AF rate for the one-way relay channel and the optimal AF rate region for the two-way relay channel under both sum and individual relay power constraints. In particular, for one-way relay channel under individual relay power constraints, we propose two suboptimal AF schemes in closed-form. It is shown that they are approximately optimal in certain conditions of interest. Furthermore, we find an interesting result that, on average, noise correlation is beneficial no matter the relays know the noise covariance matrix or not for such scenario. Overall, the obtained results recover and generalize several existing results for the uncorrelated counterpart. (unsubmitted)

Motivation & Objective

• To address the lack of optimization frameworks for AF relay channels under correlated relay noise, a more realistic model than the standard independent noise assumption.
• To develop a unified solution for both one-way and two-way relay channels under sum and individual relay power constraints.
• To analyze the impact of noise correlation on achievable rates, especially when relays lack full knowledge of the noise covariance matrix.
• To derive suboptimal AF schemes in closed-form that are approximately optimal under individual power constraints.

Proposed method

• Formulates the AF relay optimization problems as quadratically constrained fractional programs (QCFPs), which are then solved via second-order cone programming (SOCP).
• Uses SOCP to efficiently solve a class of non-convex fractional problems arising in relay rate maximization.
• Integrates the SOCP framework into both one-way and two-way relay channel models with correlated noise.
• Derives two closed-form suboptimal AF schemes for the one-way relay channel under individual relay power constraints.
• Analyzes the performance of these schemes under varying signal-to-noise ratio and noise correlation conditions.
• Evaluates the impact of noise correlation on ergodic rates, both with and without perfect knowledge of the noise covariance matrix.

Experimental results

Research questions

• RQ1 How can AF relay optimization be formulated and solved efficiently in the presence of correlated relay noise?
• RQ2 What is the impact of noise correlation on the achievable rate in one- and two-way relay channels?
• RQ3 Can suboptimal AF schemes be derived in closed-form that are approximately optimal under individual relay power constraints?
• RQ4 Is noise correlation beneficial for system performance, even when relays do not know the full noise covariance structure?
• RQ5 How does the proposed SOCP-based framework generalize existing results for uncorrelated noise scenarios?

Key findings

• The proposed SOCP-based framework provides a unified solution for optimizing AF rates in both one- and two-way relay channels under various power constraints.
• Noise correlation is beneficial on average for the one-way relay channel, regardless of whether relays know the noise covariance matrix.
• The two proposed closed-form suboptimal AF schemes achieve near-optimal performance under individual relay power constraints in high-SNR regimes.
• The framework generalizes and recovers existing results for uncorrelated noise as special cases.
• The optimization problem is reformulated as a QCQP and solved efficiently via SOCP, enabling practical implementation.