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Rapid Optimization of Superposition Codes for Multi-Hop NOMA MANETs via Deep Unfolding

Tomer Alter, Nir Shlezinger

TL;DR

This work tackles rapid design of superposition codes for multi-hop NOMA MANETs under dynamic topology and imperfect CSI. It introduces Unfolded PGDNet, a deep-unfolding learned optimizer that turns a projected gradient descent step into a fixed-depth network with trainable step-sizes, augmented by an ensemble to cope with non-convexity. The method supports both full CSI and pilot-based CSI via LMMSE features, and demonstrates transferability across topologies, enabling rapid adaptation in time-varying networks. Empirical results show substantial latency reductions (roughly 10x–80x faster) while achieving near grid-capacity performance, outperforming graph-based baselines and remaining robust to estimation errors and topology changes.

Abstract

Various communication technologies are expected to utilize mobile ad hoc networks (MANETs). By combining MANETs with non-orthogonal multiple access (NOMA) communications, one can support scalable, spectrally efficient, and flexible network topologies. To achieve these benefits of NOMA MANETs, one should determine the transmission protocol, particularly the superposition code. However, the latter involves lengthy optimization that has to be repeated when the topology changes. In this work, we propose an algorithm for rapidly optimizing superposition codes in multi-hop NOMA MANETs. To achieve reliable tunning with few iterations, we adopt the emerging deep unfolding methodology, leveraging data to boost reliable settings. Our superposition coding optimization algorithm utilizes a small number of projected gradient steps while learning its per-user hyperparameters to maximize the minimal rate over past channels in an unsupervised manner. The learned optimizer is designed for both settings with full channel state information, as well as when the channel coefficients are to be estimated from pilots. We show that the combination of principled optimization and machine learning yields a scalable optimizer, that once trained, can be applied to different topologies. We cope with the non-convex nature of the optimization problem by applying parallel-learned optimization with different starting points as a form of ensemble learning. Our numerical results demonstrate that the proposed method enables the rapid setting of high-rate superposition codes for various channels.

Rapid Optimization of Superposition Codes for Multi-Hop NOMA MANETs via Deep Unfolding

TL;DR

This work tackles rapid design of superposition codes for multi-hop NOMA MANETs under dynamic topology and imperfect CSI. It introduces Unfolded PGDNet, a deep-unfolding learned optimizer that turns a projected gradient descent step into a fixed-depth network with trainable step-sizes, augmented by an ensemble to cope with non-convexity. The method supports both full CSI and pilot-based CSI via LMMSE features, and demonstrates transferability across topologies, enabling rapid adaptation in time-varying networks. Empirical results show substantial latency reductions (roughly 10x–80x faster) while achieving near grid-capacity performance, outperforming graph-based baselines and remaining robust to estimation errors and topology changes.

Abstract

Various communication technologies are expected to utilize mobile ad hoc networks (MANETs). By combining MANETs with non-orthogonal multiple access (NOMA) communications, one can support scalable, spectrally efficient, and flexible network topologies. To achieve these benefits of NOMA MANETs, one should determine the transmission protocol, particularly the superposition code. However, the latter involves lengthy optimization that has to be repeated when the topology changes. In this work, we propose an algorithm for rapidly optimizing superposition codes in multi-hop NOMA MANETs. To achieve reliable tunning with few iterations, we adopt the emerging deep unfolding methodology, leveraging data to boost reliable settings. Our superposition coding optimization algorithm utilizes a small number of projected gradient steps while learning its per-user hyperparameters to maximize the minimal rate over past channels in an unsupervised manner. The learned optimizer is designed for both settings with full channel state information, as well as when the channel coefficients are to be estimated from pilots. We show that the combination of principled optimization and machine learning yields a scalable optimizer, that once trained, can be applied to different topologies. We cope with the non-convex nature of the optimization problem by applying parallel-learned optimization with different starting points as a form of ensemble learning. Our numerical results demonstrate that the proposed method enables the rapid setting of high-rate superposition codes for various channels.
Paper Structure (28 sections, 1 theorem, 24 equations, 17 figures, 1 table, 3 algorithms)

This paper contains 28 sections, 1 theorem, 24 equations, 17 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Communication System Model
  4. Channel State Information
  5. Problem Formulation
  6. Achievable Rates
  7. Superposition Code Optimization
  8. Challenges
  9. Unfolded Superposition Coding Optimization
  10. Projected Gradient Descent for NOMA MANETs
  11. Unfolded PGDNet
  12. PGDNet Architecture
  13. Training PGDNet
  14. PGDNet Ensemble
  15. Learned Optimization from Noisy Pilots
  16. ...and 13 more sections

Key Result

Lemma 1

For a given $n\in\mathcal{N}(t)$, let $\tilde{m}\in\{1,2,\dots,\max_i M_i(t)\}$, $\tilde{b}\in\mathcal{B}\backslash\{B\}$, and $l_{B}\in\mathcal{N}(t)$, be the indices holding $\tilde{m},\tilde{b} = \mathop{\mathrm{arg\,min}}\limits_{m,b}R_{m,n}^{(b)}$ and $l_{B} = \mathop{\mathrm{arg\,min}}\limits_ where the gradients of $R^{(1)}_{m,n}(t),R^{(b)}_{l,n}(t)$ are given in eqn:RateGrad2.

Figures (17)

  • Figure 1: Multi-hop manet illustration.
  • Figure 2: PGDNet architecture; trainable parameters are marked in red.
  • Figure 3: Unfolded PGDNet training and inference procedures
  • Figure 4: Training Unfolded PGDNet with noisy pilots
  • Figure 5: Min-rate per PGD iteration averaged over $200$ channels, $1\times 2\times 2$ static manet.
  • ...and 12 more figures

Theorems & Definitions (1)

  • Lemma 1