PaperlayerView exact revision on arXiv

Source-linked AI summary

Rate-Splitting Multiple Access for Multigroup Multicast and Multibeam Satellite Systems

Longfei Yin, Bruno Clerckx

arXiv:2008.05091v2eess.SPcs.ITmath.IT

TL;DR

Multigroup multicast with imperfect CSIT raises the question of whether rate-splitting can improve fairness over conventional linear precoding. The paper analyzes MMF-DoF and formulates a finite-SNR MMF rate optimization; satellite simulations report an RS advantage in a hotspot setting.

Abstract

from arXiv · show

This work focuses on the promising Rate-Splitting Multiple Access (RSMA) and its beamforming design problem to achieve max-min fairness (MMF) among multiple co-channel multicast groups with imperfect channel state information at the transmitter (CSIT). Contrary to the conventional linear precoding (NoRS) that relies on fully treating any residual interference as noise, we consider a novel multigroup multicast beamforming strategy based on RSMA. RSMA relies on linearly precoded Rate-Splitting (RS) at the transmitter and Successive Interference Cancellation (SIC) at the receivers, and has recently been shown to enable a flexible framework for non-orthogonal transmission and robust interference management in multi-antenna wireless networks. In this work, we characterize the MMF Degrees-of-Freedom (DoF) achieved by RS and NoRS in multigroup multicast with imperfect CSIT and demonstrate the benefits of RS strategies for both underloaded and overloaded scenarios. Motivated by the DoF analysis, we then formulate a generic transmit power constrained optimization problem to achieve MMF rate performance. The superiority of RS-based multigroup multicast beamforming compared with NoRS is demonstrated via simulations in both terrestrial and multibeam satellite systems. In particular, due to the characteristics and challenges of multibeam satellite communications, our proposed RS strategy is shown promising to manage its interbeam interference.

I. INTRODUCTION

The paper studies rate-splitting for multigroup multicast under imperfect CSIT, then develops its transmission and beamforming framework and evaluates terrestrial and satellite applications. It argues that RS addresses limitations of conventional linear precoding and reports benefits across network regimes and setups.

A. Related Works

  • Conventional NoRS decodes each desired stream while treating other streams as noise, and its effectiveness depends on network load and CSIT quality.With too few transmit antennas, it cannot eliminate inter-group interference; rate saturation occurs in overloaded systems.Source: A. Related Works · p. 2

A. Transmission Schemes

  • RS splits each group’s message into common and private parts, jointly encodes the common parts, and uses SIC before users decode their private streams.This lets RS partially decode interference and partially treat it as noise; NoRS is a special case obtained by discarding the common stream.Source: A. Related Works · p. 2, A. Transmission Schemes · pp. 3–4

B. Contributions

  • The study extends earlier RS multigroup multicast work to imperfect CSIT in both underloaded and overloaded systems.It characterizes the MMF-DoF of RS and NoRS in that setting.Source: B. Contributions · p. 2
  • With imperfect CSIT, RS provides MMF-DoF gains over NoRS in underloaded and overloaded systems, with finite-SNR rate benefits reported across a wide range of setups.The paper formulates a finite-SNR MMF beamforming problem to test whether the DoF gains translate into rate gains.Source: B. Contributions · p. 2
  • For multibeam satellites, the paper formulates a per-feed power-constrained MMF problem and evaluates RS under CSIT uncertainty, hotspots, uneven user distributions, and overload.The reported simulations confirm gains over traditional techniques and identify RS as promising for interbeam interference management.Source: B. Contributions · p. 3

II. SYSTEM MODEL

  • The model is a downlink MISO system with Nt transmit antennas serving K single-antenna users in M multicast groups, with each group seeking the same message.The framework allows total transmit-power and per-antenna power constraints; the latter are relevant to satellite payloads with individual amplifiers.Source: §II · p. 3, A. Transmission Schemes · p. 3

B. CSIT Uncertainty and Scaling

The model represents channel uncertainty as an estimate plus an error and assumes perfect CSIR. It uses a shared scaling factor to describe how CSIT uncertainty changes with transmit power.

B. CSIT Uncertainty and Scaling

  • The channel is modeled as an estimate plus an error, while channel state information at each receiver is assumed perfect.The paper describes CSIT uncertainty through a conditional channel distribution.Source: B. CSIT Uncertainty and Scaling · p. 4
  • For simplicity, users share a CSIT scaling factor α, with error uncertainty decaying as O(P^-α) as transmit power grows.A finite nonzero α models improving CSIT, for example through increasing feedback bits.Source: B. CSIT Uncertainty and Scaling · p. 4
  • The scaling factor is restricted to α ∈ [0, 1]: α = 0 represents non-scaling CSIT, and α = 1 is perfect CSIT in the DoF sense.The passage associates non-scaling CSIT with a fixed number of feedback bits.Source: B. CSIT Uncertainty and Scaling · p. 4

III. MAX-MIN FAIR DOF ANALYSIS

The section analyzes NoRS max-min fair degrees of freedom under imperfect CSIT. Its results distinguish underloaded, fully overloaded, and partially overloaded systems, with beamforming directions used to manage inter-group interference.

III. MAX-MIN FAIR DOF ANALYSIS

  • MMF-DoF is the maximum multiplexing gain simultaneously achievable across groups and represents the high-SNR MMF-rate pre-log factor.The analysis treats DoF as a rough measure of the number of interference-free streams communicated in one channel use.Source: §III · p. 4

1) Achievability of Proposition 1:

  • When enough transmit antennas are available, beamforming directions can place each precoder in the null space of unintended groups’ estimated channels, eliminating primary inter-group interference.Imperfect CSIT still leaves residual interference.Source: 1) Achievability of Proposition 1 · p. 5
  • In the underloaded case, NoRS achieves MMF-DoF α for all multicast groups.This result is stated for CSIT error variance decaying as O(P^-α).Source: 1) Achievability of Proposition 1 · p. 5
  • In a fully overloaded system, the MMF-DoF collapses to 0; in the partially overloaded case described, NoRS achieves MMF-DoF α/2.The partially overloaded case does not exist when group sizes are equal.Source: 1) Achievability of Proposition 1 · p. 5

2) Converse of Proposition 1:

The converse analysis bounds NoRS performance under imperfect CSIT across network-load regimes. Its MMF-DoF falls to α/2 in the partially overloaded case described and to zero in the fully overloaded case.

2) Converse of Proposition 1:

  • With imperfect CSIT, NoRS can eliminate primary inter-group interference but leaves at least one form of residual interference.Proposition 1's upper bound is tight for feasible NoRS beamforming.Source: 2) Converse of Proposition 1 · p. 6
  • In the partially overloaded regime, the NoRS MMF-DoF is bounded by α/2.The analysis considers Nt = K − G1 antennas; the cited discussion says further antenna reductions do not increase DoF.Source: 2) Converse of Proposition 1 · p. 6
  • In the fully overloaded regime, the NoRS MMF-DoF is bounded by zero.The argument considers Nt = K − GM antennas and states that reducing Nt further does not increase DoF.Source: 2) Converse of Proposition 1 · pp. 6–7

B. Max-Min Fair DoF of RS

This section characterizes the max-min fair degrees of freedom achieved by rate-splitting (RS). The result is stated piecewise across antenna and CSIT regimes, with group fairness determined by the minimum group DoF.

B. Max-Min Fair DoF of RS

  • For a given RS beamforming design, the MMF-DoF is the minimum of the groups' RS DoFs.Each group DoF includes its user-level DoF and its allocated common-rate portion.Source: B. Max-Min Fair DoF of RS · p. 7
  • Proposition 2 states the optimum RS MMF-DoF piecewise across antenna-count and CSIT-quality regimes.The supplied result gives branches for Nt ≥ K − G1 + 1 and 1 ≤ Nt < K − G1 + 1.Source: B. Max-Min Fair DoF of RS · p. 7
  • In overloaded systems, M*_R counts the maximum number of groups that RS beamforming can treat as underloaded; the stated inequality gives an achievable result, not necessarily an optimum.The remaining groups are not included in that underloaded subset.Source: B. Max-Min Fair DoF of RS · p. 7

1) Achievability of Proposition 2:

The achievability construction uses conventional RS in underloaded systems and a mixed scheme in overloaded systems. In the latter, it selects a subset of groups for RS beamforming and allocates common-rate and power portions to balance group DoFs.

1) Achievability of Proposition 2:

  • In overloaded systems, the construction splits groups into an RS-beamformed subset and a remaining subset served by degraded beamforming.Messages for RS-subset groups are split into common and private parts; remaining groups use only common parts, with their private beamformers set to zero.Source: 1) Achievability of Proposition 2 · p. 7
  • The maximum size of the underloaded subset depends on the antenna count: NL ≤ Nt < NL+1 permits at most L such groups.NL is the minimum antenna count needed to regard the first L groups as underloaded while disregarding the others.Source: 1) Achievability of Proposition 2 · p. 7
  • When α exceeds 1/(1+M−M*_R), the achieved MMF-DoF is independent of α and matches the perfect-CSIT result.For α at or below that threshold, the MMF-DoF diminishes as CSIT quality reduces.Source: 1) Achievability of Proposition 2 · p. 8

2) Insight:

The analysis compares RS and NoRS across underloaded and overloaded multigroup multicast regimes with imperfect CSIT. It reports RS MMF-DoF gains in both regimes and explains how group partitioning and residual interference shape the overloaded case.

2) Insight:

  • RS achieves a higher MMF-DoF than NoRS across the compared regimes, with an underloaded gain of 1−α/M.The paper summarizes the achievable MMF-DoFs of different strategies in Table I.Source: 2) Insight · pp. 8–9, Table I · p. 9
  • At Nt = NM−1, NoRS MMF-DoF collapses to zero, while RS maintains a positive MMF-DoF by using RS streams and degraded beamforming.The paper states that RS guarantees d*_RS ≥ 1/M in this case.Source: 2) Insight · p. 8
  • For overloaded systems, RS outperforms NoRS by partitioning groups between RS beamforming and degraded beamforming.The RS subset is chosen as the maximum number of groups that can achieve MMF-DoF 1−α/M + α through RS.Source: 2) Insight · p. 9
  • The DoF comparison motivates examining finite-SNR MMF-rate gains, since DoF is an asymptotic high-SNR metric and its gains need not imply rate gains.The paper notes that the beamformers achieving the DoF results are not necessarily optimal for MMF rate.Source: 2) Insight · p. 9

IV. OPTIMIZATION AND SOLUTION

This section converts long-term MMF ergodic-rate design into a stochastic short-term average-rate problem, then solves a sample-based WMMSE reformulation with alternating optimization.

  • MMF ergodic rates are evaluated by averaging short-term MMF average rates over channel-estimate variation, with each average rate reflecting CSIT-error realizations.Source: §IV · pp. 9–10
  • NoRS is the RS special case with the common-stream allocation and precoder set to zero, under the flexible transmit power constraint.Source: §IV · p. 10
  • Sample Average Approximation replaces the stochastic problem with a deterministic sample-based formulation using transmitter-available conditional channel realizations to approximate user rates.Source: §IV · p. 10
  • A modified WMMSE relationship transforms the nonconvex rate problem into an equivalent WMMSE problem, solved by alternating optimization over variable blocks.Source: §IV · pp. 10–11
  • The alternating algorithm converges because its objective is bounded above under a given power constraint, while the common-rate variable increases monotonically.Source: §IV · p. 11

A. Performance Over Rayleigh Channels

Across the simulated Rayleigh-channel deployments, RS gains over NoRS become more pronounced as loading increases and CSIT becomes imperfect; in the fully overloaded case, NoRS loses its multiplexing gains.

B. Application to Multibeam Satellite Systems

The satellite application models a GEO multibeam downlink and specifies how antenna feeds map to beams under a single-feed-per-beam architecture.

1) Multibeam Satellite Channel:

The satellite-channel section specifies a multibeam channel model and evaluates RS beamforming under practical satellite conditions. The reported simulations show RS gains over NoRS across CSIT qualities, per-feed constraints, and user distributions.

1) Multibeam Satellite Channel:

  • The satellite channel model combines propagation and multibeam antenna effects with receiver antenna gain, free-space loss, and satellite multibeam antenna gain.Multibeam antenna gain depends mainly on the satellite radiation pattern and user locations.Source: 1) Multibeam Satellite Channel · pp. 12–13
  • The model includes rain fading and phase, with fading coefficients and phases shared across feeds under the stated line-of-sight assumption.The authors attribute this shared-feed modeling to line-of-sight conditions and feed spacing small relative to communication distance.Source: 1) Multibeam Satellite Channel · p. 13

2) Performance Over Satellite Channels:

VI. CONCLUSION

  • The paper reports MMF-DoF gains for RS over NoRS in underloaded and overloaded systems and formulates an MMF optimization solved with modified WMMSE and AO.Simulations examine practical satellite conditions including CSIT uncertainty, per-feed constraints, hot spots, uneven user distributions, and overloaded regimes.Source: §VI · pp. 13–14

2) Performance Over Satellite Channels:

Loading 2008.05091v2…