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Deterministic Patterns for Multiple Access with Latency and Reliability Guarantees

Radosław Kotaba, Roope Vehkalahti, Čedomir Stefanović, Olav Tirkkonen, Petar Popovski

TL;DR

This work tackles ultra-reliable, low-latency uplink in grant-free access by comparing random slot selection to deterministic Steiner-pattern access. It analyzes two reception models—collision-based and full MRC—with and without SIC, and derives tight outage approximations that match simulations. The main finding is that Steiner-pattern access substantially enhances reliability and simplifies design by bounding per-slot interference and enabling efficient pilot allocation. The results offer practical guidance for frame design (parameters $M$ and $K$) and demonstrate the value of combinatorial designs in URLLC-enabled grant-free systems.

Abstract

We study a scenario in which multiple uncoordinated devices aim to achieve reliable transmissions within a given time frame. The devices are intermittently active and access a shared pool of channel resources in a grant-free manner by utilizing multiple transmissions (K-repetition coding). This allows them to achieve diversity and improve the reliability within a certain latency constraint. We focus on two access methods: one where devices choose K slots at random and another one where the access patterns are deterministic and follow a specific code design, namely the Steiner System. We analyze the problem under two signal models that involve different complexity for the receiver. First, collision model is considered, where only interference-free transmissions can be used and combined. Second, a model treating interference as noise is analyzed, where the receiver is capable of utilizing all K replicas, applying maximum ratio combining (MRC). For both signal models, we investigate receivers with and without successive interference cancellation (SIC). We develop approximations and bounds for the outage probabilities that very closely match simulation results. Overall, we show that deterministic access patterns have the potential to significantly outperform random selection in terms of reliability. Furthermore, deterministic access patterns offer a simplified system design.

Deterministic Patterns for Multiple Access with Latency and Reliability Guarantees

TL;DR

This work tackles ultra-reliable, low-latency uplink in grant-free access by comparing random slot selection to deterministic Steiner-pattern access. It analyzes two reception models—collision-based and full MRC—with and without SIC, and derives tight outage approximations that match simulations. The main finding is that Steiner-pattern access substantially enhances reliability and simplifies design by bounding per-slot interference and enabling efficient pilot allocation. The results offer practical guidance for frame design (parameters and ) and demonstrate the value of combinatorial designs in URLLC-enabled grant-free systems.

Abstract

We study a scenario in which multiple uncoordinated devices aim to achieve reliable transmissions within a given time frame. The devices are intermittently active and access a shared pool of channel resources in a grant-free manner by utilizing multiple transmissions (K-repetition coding). This allows them to achieve diversity and improve the reliability within a certain latency constraint. We focus on two access methods: one where devices choose K slots at random and another one where the access patterns are deterministic and follow a specific code design, namely the Steiner System. We analyze the problem under two signal models that involve different complexity for the receiver. First, collision model is considered, where only interference-free transmissions can be used and combined. Second, a model treating interference as noise is analyzed, where the receiver is capable of utilizing all K replicas, applying maximum ratio combining (MRC). For both signal models, we investigate receivers with and without successive interference cancellation (SIC). We develop approximations and bounds for the outage probabilities that very closely match simulation results. Overall, we show that deterministic access patterns have the potential to significantly outperform random selection in terms of reliability. Furthermore, deterministic access patterns offer a simplified system design.
Paper Structure (15 sections, 2 theorems, 35 equations, 9 figures, 1 table)

This paper contains 15 sections, 2 theorems, 35 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries and Related Work
  3. System model
  4. Access Patterns: Random vs. Deterministic
  5. Random selection
  6. Deterministic patterns
  7. Receiver Processing
  8. Collision model
  9. Collision model with successive interference cancellation
  10. Model with Full MRC
  11. System Design favors Steiner Sequences over Random Selection
  12. Performance Evaluation: Choice of Frame Parameters $M$ and $K$
  13. Conclusions
  14. Proof of Proposition \ref{['proposition:free:random']}
  15. Proof of Proposition \ref{['proposition:free:steiner']}

Key Result

Proposition 1

When $U$ devices employ random access patterns with $K$ repetitions in $M$ slots, the probability that an arbitrary user has $K'$ out of $K$ collision-free slots is where $a_n = \binom{K-K'}{n}$ and $T_n = \left(\binom{M-K'-n}{K}/\binom{M}{K}\right)^{U-1}$.

Figures (9)

  • Figure 1: Example of the uplink access scenario with $K=3$ multiple transmissions over a frame of $M=7$ slots. There are $N=4$ UEs out of which $U=3$ happen to be active. Their transmissions cause collisions in slots $3$ and $6$.
  • Figure 2: Comparison of the Steiner system (solid line) and Random selection (dotted) with $K=4$ and $M=25$ in terms of their distributions of interference free slots $K'$ and number of interferers $L$. In the first two subfigures, the x-axis represents the mean traffic intensity $bN$. The third subfigure is a CMF of $L$.
  • Figure 3: Outage probability performance of the system employing random and deterministic patterns as a function of the average received SNR for different mean number of active devices $bN$.
  • Figure 4: Comparison of the simulation results involving the exact procedure and the proposed approximation
  • Figure 5: Outage probability in the Full MRC model (a) without SIC and (b) with SIC.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • proof
  • proof