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Probabilistic Constellation Shaping for Enhancing Spectral Efficiency in NOMA VLC Systems

Amanat Kafizov, Ahmed Elzanaty, Mohamed-Slim Alouini

TL;DR

This work tackles spectral efficiency limits in visible light communication (VLC) caused by LED bandwidth by proposing an OSNR-aware adaptive coded probabilistic shaping (PS) scheme for uplink NOMA. The approach combines CCDM-based distribution matching, an efficient reverse-concatenation encoder with rate adaptation, and an alternating optimization that jointly selects constellation spacing and symbol PMF per user to approach NOMA capacity while respecting IM/DD constraints. The decoder uses SIC with MAP-based soft demodulation and demodulation/dematching to recover data, enabling dynamic adjustment of the FEC rate and shaping to OSNR. Numerical results for two users show significant SE gains over PCM, GS, and uniform signaling, with the PS-NOMA scheme approaching capacity and providing practical benefits for high-rate VLC systems.

Abstract

The limited modulation bandwidth of the light emitting diodes (LEDs) presents a challenge in the development of practical high-data-rate visible light communication (VLC) systems. In this paper, a novel adaptive coded probabilistic shaping (PS)-based nonorthogonal multiple access (NOMA) scheme is proposed to improve spectral efficiency (SE) of VLC systems in multiuser uplink communication scenarios. The proposed scheme adapts its rate to the optical signal-to-noise ratio (OSNR) by utilizing non-uniformly distributed discrete constellation symbols and low complexity channel encoder. Furthermore, an alternate optimization algorithm is proposed to determine the optimal channel coding rate, constellation spacing, and probability mass function (PMF) of each user. The extensive numerical results show that the proposed PS-based NOMA scheme closely approaches the capacity of NOMA with fine granularity. Presented results demonstrate the effectiveness of our scheme in improving the SE of VLC systems in multiuser scenarios. For instance, our scheme exhibits substantial SE gains over existing schemes, namely, the pairwise coded modulation (PCM), geometric shaping (GS), and uniform-distribution schemes. These findings highlight the potential of our approach to significantly enhance VLC systems.

Probabilistic Constellation Shaping for Enhancing Spectral Efficiency in NOMA VLC Systems

TL;DR

This work tackles spectral efficiency limits in visible light communication (VLC) caused by LED bandwidth by proposing an OSNR-aware adaptive coded probabilistic shaping (PS) scheme for uplink NOMA. The approach combines CCDM-based distribution matching, an efficient reverse-concatenation encoder with rate adaptation, and an alternating optimization that jointly selects constellation spacing and symbol PMF per user to approach NOMA capacity while respecting IM/DD constraints. The decoder uses SIC with MAP-based soft demodulation and demodulation/dematching to recover data, enabling dynamic adjustment of the FEC rate and shaping to OSNR. Numerical results for two users show significant SE gains over PCM, GS, and uniform signaling, with the PS-NOMA scheme approaching capacity and providing practical benefits for high-rate VLC systems.

Abstract

The limited modulation bandwidth of the light emitting diodes (LEDs) presents a challenge in the development of practical high-data-rate visible light communication (VLC) systems. In this paper, a novel adaptive coded probabilistic shaping (PS)-based nonorthogonal multiple access (NOMA) scheme is proposed to improve spectral efficiency (SE) of VLC systems in multiuser uplink communication scenarios. The proposed scheme adapts its rate to the optical signal-to-noise ratio (OSNR) by utilizing non-uniformly distributed discrete constellation symbols and low complexity channel encoder. Furthermore, an alternate optimization algorithm is proposed to determine the optimal channel coding rate, constellation spacing, and probability mass function (PMF) of each user. The extensive numerical results show that the proposed PS-based NOMA scheme closely approaches the capacity of NOMA with fine granularity. Presented results demonstrate the effectiveness of our scheme in improving the SE of VLC systems in multiuser scenarios. For instance, our scheme exhibits substantial SE gains over existing schemes, namely, the pairwise coded modulation (PCM), geometric shaping (GS), and uniform-distribution schemes. These findings highlight the potential of our approach to significantly enhance VLC systems.
Paper Structure (25 sections, 1 theorem, 58 equations, 8 figures, 3 tables, 1 algorithm)

This paper contains 25 sections, 1 theorem, 58 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Main Contributions
  3. Paper Organization and Notations
  4. Systems Model
  5. Proposed NOMA VLC scheme with PS
  6. Encoder
  7. Symbol Distribution Optimizer
  8. Distribution Matcher
  9. Channel Encoder
  10. Sparse-Dense Signal
  11. Decoder
  12. SIC
  13. MAP Calculation
  14. FEC Decoder and Dematcher
  15. Rate Analysis
  16. ...and 10 more sections

Key Result

Lemma 5.1

For the given $\Delta_{j}$, $\mathrm{R}_{\mathrm{FEC}}$, $\hat{\mathbf{p}}_{j}$, and OSNR, where and where $D=\left(1-\mathrm{R}_{\text{FEC}}\right)\mathrm{R}_{j}\!\left(\Delta_{j},\mathbf{p}^{u}_{j},\mathbf{a}_{\widehat{y}_{j}}^{\star}\right)-\mathrm{R}_{\text{bf}}$, $\tau$ and $\eta$ are any positive real numbers.

Figures (8)

  • Figure 1: Uplink NOMA transmission scenario for $N$ users.
  • Figure 2: Architecture of NOMA with PS in VLC systems.
  • Figure 3: Encoder and decoder for user $j$ of the proposed NOMA VLC scheme with PS.
  • Figure 4: Capacity region of NOMA for $M=8$ and at OSNR $P_{r1}/\sigma=6$ dB.
  • Figure 5: Transmission rates vs OSNR for $M=8$.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Lemma 5.1: KKT solution to \ref{['optimization:ch4:MI:Tx:convex']}
  • proof