[Paper Review] Power Allocation for Multi-Pair Massive MIMO Two-Way AF Relaying with Linear Processing

Yongyu Dai, Xiaodai Dong|arXiv (Cornell University)|Aug 26, 2015

Cooperative Communication and Network Coding20 references3 citations

TL;DR

This paper proposes an optimal power allocation (OPA) scheme for multi-pair massive MIMO two-way amplify-and-forward (AF) relaying with imperfect channel state information (CSI), using MRC/MRT or ZFR/ZFT beamforming. It derives closed-form lower bounds for ergodic achievable rates and formulates an OPA via geometric programming that maximizes sum spectral efficiency, with asymptotic OPA solutions showing that optimal power is inversely proportional to large-scale fading factors under MRC/MRT.

ABSTRACT

In this paper, we consider a multi-pair two-way amplify-and-forward relaying system where multiple sources exchange information via a relay node equipped with large-scale antenna arrays. Given that channel estimation is non-ideal, and that the relay employs either maximum-ratio combining/maximum-ratio transmission (MRC/MRT) or zero-forcing reception/zero-forcing transmission (ZFR/ZFT) beamforming, we derive two corresponding closed-form lower bound expressions for the ergodic achievable rate of each pair sources. The closed-form expressions enable us to design an optimal power allocation (OPA) scheme that maximizes the sum spectral efficiency under certain practical constraints. As the antenna array size tends to infinity and the signal to noise ratios become very large, asymptotically optimal power allocation schemes in simple closed-form are derived. The capacity lower bounds are verified to be accurate predictors of the system performance by simulations, and the proposed OPA outperforms equal power allocation (EPA). It is also found that in the asymptotic regime, when MRC/MRT is used at the relay and the link end-to-end large-scale fading factors among all pairs are equal, the optimal power allocated to a user is inverse to the large-scale fading factor of the channel from the user to the relay, while OPA approaches EPA when ZFR/ZFT is adopted.

Motivation & Objective

• To address the lack of power allocation schemes in massive MIMO two-way AF relaying with imperfect CSI.
• To derive closed-form ergodic achievable rate lower bounds for both MRC/MRT and ZFR/ZFT beamforming strategies.
• To design an optimal power allocation (OPA) scheme that maximizes sum spectral efficiency under practical constraints.
• To analyze asymptotic OPA behavior as the number of relay antennas tends to infinity.
• To validate the accuracy of rate bounds and the superiority of OPA over equal power allocation (EPA) via simulations.

Proposed method

• Derives statistical CSI (SCSI)-based closed-form lower bounds for ergodic achievable rates using Wishart and inverse Wishart matrix properties.
• Applies techniques from [16,17] to model channel estimation errors and beamforming gain under finite relay antennas.
• Uses geometric programming (GP) to solve the OPA problem for sum spectral efficiency maximization under power and quality-of-service constraints.
• Derives asymptotic OPA solutions in closed form as the number of relay antennas approaches infinity.
• Validates rate bounds via Monte Carlo simulations and compares OPA performance against EPA in terms of spectral efficiency.
• Considers both MRC/MRT and ZFR/ZFT beamforming strategies under imperfect CSI and non-ideal channel estimation.

Experimental results

Research questions

• RQ1 What is the closed-form lower bound for the ergodic achievable rate in multi-pair massive MIMO two-way AF relaying with imperfect CSI and MRC/MRT beamforming?
• RQ2 How does the ergodic achievable rate behave under ZFR/ZFT beamforming with imperfect CSI and finite relay antennas?
• RQ3 What is the optimal power allocation strategy that maximizes sum spectral efficiency under practical constraints?
• RQ4 How does the asymptotic OPA behave as the number of relay antennas tends to infinity?
• RQ5 How does the OPA scheme compare to equal power allocation (EPA) in terms of spectral efficiency and fairness under different fading conditions?

Key findings

• The derived closed-form ergodic achievable rate lower bounds are accurate predictors of actual system performance, validated via Monte Carlo simulations.
• The proposed OPA scheme outperforms equal power allocation (EPA) in terms of sum spectral efficiency across all system configurations.
• In the asymptotic regime with MRC/MRT beamforming, optimal power is inversely proportional to the large-scale fading factor from the user to the relay.
• When ZFR/ZFT beamforming is used, the OPA scheme approaches EPA, indicating reduced sensitivity to channel variations.
• As the number of relay antennas increases, the OPA converges to a simple closed-form solution, enabling low-complexity implementation.
• The OPA based on geometric programming is efficiently solvable using standard tools like CVX, ensuring practical deployability.