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Phase Noise Resilient Codebook Design for Sparse Code Multiple Access

Haibo Liu, Qu Luo, Zilong Liu, Shan Luo, Pei Xiao, Xiaojun Yuan

TL;DR

This work tackles phase-noise (PN) impairments in sparse code multiple access (SCMA) by introducing a PN-aware codebook design framework. It defines a minimum PN metric (MPNM) from PN-augmented pairwise error probability and develops an LP-PAM based low projection mother constellation (LP-MC) to enhance PN resilience. By rotating and scaling the MC per user and optimizing these parameters to maximize MPNM, the authors construct PN resilient sparse codebooks (PNCBs) that outperform state-of-the-art codebooks in simulations for multiple SCMA configurations. The approach provides a practical pathway to robust SCMA deployment in PN-prone IoT and massive connectivity scenarios, with demonstrated improvements in error rate performance and design-guided intuition validated by numerical results.

Abstract

Sparse code multiple access (SCMA) is a promising technique for future machine type communication systems due to its superior spectral efficiency and capability for supporting massive connectivity. This paper proposes a novel class of sparse codebooks to improve the error rate performance of SCMA in the presence of phase noise (PN). Specifically, we first analyze the error rate performance of SCMA impaired by looking into the pair-wise error probability. Then, a novel codebook design metric, called minimum PN metric (MPNM), is proposed. In addition, to design PN resilient codebooks, we propose a novel pulse-amplitude modulation (PAM)-based low projection mother constellation (LP-MC), called LP-PAM. The codebooks for different users are obtained by rotating and scaling the MC, where the phase rotation angles and scaling factors for different users are optimized by maximizing the proposed MPNM. Numerical results show that the proposed PNCBs have larger MPNM values and achieve improved error rate performance than the-state-of-the-art codebooks.

Phase Noise Resilient Codebook Design for Sparse Code Multiple Access

TL;DR

This work tackles phase-noise (PN) impairments in sparse code multiple access (SCMA) by introducing a PN-aware codebook design framework. It defines a minimum PN metric (MPNM) from PN-augmented pairwise error probability and develops an LP-PAM based low projection mother constellation (LP-MC) to enhance PN resilience. By rotating and scaling the MC per user and optimizing these parameters to maximize MPNM, the authors construct PN resilient sparse codebooks (PNCBs) that outperform state-of-the-art codebooks in simulations for multiple SCMA configurations. The approach provides a practical pathway to robust SCMA deployment in PN-prone IoT and massive connectivity scenarios, with demonstrated improvements in error rate performance and design-guided intuition validated by numerical results.

Abstract

Sparse code multiple access (SCMA) is a promising technique for future machine type communication systems due to its superior spectral efficiency and capability for supporting massive connectivity. This paper proposes a novel class of sparse codebooks to improve the error rate performance of SCMA in the presence of phase noise (PN). Specifically, we first analyze the error rate performance of SCMA impaired by looking into the pair-wise error probability. Then, a novel codebook design metric, called minimum PN metric (MPNM), is proposed. In addition, to design PN resilient codebooks, we propose a novel pulse-amplitude modulation (PAM)-based low projection mother constellation (LP-MC), called LP-PAM. The codebooks for different users are obtained by rotating and scaling the MC, where the phase rotation angles and scaling factors for different users are optimized by maximizing the proposed MPNM. Numerical results show that the proposed PNCBs have larger MPNM values and achieve improved error rate performance than the-state-of-the-art codebooks.

Paper Structure

This paper contains 12 sections, 26 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. SCMA Communication Model Impaired by Phase Noise
  4. Proposed Design Criteria of Sparse Codebook in the Presence of PN
  5. ML Decision Rule Based on Phase Error Approximation
  6. PEP Analysis of SCMA Impaired by PN
  7. Proposed PN Resilient Codebook Design
  8. LP Inspired One-dimensional Constellation Design
  9. Construction of the $N$-dimension MC
  10. Optimization of Sparse Codebooks
  11. Numerical Results
  12. Conclusion

Figures (4)

  • Figure 1: An example of SCMA factor graph ($K=4$, $J=6$).
  • Figure 2: The effect of PN on different SCMA codebooks with $\sigma_{\mathrm{p}}^{2}=0.01$ and $E_b/N_0=10 \text{dB}$.
  • Figure 3: Example of $\boldsymbol{\mathcal{C}}_{M}$ and $\pi_{2}^{\mathcal{T}}\left(\boldsymbol{\mathcal{C}}_{M}\right)$.
  • Figure 4: BER performance comparison of different codebooks under different PN levels.