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CSIT-Free Beamforming for Multi-Group Multicast in Overloaded mmWave Systems

Wonseok Choi, Jeongjae Lee, Songnam Hong

TL;DR

The paper tackles fairness in downlink MGM for overloaded mmWave systems where $K \\gg N$, showing that conventional single-slot MGM experiences a fundamental MMF-DoF collapse under LoS-dominant geometries. It introduces CF-MGM, a CSIT-free framework using a deterministic multi-slot CP-DFT precoding and receiver-side combining to cancel inter-group interference by construction, yielding a positive MMF-DoF of $d_{ m MMF}^{\rm CF-MGM}=1/N$. The design reduces the problem to a low-dimensional, closed-form power allocation based on large-scale channel gains, avoiding per-block CSIT and heavy signaling. Simulations demonstrate substantial gains over state-of-the-art CSIT-based MGM schemes in LoS mmWave channels, with lower complexity and reduced overhead, highlighting CF-MGM’s practical impact for scalable fairness in future dense mmWave networks.

Abstract

We study downlink multi-group multicast (MGM) transmission in overloaded millimeter-wave (mmWave) systems, where the number of users exceeds the number of transmit antennas. We first show that, under realistic line-of-sight (LoS)-dominant user geometries, the conventional single-slot MGM scheme suffers from a fundamental collapse of the max-min fairness degrees of freedom (MMF-DoF), regardless of beamforming optimization. Although this collapse can in principle be avoided via aggressive time-division scheduling, it requires excessive time sharing and results in severe throughput loss in overloaded regimes. To address this limitation, we propose a CSIT-free multi-group multicast framework (CF-MGM) that does not rely on instantaneous channel state information at the transmitter (CSIT) and is based on a deterministic multi-slot transmission structure. By exploiting structured precoding and receiver-side combining across multiple slots, the proposed framework eliminates inter-group interference by construction. We show that CF-MGM guarantees a strictly positive MMF-DoF in overloaded LoS mmWave systems, in sharp contrast to the DoF collapse of conventional single-slot MGM. Simulation results demonstrate that CF-MGM significantly outperforms state-of-the-art CSIT-based MGM schemes while substantially reducing signaling overhead.

CSIT-Free Beamforming for Multi-Group Multicast in Overloaded mmWave Systems

TL;DR

The paper tackles fairness in downlink MGM for overloaded mmWave systems where , showing that conventional single-slot MGM experiences a fundamental MMF-DoF collapse under LoS-dominant geometries. It introduces CF-MGM, a CSIT-free framework using a deterministic multi-slot CP-DFT precoding and receiver-side combining to cancel inter-group interference by construction, yielding a positive MMF-DoF of . The design reduces the problem to a low-dimensional, closed-form power allocation based on large-scale channel gains, avoiding per-block CSIT and heavy signaling. Simulations demonstrate substantial gains over state-of-the-art CSIT-based MGM schemes in LoS mmWave channels, with lower complexity and reduced overhead, highlighting CF-MGM’s practical impact for scalable fairness in future dense mmWave networks.

Abstract

We study downlink multi-group multicast (MGM) transmission in overloaded millimeter-wave (mmWave) systems, where the number of users exceeds the number of transmit antennas. We first show that, under realistic line-of-sight (LoS)-dominant user geometries, the conventional single-slot MGM scheme suffers from a fundamental collapse of the max-min fairness degrees of freedom (MMF-DoF), regardless of beamforming optimization. Although this collapse can in principle be avoided via aggressive time-division scheduling, it requires excessive time sharing and results in severe throughput loss in overloaded regimes. To address this limitation, we propose a CSIT-free multi-group multicast framework (CF-MGM) that does not rely on instantaneous channel state information at the transmitter (CSIT) and is based on a deterministic multi-slot transmission structure. By exploiting structured precoding and receiver-side combining across multiple slots, the proposed framework eliminates inter-group interference by construction. We show that CF-MGM guarantees a strictly positive MMF-DoF in overloaded LoS mmWave systems, in sharp contrast to the DoF collapse of conventional single-slot MGM. Simulation results demonstrate that CF-MGM significantly outperforms state-of-the-art CSIT-based MGM schemes while substantially reducing signaling overhead.

Paper Structure

This paper contains 20 sections, 52 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Challenges
  3. Contributions
  4. Organization
  5. Preliminaries
  6. System Model
  7. Multi-Slot Frame Structure
  8. Time-Division MGM Framework
  9. Fundamental Limitations of Single-Slot MGM
  10. Upper Bound on the Single-Slot MMF--DoF
  11. Realistic LoS geometry and MMF--DoF Collapse
  12. Formulation of Time-division MGM Problem
  13. Proposed CSIT-free Approach
  14. Proposed CF-MGM Framework
  15. CSIT-free Beamforming
  16. ...and 5 more sections

Figures (7)

  • Figure 1: Single-slot MGM MMF rate versus ${\sf SNR} = P_t/\sigma^2$ for different angular sector widths $\Delta_\theta \in \{0, 0.1, 0.2, 0.3, 0.4, 0.5\}$ radian. System parameters: $N=8$ transmit antennas, $G=6$ multicast groups, and $K_g=8$ users per group.
  • Figure 2: Illustration of the conventional CSIT-based MGM framework, and the proposed CF-MGM framework.
  • Figure 3: Empirical CDF of group rates under different utility functions.
  • Figure 4: Minimum rate versus number of users per group.
  • Figure 5: Minimum user rate versus Rician-$\kappa$ factor.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1: Single-slot MMF--DoF
  • Remark 1
  • Remark 2