UR2M: Unsourced Two-Step Random Access

• UR2M is a grant-free unsourced random access protocol that enables scalable, high-density mMTC using a common codebook and advanced two-step access techniques.
• It employs sparse block interleaving, joint sparse recovery, and successive interference cancellation to achieve near-optimal error rates and enhanced spectral efficiency.
• The framework extends to massive MIMO and compressed sensing, reducing energy per bit and latency while supporting large device populations in IoT and TinyML environments.

UR2M (Unsourced Random Two-Step Multiple Access) refers to a class of grant-free random access protocols and analytical frameworks designed for reliable, energy-efficient, and highly scalable communication in massive machine-type communication (mMTC), particularly for next-generation wireless systems. The UR2M framework implements the core principles of unsourced random access—where device/user identities are not tied to dedicated resources—enabling high-density device connectivity, fast access, and significant improvements in both algorithmic and physical-layer efficiency. UR2M architectures and algorithms have been developed for both single-antenna and massive MIMO scenarios, as well as for specific deployment environments such as microcontrollers in the TinyML domain, using advanced coding, inference, and signal processing techniques (Agostini et al., 2024, Jiang et al., 2023, Yang et al., 2020, Jia et al., 2024).

1. System Model and Theoretical Foundations

UR2M operates within the unsourced MAC (UMAC) paradigm, where $K_a$ active devices out of a much larger population each transmit one message of $k$ bits over $n$ channel uses. Rather than associating codebooks with individual users, all devices use a common codebook $\mathcal C$ of size $2^k$, and the receiver outputs an unordered list of $K_a$ candidate messages. The principal information-theoretic performance metric is the per-user probability of error (PUPE), defined as

$$\text{PUPE} = \frac{1}{K_a}\sum_{i=1}^{K_a} \mathbb{P}\left[x^{(i)} \notin \mathcal{L}\right]$$

where $\mathcal{L}$ is the list output by the receiver. The UR2M system may consider block-fading AWGN MAC or quasi-static Rayleigh fading models:

• AWGN: $y_t = \sum_{i=1}^{K_a} x_t^{(i)} + z_t$, $z_t \sim \mathcal{CN}(0, \sigma^2)$
• Fading: $k$0, $k$1

The coding and medium access protocol must approach the finite-blocklength random-coding bound (RCU) for a given $k$2, $k$3, $k$4, and target PUPE.

2. Two-Step Protocols and Mapping from 5G-NR

UR2M generalizes the 5G New Radio (NR) “two-step random access” (2SRA) protocol into an unsourced framework suitable for mMTC:

Classical 2SRA:

• Step 1: Devices send a randomly selected preamble (from $k$5 Zadoff–Chu sequences) followed by immediate data on an associated resource occasion.
• Step 2: The base station detects preambles, decodes data, and provides acknowledgment; unresolved transmissions fall back to a slower four-step process.

UR2M Extensions:

• The preamble is replaced or extended (e.g., with random coded preambles) to enlarge the access pattern space and support orthogonal collision resolution.
• The user codeword is a concatenation of preamble and message—mapping both to a high-diversity channel access pattern, facilitating multi-packet reception (MPR) without explicit grants.
• Coding schemes exploit sparse block interleaving (SB-IDMA) and joint sparse recovery to enable efficient message and identity extraction (Agostini et al., 2024).

Key system metrics—PUPE, user-per-bit energy ($k$6), and spectral efficiency—are analytically benchmarked against UMAC lower bounds.

3. Design Features: Coding, Interleaving, and Collision Resolution

UR2M enables high throughput and reliability by leveraging advanced coding and scheduling mechanisms:

Sparse Block Interleaver Multiple Access (SB-IDMA):

• All devices use the same binary $k$7 linear code (e.g., LDPC or polar), QPSK-modulated.
• Each message is hashed into a configuration tuple: extended preamble index, pilot set, and access pattern over multiple data segments.
• Codewords are split into $k$8 segments, each randomly mapped (“interleaved”) onto one of $k$9 resource occasions, greatly reducing collision probability and enhancing robustness through diversity.

Decoding Architecture:

• The receiver detects candidate preamble indices, infers predicted segment locations, demodulates per-slot observations, and merges likelihoods from multiple repetitions for each code bit.
• Iterative successive interference cancellation (SIC) is applied across both preamble and data segments, leveraging joint decoding and collision resolution akin to coded slotted ALOHA.

The coding and repetition structure yields scalability to $n$0 at finite SNR and near-optimal error floors relative to the PUPE limits.

4. Algorithmic and Analytical Performance

UR2M performance has been quantified using a suite of metrics and benchmarking against legacy and state-of-the-art approaches:

Scheme	Max $n$1 (AWGN, 4dB)	$n$2 for $n$3	Gap to RCU Bound
2SRA OTO (64 preambles)	15	5.8 dB	$n$45 dB
SB-IDMA LDPC $n$5	80	1.8 dB	$n$61.8 dB
SB-IDMA Polar $n$7	95	1.0 dB	$n$81.0 dB
RCU Bound	—	0.0 dB	—

In quasi-static fading, SB-IDMA enables hundreds of simultaneously active users (e.g., $n$9 at $\mathcal C$0 dB SNR, far exceeding conventional 2SRA) (Agostini et al., 2024).

Energy and spectral efficiency gains are achieved through a combination of reduced fallback, efficient collision resolution, and optimal resource mapping:

• Energy per bit is reduced by $\mathcal C$12.8 dB due to minimized preamble repetition and overhead, with an additional 0.8 dB from higher code rates.
• Spectral efficiency for $\mathcal C$2 users nearly triples relative to baseline 2SRA, under the same error constraint.

5. Massive MIMO Extensions and Compressed Sensing Decoding

UR2M approaches have been extended to massive MIMO regimes via a two-phase design (Jiang et al., 2023):

1. Phase I: Simultaneous joint user activity detection, channel state information (CSI) acquisition, and reception of the first $\mathcal C$3 payload bits. CS-based algorithms (e.g., approximate message passing, AMP) are used for joint activity and data recovery.
2. Phase II: Remaining payload transmitted in very short sub-blocks using orthonormal codebooks, exploiting the CSI obtained in phase I. The problem becomes multiple measurement vector (MMV) compressed sensing, solved via hybrid-GAMP or related algorithms, with per-user, per-sub-block complexity $\mathcal C$4 (for $\mathcal C$5 users, $\mathcal C$6 antennas, $\mathcal C$7 bits per block).

Performance and algorithmic phase transitions are rigorously characterized via replica analysis. The Bayes-optimal mean-square error and the performance of low-complexity AMP decoders exhibit sharp thresholds as a function of the ratio $\mathcal C$8 and support accurate prediction of achievable reliability. Compared to prior divide-and-conquer and pilot-based schemes, UR2M demonstrates orders-of-magnitude improvement in user error probability for given resources or can operate with substantially fewer antennas, maintaining low $\mathcal C$9 (Jiang et al., 2023).

6. Comparison with Reed-Muller-Coded Massive Access

Alternative UR2M-like protocols employ second-order Reed–Muller codes for device identification and payload encoding (Yang et al., 2020):

• Enormous codebook size $2^k$0, supporting massive numbers of users.
• Enhanced slotting (“Algorithm 2”) maps segments of each RM codeword into distinct mini-slots, enabling sparse transmission and increased robustness.
• Decoder complexity is $2^k$1, several-fold lower than previous list-based decoders.
• Supports hundreds of simultaneous users with empirically observed $2^k$2 higher success rate at high user counts, and at least $2^k$3 lower per-frame decoding latency.

Success rates, miss/false-alarm rates, channel estimation error, and computational complexity all mark substantial advantages over baseline RM decoders, especially in heavily loaded or grant-free scenarios.

7. Implications and Deployment for mMTC and TinyML

UR2M provides a general framework for high-efficiency, scalable random access in grant-free mMTC, suitablility spanning from cellular IoT to embedded ML on constrained hardware (e.g., TinyML/WED MCUs) (Jia et al., 2024). The UR2M design emphasizes:

• Achieving near-UMAC limits with lightweight modifications to existing random access protocols.
• Enabling dense device populations ($2^k$4) with minimal per-user coordination, no grants, and low latency.
• Application of the unsourced principle to embedded and wearable systems, supporting uncertainty estimation and reliable event detection under tight compute/memory/energy budgets.

The versatility of UR2M unlocks a path toward 6G massive IoT networks, with a projected $2^k$5–$2^k$6 increase in sporadic device support at equal or lower energy per bit and immediate applicability via minor protocol updates (Agostini et al., 2024, Jiang et al., 2023, Yang et al., 2020, Jia et al., 2024).