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Fairness Designs for Load Balancing Optimization in Satellite-Cell-Free Massive MIMO Systems

Trinh Van Chien, Ngo Tran Anh Thu, Nguyen Hoang Lam, Hien Quoc Ngo, Symeon Chatzinotas, Huynh Thi Thanh Binh

TL;DR

This article considers the fairness designs under a load-balancing framework with heterogeneous receivers comprising access points (APs) and a satellite and designs a low computational complexity algorithm for large-scale networks based on evolutionary computation that obtains good patterns in polynomial time.

Abstract

Space-ground communication systems are important in providing ubiquitous services in a large area. This paper considers the fairness designs under a load-balancing framework with heterogeneous receivers comprising access points (APs) and a satellite. We derive an ergodic throughput of each user in the uplink data transmission for an arbitrary association pattern and imperfect channel state information, followed by a closed-form expression with the maximum-ratio combining and rich scattering environments. We further formulate a generic fairness optimization problem, subject to the optimal association patterns for all the users. Despite the combinatorial structure, the global optimal solution to the association patterns can be obtained by an exhaustive search for small-scale networks with several APs and users. We design a low computational complexity algorithm for large-scale networks based on evolutionary computation that obtains good patterns in polynomial time. Specifically, the genetic algorithm (GA) is adapted to the discrete feasible region and the concrete fairness metrics. We extensively observe the fairness design problem by incorporating transmit power control and propose a hybrid genetic algorithm to address the problem. Numerical results demonstrate that the association pattern to each user has a significant impact on the network throughput. Moreover, the proposed GA-based algorithm offers the same performance as an exhaustive search for small-scale networks, while it unveils interesting practical association patterns as the network dimensions go large. The load-balancing approach, combined with power control factors, significantly enhances system performance compared to conventional schemes and configurations with fixed factors.

Fairness Designs for Load Balancing Optimization in Satellite-Cell-Free Massive MIMO Systems

TL;DR

This article considers the fairness designs under a load-balancing framework with heterogeneous receivers comprising access points (APs) and a satellite and designs a low computational complexity algorithm for large-scale networks based on evolutionary computation that obtains good patterns in polynomial time.

Abstract

Space-ground communication systems are important in providing ubiquitous services in a large area. This paper considers the fairness designs under a load-balancing framework with heterogeneous receivers comprising access points (APs) and a satellite. We derive an ergodic throughput of each user in the uplink data transmission for an arbitrary association pattern and imperfect channel state information, followed by a closed-form expression with the maximum-ratio combining and rich scattering environments. We further formulate a generic fairness optimization problem, subject to the optimal association patterns for all the users. Despite the combinatorial structure, the global optimal solution to the association patterns can be obtained by an exhaustive search for small-scale networks with several APs and users. We design a low computational complexity algorithm for large-scale networks based on evolutionary computation that obtains good patterns in polynomial time. Specifically, the genetic algorithm (GA) is adapted to the discrete feasible region and the concrete fairness metrics. We extensively observe the fairness design problem by incorporating transmit power control and propose a hybrid genetic algorithm to address the problem. Numerical results demonstrate that the association pattern to each user has a significant impact on the network throughput. Moreover, the proposed GA-based algorithm offers the same performance as an exhaustive search for small-scale networks, while it unveils interesting practical association patterns as the network dimensions go large. The load-balancing approach, combined with power control factors, significantly enhances system performance compared to conventional schemes and configurations with fixed factors.

Paper Structure

This paper contains 28 sections, 7 theorems, 56 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Load Balancing Integrated System, Pilot Training, and Channel Estimation
  3. System and Channel Models
  4. Uplink Pilot Training Phase
  5. Uplink Data Transmission and Ergodic Throughput Analysis
  6. Uplink Data Transmission
  7. Ergodic Throughput Analysis
  8. Fairness Optimization for Integrated System
  9. Problem Formulation
  10. Globally Optimal Solution to the Fairness Design Problem
  11. Binary-Coded Genetic Algorithm (BCGA)
  12. Solution representation and Initialization
  13. Binary crossover operator
  14. Bitwise mutation operator
  15. Survival selection operator
  16. ...and 13 more sections

Key Result

Lemma 1

If the MMSE estimation is exploited to estimate the channel $g_{nk}$, then the channel estimate $\hat{g}_{nk}$ is distributed as $\hat{g}_{nk} \sim \mathcal{CN}(0, \varrho_{nk} )$ and the variance $\varrho_{nk}$ as The estimation error, defined as $e_{mk} = g_{mk} - \hat{g}_{mk}$, is distributes as $e_{mk} \sim \mathcal{CN}(0, \beta_{mk} - \varrho_{mk})$. Note that the channel estimate $\hat{g}_

Figures (5)

  • Figure 1: Illustration of a Satellite-Cell-Free MIMO network.
  • Figure 2: The optimal results of the proposed algorithms compared the fully connected model.
  • Figure 3: The system performances of different evolutionary algorithms within model in Problem (19): (a) The convergence rate as the number of generations increases; (b) The evaluation of the gap between the optimal values of different algorithms as the test sets vary; (c) The evaluation of the gap between the optimal values of different algorithms as the test sets vary.
  • Figure 4: The comparison of ergodic throughput across different network architectures.
  • Figure 5: The system performance comparison between the fixed and optimized power allocation systems based on the optimal results obtained by BCGA and HGA.

Theorems & Definitions (15)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 1
  • Lemma 2
  • proof
  • Theorem 3
  • ...and 5 more