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Efficient Massive Machine Type Communication (mMTC) via AMP

Mostafa Mohammadkarimi, Masoud Ardakani

TL;DR

This work addresses efficient multiuser detection for massive machine-type communications over a Gaussian MAC with short packets. It frames MUD as sparse signal recovery and leverages Bayesian AMP with both separable and non-separable MMSE denoisers by exploiting exact and approximate priors for the transmitted vector, enabling low-complexity yet near-optimal decoding. The authors propose two algorithms: Relaxed Block Sparsity AMP (RBS-AMP) and Block Sparsity AMP (BS-AMP); they derive state evolution and multiuser efficiency expressions, showing BS-AMP achieves a closer match to the upper bound than prior approaches. Simulation results demonstrate that, for 8 information-bit packets, BS-AMP reaches about 4/7 of the upper bound at Eb/N0 = 4 dB, while RBS-AMP reaches about 1/2, illustrating significant practical gains in spectral efficiency with scalable complexity.

Abstract

We propose efficient and low-complexity multiuser detection (MUD) algorithms for Gaussian multiple access channel (G-MAC) for short-packet transmission in massive machine type communications. To do so, we first formulate the G-MAC MUD problem as a sparse signal recovery problem and obtain the exact and approximate joint prior distribution of the sparse vector to be recovered. Then, we employ the Bayesian approximate message passing (AMP) algorithms with the optimal separable and non-separable minimum mean squared error (MMSE) denoisers for soft decoding of the sparse vector. The effectiveness of the proposed MUD algorithms for a large number of devices is supported by simulation results. For packets of 8 information bits, while the state-of-the-art AMP with soft-threshold denoising achieves 8/100 of the upper bound at Eb/N0 = 4 dB, the proposed algorithms reach 4/7 and 1/2 of the upper bound.

Efficient Massive Machine Type Communication (mMTC) via AMP

TL;DR

This work addresses efficient multiuser detection for massive machine-type communications over a Gaussian MAC with short packets. It frames MUD as sparse signal recovery and leverages Bayesian AMP with both separable and non-separable MMSE denoisers by exploiting exact and approximate priors for the transmitted vector, enabling low-complexity yet near-optimal decoding. The authors propose two algorithms: Relaxed Block Sparsity AMP (RBS-AMP) and Block Sparsity AMP (BS-AMP); they derive state evolution and multiuser efficiency expressions, showing BS-AMP achieves a closer match to the upper bound than prior approaches. Simulation results demonstrate that, for 8 information-bit packets, BS-AMP reaches about 4/7 of the upper bound at Eb/N0 = 4 dB, while RBS-AMP reaches about 1/2, illustrating significant practical gains in spectral efficiency with scalable complexity.

Abstract

We propose efficient and low-complexity multiuser detection (MUD) algorithms for Gaussian multiple access channel (G-MAC) for short-packet transmission in massive machine type communications. To do so, we first formulate the G-MAC MUD problem as a sparse signal recovery problem and obtain the exact and approximate joint prior distribution of the sparse vector to be recovered. Then, we employ the Bayesian approximate message passing (AMP) algorithms with the optimal separable and non-separable minimum mean squared error (MMSE) denoisers for soft decoding of the sparse vector. The effectiveness of the proposed MUD algorithms for a large number of devices is supported by simulation results. For packets of 8 information bits, while the state-of-the-art AMP with soft-threshold denoising achieves 8/100 of the upper bound at Eb/N0 = 4 dB, the proposed algorithms reach 4/7 and 1/2 of the upper bound.
Paper Structure (14 sections, 2 theorems, 34 equations, 2 figures)

This paper contains 14 sections, 2 theorems, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Review of AMP
  4. AMP Algorithm with Separable Denoiser
  5. SE of AMP with Separable Denoiser
  6. RBS-AMP MUD Algorithm
  7. RBS-AMP MUD Algorithm with Separate Denoiser
  8. MUE of the RBS-AMP MUD algorithm
  9. BS-AMP MUD Algorithm
  10. SE of AMP with Non-separable Denoiser
  11. BS-AMP MUD Algorithm with Non-separable Denoiser
  12. MUE of the BS-AMP MUD algorithm
  13. Simulation Results
  14. Conclusion

Key Result

Theorem 1

The MUE of the RBS-AMP MUD algorithm at the $(t+1)$th iteration is given by where $\xi^{t+1}_{\rm RB} \in [0,1]$, and $\sigma^2_{t+1}$ is given in Equation_18-Equation_19 for $U=X$ in Eq_PDF_DELTA (Proof in Appendix Appx_3).

Figures (2)

  • Figure 1: State evolution of the RBS-AMP and BS-AMP MUD algorithms for $K=8$ and $D=256$ at ${E_{\rm b}} / {N_0}=6$ dB.
  • Figure 2: Spectral efficiency versus $10 \log_{10} ({E_{\rm b}} / {N_0})$ for the average block error rate $P_{\rm{e}}=15 \times 10^{-4}$, $K=8$, and $D=256$.

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2