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ODMA-based MIMO Massive Unsourced Random Access with Soft-Output Polar Codes

Tianya Li, Xiaoran Zhang, Nan Hu, Yongpeng Wu, Wenjun Zhang, Xiang-Gen Xia, Chengshan Xiao

arXiv:2608.28085v1cs.ITeess.SP

TL;DR

Massive MIMO URA requires efficient transmission and accurate pattern detection, while short-blocklength decoding remains challenging. This paper combines pilot-uncoupled ODMA, hierarchical message-passing/MAP pattern detection, and soft-output polar decoding; simulations report improved energy efficiency and decoding performance.

  • Problem

    Massive uncoordinated access creates challenges for connectivity, capacity, transmission efficiency, and energy efficiency, while existing pilot-uncoupled detection schemes have inferior short-blocklength decoding performance to polar codes.

  • Method

    The scheme uses a three-segment pilot-uncoupled ODMA architecture, hierarchical MMSE/correlation, message-passing and MAP pattern detection, and iterative exchange of bit-wise soft information with an SCL-based polar decoder.

  • Results

    The proposed ODMA-Polar scheme outperforms IDMA-Polar by approximately 1 dB and FASURA by more than 2 dB at target PUPE Pe = 10^-3, while pattern detection reaches approximately −6 dB Eb/N0 at e = 10^-2.

  • Takeaways & Limitations

    The framework combines ODMA transmission gain, short-blocklength polar-coding gain, soft-information iterative decoding gain, and reduced detection complexity.

Abstract

from arXiv · show

This paper investigates the design of the on-off division multiple access (ODMA) transmission scheme for multiple-input multiple-output (MIMO) massive unsourced random access (URA) systems with soft-output (SO) polar codes. First, a three-segment pilot-uncoupled coding scheme is introduced under the ODMA framework, which reduces the coding rate of the data segment without increasing the transmission overhead, improving the overall system performance. Building upon this architecture, a hierarchical pattern detection framework is developed. Specifically, a coarse-grained candidate set of transmission patterns is first identified through correlation operations. Based on this, a message-passing (MP)-based pattern detection algorithm is developed to iteratively estimate the posterior probabilities of transmission patterns, followed by the \textit{maximum a posteriori} (MAP) estimation to obtain the precise pattern detection result. Furthermore, a joint pattern detection and data decoding algorithm based on the bit-wise SO information of polar decoder is investigated, where the posterior probability information provided by the polar decoder is exploited to refine the pattern detection and contribute to an improved accuracy. In addition, by leveraging bit-wise SO information of the successive cancellation list polar decoder, an MP-based iterative decoding algorithm is developed to significantly enhance the decoding performance. The proposed scheme simultaneously exploits the transmission gain of uncoupled-ODMA framework, the coding gain of polar codes in the short-blocklength regime, and the iterative decoding gain enabled by SO information, while the computational complexity is significantly reduced through the hierarchical detection framework. Simulation results demonstrate that the proposed scheme achieves strong robustness ...

I. INTRODUCTION

The paper targets efficient and reliable massive URA for dense IoT connectivity by combining pilot-uncoupled ODMA, hierarchical pattern detection, and SO polar decoding in MIMO systems.

  • URA addresses massive uncoordinated access through a shared codebook, reducing signaling overhead while targeting high connectivity and transmission efficiency.
  • ODMA uses sparse on-off patterns instead of repetition and interleaving, offering a promising architecture for mitigating multi-user interference in URA.
  • The proposed three-segment pilot-uncoupled architecture embeds part of the data into transmission patterns, reducing payload and coding rate without increasing transmission overhead.
  • Hierarchical detection combines MMSE and correlation-based candidate selection, MP posterior updates, MAP refinement, and SO-assisted likelihood refinement to reduce complexity and improve detection.
  • The SO polar-coded JDD framework exchanges bit-wise posterior information between the multi-user detector and SCL polar decoder for iterative recovery.
  • At target PUPE 10^-3, the proposed scheme outperforms state-of-the-art schemes while mitigating multi-user interference.

III. ENCODING SCHEME

The ODMA encoder divides each user’s data into three segments for pilot/interleaving mapping, transmission-pattern mapping, and coded data transmission. Embedding pattern-control data into the third segment reduces the coding rate without increasing transmission overhead.

  • Each user’s data is partitioned into three segments serving distinct functions in the ODMA transmission architecture.The segments support preamble/control signaling, on-off pattern specification, and coded data payload transmission.
  • The first segment maps preamble bits to a Gaussian-codebook codeword used for channel estimation and control information such as the interleaving pattern.The bit sequence is converted to an index and used for codeword selection.
  • The second segment maps data bits to a sparse binary codebook whose selected pattern determines which channel uses carry the third data segment.Each pattern has Hamming weight n_c, leaving n_2−n_c positions idle.
  • The third segment carries the primary payload through CRC-augmented polar coding, BPSK modulation, interleaving, and placement on the selected on positions.The polar code has parameters (n_c, B_c+B_crc), and the interleaver is coupled to the preamble pattern.
  • The pattern-control data is implicitly conveyed through the on-off pattern, reducing the data-segment coding rate while maintaining transmission overhead.The paper attributes the resulting gain to polar decoding at lower coding rate and increased effective energy per information bit.
  • Unlike prior uncoupled frameworks, the proposed scheme combines hierarchical MP-based pattern detection with SCL-polar soft-output information for iterative refinement.The design targets lower detection complexity and higher pattern-recovery accuracy.

IV. DECODING SCHEME

The decoding scheme comprises MMV-AMP-based activity detection and channel estimation, followed by correlation-based, MP-based, and joint pattern/data decoding procedures.

  • The receiver first uses MMV-AMP-based JADCE, then applies correlation-based, MP-based, and joint pattern detection and data decoding algorithms.These procedures are presented as successive components of the decoding scheme.

A. Joint Activity Detection and Channel Estimation

The JADCE stage recovers active-user supports and channels by treating the equivalent channel as a row-sparse MMV compressed-sensing problem. MMV-AMP produces estimates that are thresholded by energy detection before reverse mapping.

  • The first data segment is rewritten to support joint activity detection and channel estimation.This segment primarily provides channel-estimation and control information.
  • The one-hot selection matrix creates an equivalent channel matrix with row sparsity because the codebook size greatly exceeds the number of active users.Recovering its nonzero-row support and values forms the JADCE problem.
  • MMV-AMP uses a vector-wise denoiser on matched-filter row vectors to estimate the equivalent channel matrix.The algorithm iterates until a maximum-iteration limit or stopping criterion is reached.
  • Energy detection identifies the nonzero rows of the estimated equivalent channel, yielding estimated active users and their channel estimates.The first data segment is then recovered by reverse mapping.

B. Coarse Detection: Correlation-based Pattern Detection

Coarse pattern detection first estimates the third-segment data and correlates it with the shared sparse ODMA codebook. The highest-correlation candidates are retained for MP-based posterior estimation and MAP selection.

  • Detecting embedded on-off patterns is necessary to identify allocated channel uses and enable reliable data decoding.
  • In MIMO channels, pattern detection is coupled with channel estimation, expanding the search space to N_o ˆK_a.This motivates reducing the search space before iterative detection.
  • An LMMSE estimator first produces estimates of the third-segment data sequences before correlation-based pattern detection.
  • Correlation operations compare each estimated data sequence with the shared ODMA pattern codebook to identify its most compatible on-off pattern.This is the matching operation illustrated in Fig. 2.
  • For each user, the detector retains the top-N_c highest-correlation patterns as a coarse candidate set.MP then computes candidate posterior LLRs, followed by MAP estimation of the transmission pattern.

C. Precise Detection: MP-based Pattern Detection

The MP-based detector refines a correlation-derived candidate pattern set by iteratively updating posterior probabilities and applying MAP estimation. A hierarchical search reduces the pattern space while adapting likelihood computation to MIMO channels.

  • MP-based pattern detection: MPA iteratively updates posterior probabilities and pattern likelihoods for candidate transmission patterns before MAP selects the precise detection result.The procedure initializes symbol posteriors, computes conditional likelihoods and extrinsic information, and alternates updates across users.
  • MIMO likelihood computation: For MIMO channels, conditional pattern likelihoods are reformulated to account for coupling between transmission patterns and channel coefficients.The method uses Gaussian approximations for interference terms and computes their means and variances from posterior symbol information.
  • Complexity reduction: To reduce complexity during MP iterations, other users’ patterns are fixed to their highest-correlation candidates while the current user is updated.The resulting LLRs are used to select the final pattern with the highest posterior likelihood.

D. Enhanced Detection: Joint Pattern Detection and Data Decoding

The enhanced scheme jointly detects transmission patterns and decodes polar-coded data by exchanging soft posterior information. Decoder outputs refine pattern likelihoods, while updated patterns feed subsequent decoding iterations.

  • Soft-information exchange: The joint algorithm uses soft-output SCL polar decoding to exchange posterior information with MP-based pattern detection.Extrinsic and posterior messages are iteratively passed between received-signal sum nodes and codeword variable nodes.
  • SO polar decoding: The SCL soft-output decoder represents codeword probabilities using bit-wise APPs and an approximate computation over the decoding tree.Exhaustive enumeration of all valid codewords is avoided because it has prohibitive complexity.
  • Joint detection and decoding: Decoder posterior probabilities refine transmission-pattern posteriors, addressing pattern errors that can otherwise propagate into data decoding.Updated pattern results are fed back to the decoder for subsequent iterations.
  • Final detection and decoding: After iterative updates, MAP selects the candidate pattern with the maximum LLR, and the corresponding polar transform yields the decoded data.The process can terminate when the maximum iteration count is reached or CRC checks are satisfied.
  • Implementation: Updating pattern posterior LLRs with decoder information only once is reported as sufficient for satisfactory performance under the stated complexity consideration.The information-exchange process is summarized in Fig. 3 and Algorithm 2.

MINISTIC PATTERNS

The deterministic-pattern decoding procedure exchanges extrinsic and posterior messages, checks CRC termination, and recovers user data through the polar transform.

  • Iterative decoding: MPA exchanges extrinsic messages from received-signal sum nodes with posterior messages from codeword variable nodes during iterative decoding.These updates use the message equations associated with the deterministic transmission pattern.
  • Termination and data recovery: The decoder terminates when the CRC check is satisfied for all users, after which decoded codewords are transformed into data vectors.The recovered data is obtained from the decoded codewords through the polar transform.
  • Special case: The described procedure includes the single-antenna case as the special case M = 1 of the multi-antenna scenario.

E. Complexity Analysis

The complexity analysis measures per-iteration computational cost by floating-point multiplications and identifies the dominant orders for the compared algorithms.

  • Per-iteration complexity: The MMV-AMP algorithm has per-iteration complexity O(n1N_pM), while the proposed pattern detector has dominant complexity O(K_aN_cn2M).The pattern-detection cost arises primarily from Eq. (20).

V. NUMERICAL RESULTS

The numerical-results section evaluates the proposed algorithms for pattern detection and data decoding across transmission energy, active-user load, and received-antenna count.

  • The simulations assess system performance with respect to transmission energy, the number of active users, and the number of received antennas.

A. Parameter Settings

The evaluation compares hierarchical pattern detection, SO polar decoding, and URA schemes under varying energy, user load, and antenna configurations. Results show improved detection and decoding performance for the proposed ODMA-Polar design, especially in large-scale antenna settings.

  • B. Pattern Detection Performance: The study compares correlation-based, MP-based, and Polar-LLR pattern detection schemes.Polar-LLR incorporates SO information from polar decoding into iterative pattern updates.
  • B. Pattern Detection Performance: The proposed SO polar pattern detector achieves the best performance across active-user and received-antenna settings.For varying active users, codeword lengths are adjusted for Ka = 120 and 140; antenna-scaling results are evaluated separately.
  • C. Data Decoding Performance: The Joint SCL strategy substantially improves decoding over Hard SCL by combining SO polar decoding with iterative pattern detection.Joint SCL is adopted as the default ODMA-Polar decoding method in subsequent simulations.
  • C. Data Decoding Performance: IDMA-Polar performs best for Eb/N0 ∈ [−5 dB, 2 dB], while FASURA performs best in [−8 dB, −5 dB].The ODMA-based polar scheme slightly outperforms IDMA-Polar in the lower-energy region but falls slightly behind in the higher-energy region.
  • C. Data Decoding Performance: When M ≥ 30, the ODMA-based polar coding scheme outperforms the other evaluated URA schemes.The paper attributes this result primarily to multi-antenna diversity improving pattern detection accuracy.
  • C. Data Decoding Performance: At Pe = 10−3, ODMA-Polar gains approximately 1 dB over IDMA-Polar and more than 2 dB over FASURA.At Pe = 5 × 10−3, coupled-ODMA performs better for Ka < 80 but ceases to function above Ka = 80, whereas ODMA-Polar remains robust from Ka = 40 to 160.

VI. CONCLUSION

The paper proposes an ODMA-based MIMO massive URA scheme with SO polar codes, combining hierarchical pattern detection with joint pattern detection and data decoding. Simulations report significant gains over existing URA techniques, particularly with large-scale antenna configurations.

  • The proposed architecture uses pilot-uncoupled three-segment coding, MMV-AMP user detection and channel estimation, and hierarchical pattern detection.Pattern detection proceeds from correlation-based coarse estimation to MP posterior updates and MAP detection.
  • The joint detector and decoder exploit SO polar posterior information to improve both pattern detection and data decoding.
  • The proposed scheme achieves significant performance improvements over existing URA techniques, especially under large-scale antenna configurations.
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