Probabilistic ODMA Receiver with Low-Complexity Algorithm for MIMO Unsourced Random Access

TL;DR

This paper tackles unsourced random access for MIMO systems using pilot-free and pilot-uncoupled ODMA. It introduces a probabilistic receiver that combines low-rank matrix factorization with an AMP-based joint pattern and data detector, initialized by pilot-free alternating minimization, to achieve linear rather than quadratic decoding complexity. The approach yields up to about 13 dB capacity gains over pilot-free baselines and performs robustly in under-determined regimes, while maintaining favorable complexity-capacity trade-offs. The results suggest substantial practical benefits for next-generation massive connectivity, with future work targeting asynchronous transmission and more advanced MIMO configurations.

Abstract

In this work, we present the design for both pilot-uncoupled and pilot-free on-off multiple access (ODMA) receivers in unsourced random access (URA) for multiple-input multiple-output (MIMO) systems. Unlike pilot-coupled ODMA, where on-off patterns are linked to pilot selection, pilot-uncoupled and pilot-free ODMA reduce transmission redundancy but face challenges in processing complexity and capacity performance. The joint pattern and data detector (JPDD) design is critical for these schemes, but the current JPDD algorithm has high complexity with quadratic computational costs. To address this, we propose a low-complexity detector based on approximate message passing (AMP), which offers linear complexity, providing reduced cost and improved performance in the under-determined linear regression case. Decoding is initialized via pilot-free matrix factorization through alternating minimization, resolving phase and scalar ambiguities. Compared to existing pilot-free schemes, the proposed method achieves a 13 dB improvement and favorable trade-offs in complexity and capacity performance when compared to benchmarks.

Figures (5)

• Figure 1: Illustration of transmission in single chunk and the proposed encoder procedures where $\mathcal{Q}$ denotes modulation with order $Q$, $\boldsymbol{A}$ and $\mathcal{C}$ denote pattern codebooks. The $B_2$ bits are used to select patterns only and not transmitted at all and the chunk has length equal to $T=L/J$
• Figure 2: Symbol error rate (SER) comparison between the proposed JPDD-AMP detector and the JPDD-PDA detector in IOTJ_ODMA under different $\mathrm{SNR}$ (dB) and number of antenna $M$.
• Figure 3: SER comparison in cases of determined and under-determined estimation with $\mathrm{SNR}=5$dB, $M=50$ and different modulation order $Q=|\mathcal{Q}|$ for $\{0,\mathcal{Q}\}$.
• Figure 4: PUPE Comparisons between the proposed scheme with IDMA and computational complexity comparison with recent works: a) PUPE versus energy-per-bit $E_b/N_0$(dB) with $M=50$; b) PUPE versus the number of antenna $M$ under $E_b/N_0=-6$dB; c) Complexity versus number of active users $K_a$.
• Figure 5: Minimum required $E_b/N_0$ (dB) to reach PUPE $P_e=0.05$ under $L=3200$, $M=50$: The capacity performance of the pilot-free receiver is significantly enhanced, ranging from 8 dB to 13.2 dB.