Design and Analysis of Massive Uncoupled Unsourced Random Access with Bayesian Joint Decoding

TL;DR

This work tackles scalable unsourced random access for 6G mMTC by proposing a high-efficiency uncoupled framework that omits parity bits and leverages Bayesian joint decoding. The receiver uses a divergence-free orthogonal AMP-based detector to identify codewords and a Bayesian classifier to stitch them across sub-slots using long-term channel statistics, with EM-based learning of priors guiding the process. The approach yields low complexity and strong performance, supported by state-evolution-based asymptotics showing vanishing codeword-detection error with large $M$ and high transmit power, and simulations demonstrating competitive spectral efficiency against coupled schemes. The results indicate promising practical impact for massive connectivity in 6G networks, enabling reliable, low-overhead uplink access with limited signaling.

Abstract

In this paper, we investigate unsourced random access for massive machine-type communications (mMTC) in the sixth-generation (6G) wireless networks. Firstly, we establish a high-efficiency uncoupled framework for massive unsourced random access without extra parity check bits. Then, we design a low-complexity Bayesian joint decoding algorithm, including codeword detection and stitching. In particular, we present a Bayesian codeword detection approach by exploiting Bayes-optimal divergence-free orthogonal approximate message passing in the case of unknown priors. The output long-term channel statistic information is well leveraged to stitch codewords for recovering the original message. Thus, the spectral efficiency is improved by avoiding the use of parity bits. Moreover, we analyze the performance of the proposed Bayesian joint decoding-based massive uncoupled unsourced random access scheme in terms of computational complexity and error probability of decoding. Furthermore, by asymptotic analysis, we obtain some useful insights for the design of massive unsourced random access. Finally, extensive simulation results confirm the effectiveness of the proposed scheme in 6G wireless networks.

Figures (7)

• Figure 1: The flow chart of Bayesian joint decoding. The decoder consists of four local modules, these modules work together to recover the original messages $\hat{\bm{m}}_k$ sent from multiple active UEs according to the noisy received signals $\textbf{Y}$. In particular, the OAMP detector including linear estimator $\gamma(\cdot)$ and non-linear estimator $\phi(\cdot)$ aims to detect the codeword state matrix $\textbf{X}$. The iteration between $\textbf{R}$ and $\textbf{S}$ has been defined in \ref{['Ite_LE']} and \ref{['Ite_NLE']}. By leveraging the MMSE estimations $[\pi, \boldsymbol{\lambda}, \rho]$ of OAMP detector, parameter estimator $\psi(\cdot)$ estimates the unknown system parameters $[\sigma^2,\varepsilon,g]$ and then feeds them back. With the estimated codeword state matrix $\hat{\textbf{X}}$ and channel statistics $\hat{g}$, the original messages $\hat{\bm{m}}_k$ can be reconstructed in codeword splicer $\mu(\cdot)$.
• Figure 2: The Convergence behaviour for different numbers of active UEs. $J=14$ and $b=112$.
• Figure 3: The error probability of $\hat{K}_a$ versus SNR and the final error probability $P_2$ versus SNR for perfect and imperfect $\hat{K}_a$.
• Figure 4: The final error probability versus the number of BS antennas for different unsourced random access schemes.
• Figure 5: The final error probability $P_2$ of the proposed Bayesian joint decoding versus SNR for different numbers of BS antennas.

Theorems & Definitions (2)

• Lemma 1
• Lemma 2