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Hierarchical Cell-Free Massive MIMO: A Simplified Design for Uniform Service Quality

Wei Jiang, Hans Dieter Schotten

TL;DR

This work tackles the cell-edge QoS gap and high fronthaul costs inherent in cell-free MIMO by proposing hierarchical cell-free (HCF) massive MIMO, which centralizes a portion of the antennas at a central base station (cBS) while keeping some edge APs. It derives closed-form uplink and downlink SE expressions for HCF, CF, and cellular systems under pilot contamination and spatially correlated fading, and introduces max-min power control to improve fairness and energy efficiency. Numerical results show HCF can match CF in 95th-percentile per-user SE while dramatically reducing fronthaul complexity, and can outperform cellular systems by over 100x at the cell edge; centralized configurations offer substantial uplink power savings, especially when using max-min power control. Collectively, the hierarchical design provides a cost-effective, scalable path to uniform QoS and improved energy efficiency in next-generation networks.

Abstract

In traditional cellular networks, users at the cell edge often suffer from poor quality of service (QoS) due to large distance-dependent path loss and severe inter-cell interference. While cell-free (CF) massive multi-input multi-out (MIMO) mitigates this issue by distributing access points (APs) to ensure uniform QoS, the deployment of numerous distributed APs and a fronthaul network incurs high infrastructure costs. To balance performance and cost efficiency, this article proposes a simplified design called hierarchical cell-free (HCF) massive MIMO. The key idea is to reduce the number of APs, thus minimizing the scale of the fronthaul network. The antennas from the decommissioned APs are aggregated at a central base station (cBS), which also serves as the coordinator for distributed APs. We derive closed-form expressions for uplink and downlink spectral efficiency (SE) for HCF, CF, and cellular massive MIMO under pilot contamination and correlated fading channels, considering the use of multi-antenna APs. Numerical results confirm that the hierarchical architecture achieves $95\%$-likely per-user SE comparable to CF, enhancing cell-edge user rates in cellular systems by over 100 times, while significantly reducing the complexity and cost of the fronthaul network in CF. We develop max-min fairness algorithms for joint power control of the cBS and APs in the downlink, and the users in the uplink. These algorithms not only boost fairness and system capacity but also dramatically lower transmission power, e.g., achieving over $70\%$ savings in uplink, particularly beneficial for battery-powered mobile devices.

Hierarchical Cell-Free Massive MIMO: A Simplified Design for Uniform Service Quality

TL;DR

This work tackles the cell-edge QoS gap and high fronthaul costs inherent in cell-free MIMO by proposing hierarchical cell-free (HCF) massive MIMO, which centralizes a portion of the antennas at a central base station (cBS) while keeping some edge APs. It derives closed-form uplink and downlink SE expressions for HCF, CF, and cellular systems under pilot contamination and spatially correlated fading, and introduces max-min power control to improve fairness and energy efficiency. Numerical results show HCF can match CF in 95th-percentile per-user SE while dramatically reducing fronthaul complexity, and can outperform cellular systems by over 100x at the cell edge; centralized configurations offer substantial uplink power savings, especially when using max-min power control. Collectively, the hierarchical design provides a cost-effective, scalable path to uniform QoS and improved energy efficiency in next-generation networks.

Abstract

In traditional cellular networks, users at the cell edge often suffer from poor quality of service (QoS) due to large distance-dependent path loss and severe inter-cell interference. While cell-free (CF) massive multi-input multi-out (MIMO) mitigates this issue by distributing access points (APs) to ensure uniform QoS, the deployment of numerous distributed APs and a fronthaul network incurs high infrastructure costs. To balance performance and cost efficiency, this article proposes a simplified design called hierarchical cell-free (HCF) massive MIMO. The key idea is to reduce the number of APs, thus minimizing the scale of the fronthaul network. The antennas from the decommissioned APs are aggregated at a central base station (cBS), which also serves as the coordinator for distributed APs. We derive closed-form expressions for uplink and downlink spectral efficiency (SE) for HCF, CF, and cellular massive MIMO under pilot contamination and correlated fading channels, considering the use of multi-antenna APs. Numerical results confirm that the hierarchical architecture achieves -likely per-user SE comparable to CF, enhancing cell-edge user rates in cellular systems by over 100 times, while significantly reducing the complexity and cost of the fronthaul network in CF. We develop max-min fairness algorithms for joint power control of the cBS and APs in the downlink, and the users in the uplink. These algorithms not only boost fairness and system capacity but also dramatically lower transmission power, e.g., achieving over savings in uplink, particularly beneficial for battery-powered mobile devices.

Paper Structure

This paper contains 21 sections, 6 theorems, 76 equations, 5 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Uplink Training
  4. eAP-UE Channel Estimation
  5. cBS-UE Channel Estimation
  6. Uplink Data Transmission
  7. Signal Detection for HCF Massive MIMO
  8. Max-Min Uplink Power Optimization
  9. Cellular Massive MIMO
  10. Cell-Free Massive MIMO
  11. Downlink Data Transmission
  12. Linear Precoding for HCF Massive MIMO
  13. Joint Max-Min Downlink Power Optimization
  14. Cellular Massive MIMO
  15. Cell-Free Massive MIMO
  16. ...and 6 more sections

Key Result

Proposition 1

The achievable SE for user $k$ in the uplink of HCF massive MIMO systems is expressed as where the pre-log factor $1-\tau_p/\tau_u$ accounts for the overhead of uplink pilots, and the instantaneous effective signal-to-interference-plus-noise ratio (SINR) is given by

Figures (5)

  • Figure 1: A comparative illustration of cell-free and hierarchical cell-free massive MIMO networks.
  • Figure 2: Downlink performance comparison of HCF, CF, and cellular systems in (a) microcell and (b) marcocell under equal and max-min power control.
  • Figure 3: Uplink performance comparison of HCF, CF, and cellular systems in (a) microcell and (b) marcocell under full power and max-min power control.
  • Figure 4: Variations in optimal max-min power coefficients.
  • Figure 5: System Capacity Comparison. Note that: marker identifiers align with those in previous figures.

Theorems & Definitions (6)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Proposition 6