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Analyzing Grant-Free Access for URLLC Service

Yan Liu, Yansha Deng, Maged Elkashlan, Arumugam Nallanathan, George K. Karagiannidis

arXiv:2002.07842v2eess.SPcs.NI

TL;DR

URLLC needs reliable, low-latency small-packet uplink access, while grant-based LTE access incurs delay. The paper develops a spatio-temporal analytical framework for contention-based grant-free HARQ and evaluates Reactive, K-repetition, and Proactive schemes. Proactive performs best under shorter latency constraints, whereas K-repetition performs best under longer constraints, depending on K.

  • Problem

    Grant-based uplink access can hardly meet URLLC latency and reliability requirements, motivating analytical comparison of grant-free HARQ schemes.

  • Method

    The paper uses a spatio-temporal mathematical framework to derive latent access failure probabilities for Reactive, K-repetition, and Proactive grant-free HARQ schemes.

  • Results

    Under shorter latency constraints, Proactive has the lowest latent access failure probability; under longer constraints, K-repetition has the lowest, depending on K.

  • Takeaways & Limitations

    Scheme selection depends on the latency constraint and repetition value, with Proactive favored for shorter constraints and K-repetition for longer ones.

  • Takeaways & Limitations

    At sufficiently high UE density, GF access cannot succeed regardless of the scheme; the analysis also assumes error-free downlink feedback.

Abstract

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5G New Radio (NR) is expected to support new ultra-reliable low-latency communication (URLLC) service targeting at supporting the small packets transmissions with very stringent latency and reliability requirements. Current Long Term Evolution (LTE) system has been designed based on grantbased (GB) (i.e., dynamic grant) random access, which can hardly support the URLLC requirements. Grant-free (GF) (i.e., configured grant) access is proposed as a feasible and promising technology to meet such requirements, especially for uplink transmissions, which effectively saves the time of requesting/waiting for a grant. While some basic GF access features have been proposed and standardized in NR Release-15, there is still much space to improve. Being proposed as 3GPP study items, three GF access schemes with Hybrid Automatic Repeat reQuest (HARQ) retransmissions including Reactive, K-repetition, and Proactive, are analyzed in this paper. Specifically, we present a spatiotemporal analytical framework for the contention-based GF access analysis. Based on this framework, we define the latent access failure probability to characterize URLLC reliability and latency performances. We propose a tractable approach to derive and analyze the latent access failure probability of the typical UE under three GF HARQ schemes. Our results show that under shorter latency constraints, the Proactive scheme provides the lowest latent access failure probability, whereas, under longer latency constraints, the K-repetition scheme achieves the lowest latent access failure probability, which depends on K. If K is overestimated, the Proactive scheme provides lower latent access failure probability than the K-repetition scheme.

I. INTRODUCTION

URLLC requires low latency and high reliability for small-packet transmissions, but LTE grant-based uplink access introduces substantial delay. This paper studies contention-based grant-free HARQ schemes using a spatio-temporal analytical framework and compares their performance.

  • URLLC targets small-packet transmissions with stringent latency and reliability requirements for applications such as factory automation and remote control.
  • LTE grant-based uplink access requires a request and grant through a four-step random-access procedure, taking at least 10ms before data transmission.
  • Contention-based grant-free transmission avoids scheduling requests and grants, but simultaneous transmissions by neighboring UEs can cause collisions and reduce reliability.
  • Reactive HARQ waits for feedback before retransmission, adding round-trip-time latency and limiting retransmissions under URLLC constraints.
  • K-repetition sends a predefined number of consecutive replicas without waiting for feedback, while Proactive repetition stops early after an ACK.
  • The paper develops a stochastic-geometry and probability-based spatio-temporal framework, defines latent access failure probability, and compares three GF HARQ schemes using analytical and simulation approaches.The schemes are Reactive, K-repetition, and Proactive.

C. Grant-Free Access Schemes

The paper models Reactive, K-repetition, and Proactive grant-free HARQ schemes, differing in when retransmissions occur and how feedback controls repetitions.

  • Reactive scheme: Reactive retransmits the packet only after the UE receives NACK feedback from the BS.The UE waits through transmission, BS processing, feedback, and UE processing before retransmitting.
  • K-repetition scheme: K-repetition autonomously transmits the same packet for a configured number of consecutive repetitions before BS combining and feedback.The scheme does not wait for feedback between its configured repetitions.
  • Proactive scheme: Proactive repeats transmissions up to KProa times but can terminate early after receiving ACK.Its round-trip duration depends on whether success occurs during the repetition sequence.
  • Proactive scheme: For Proactive access, an unsuccessful sequence continues to a later HARQ round trip, while success in repetition l determines the final-round latency.The latency is l + 4 + (m −1)(KProa + 3) TTIs when success occurs at repetition l.

D. Signal to Noise plus Interference Ratio (SINR)

The analysis characterizes contention-based grant-free access through SINR, interference, collision, and latent access failure probability under URLLC latency constraints.

  • SINR and access failure: GF access can fail when a pilot falls below the SINR threshold or when simultaneous identical pilots collide.The collision model assumes collided UEs are not decoded by the BS.
  • Interference model: The analytical framework considers both intra-cell and inter-cell interference in a general cellular-network model.Intra-cell interference arises from UEs sharing a BS, while inter-cell interference arises from shared preamble pools across BSs.
  • SINR model: SINR depends on received power, channel gain, aggregate interference, and noise, with retransmission power adjusted through gm.The power levels satisfy g1 < g2 < ... < gm < ... < gJ.
  • Performance objective: Latent access failure probability measures whether payload delivery exceeds latency T or fails to meet target probability ε.The framework analyzes a randomly chosen active UE under the three GF schemes.

A. Reactive scheme

The Reactive scheme’s latent access failure probability evolves across HARQ round trips, with retransmission opportunities limited by the latency constraint.

  • Reactive latency evolution: Reactive failure probability remains unchanged during a HARQ round trip and changes after UE processing of feedback.The UE cannot update its retransmission decision before feedback is received.
  • Reactive latency evolution: When feedback arrives too late, the latent failure probability equals its value at the preceding latency point.This occurs during portions of the round trip before the UE can act on feedback.
  • Reactive latency evolution: After ACK or NACK feedback, the latent failure probability changes according to whether the UE stops or retransmits.The update occurs after the UE receives and processes the feedback.
  • Reactive access analysis: The latency constraint determines the maximum number M of Reactive HARQ round trips available for delivery.The active probability in round trip m depends on failures in the preceding m − 1 round trips.
  • Reactive access analysis: The paper derives the Reactive latent access failure probability from round-trip success probabilities and interference-related terms.The success expression separates typical-UE transmission success, interfering-UE behavior, and the distribution of intra-cell interferers.
  • Reactive access analysis: Transmission success decreases with SINR threshold and active-to-BS density ratio, while non-collision probability increases with both quantities.These opposing dependencies create a tradeoff in Reactive access performance.

B. K-repetition scheme

The K-repetition scheme derives latent access failure under arbitrary latency by iterating across HARQ round trips. Increasing repetitions improves transmission success but can increase collisions and reduce overall access success in overloaded traffic.

  • B. K-repetition scheme: The K-repetition scheme derives latent access failure under arbitrary latency through an iterative HARQ-round-trip process.The process computes the maximum round trips, active probability, round-trip access success, and latent failure probability until the latency limit is reached.
  • B. K-repetition scheme: The framework separates intra-cell interferer count, conditional transmission success, and non-collision probability when deriving K-repetition access performance.
  • B. K-repetition scheme: Increasing K_Krep raises transmission success probability but lowers non-collision probability, creating a reliability–collision tradeoff.
  • B. K-repetition scheme: When λ_D/λ_B > 4 × 10^4 and γ_th = −10 dB, increasing K_Krep can degrade GF access success by increasing collisions and wasting resources.
  • B. K-repetition scheme: Reactive access is a special case of K-repetition when K_Krep = 1.

C. Proactive scheme

The Proactive scheme models feedback-dependent repetitions, allowing a UE to terminate after receiving ACK and accounting for feedback delays in its latent access-failure analysis. Feedback can reduce later interference when enough repetitions remain after the feedback delay.

  • C. Proactive scheme: The Proactive scheme is analytically more complex because latent access failure can change at several TTIs within one HARQ round trip.
  • C. Proactive scheme: For K_Proa ≤ 4, feedback arrives too late, so the UE completes all repetitions without early termination.
  • C. Proactive scheme: For K_Proa ≥ 5, ACK received three TTIs after a successful repetition reduces later interfering users by terminating remaining repetitions.
  • C. Proactive scheme: The feedback factor η_1,l captures failures among earlier repetitions whose ACK/NACK information can affect repetition l.
  • C. Proactive scheme: The scheme’s access-success derivation distinguishes transmission success in repetition l, success across l repetitions, and access success including collisions.

2) Proactive scheme with HARQ retransmissions:

With HARQ retransmissions, the Proactive scheme tracks whether a UE remains active across round trips and iteratively computes access success and latent failure under arbitrary latency constraints.

  • 2) Proactive scheme with HARQ retransmissions:: A UE remains active in a Proactive HARQ round trip only if all repetitions in earlier round trips failed.
  • 2) Proactive scheme with HARQ retransmissions:: For each repetition, access success depends on whether the repetition index is within the initial four TTIs or follows feedback from earlier repetitions.
  • 2) Proactive scheme with HARQ retransmissions:: Under arbitrary latency, the Proactive flowchart first determines latency indexes μ and ν, then iterates through round-trip and repetition-level calculations.
  • 2) Proactive scheme with HARQ retransmissions:: The Proactive analysis computes active probability and round-trip access success across up to M HARQ round trips.
  • 2) Proactive scheme with HARQ retransmissions:: The procedure concludes by calculating latent access failure from the resulting Proactive access-success probabilities.

IV. SIMULATION AND DISCUSSION

The simulations validate the analytical framework and compare latent access failure across HARQ schemes, latency constraints, density ratios, SINR thresholds, and power boosting. Proactive is favored at shorter latency, while K-repetition can perform best under longer latency or suitable conditions.

  • Validation: The analytical curves closely match Monte Carlo simulation points, validating the developed spatio-temporal mathematical framework.The comparison covers Reactive, K-repetition, and Proactive schemes at SINR thresholds of −10 dB and −2 dB.
  • HARQ comparison: Proactive has the lowest latent access failure probability for latency constraints up to 8 TTIs, while K-repetition is favored at longer constraints.For shorter constraints, Proactive can terminate earlier; for longer constraints, K-repetition benefits from completing repetitions and receiving feedback.
  • HARQ comparison: Overestimating K can increase latent access failure because excessive repetitions consume waiting time and reduce resource efficiency.With longer latency constraints, the 8-repetition scheme can have the highest failure probability; Proactive is preferred when K is overestimated.
  • Density and SINR: Increasing density ratio raises latent access failure because it increases both interference and collision probability.The simulations examine density ratios under latency constraints of 8 TTIs and 12 TTIs.
  • Density and SINR: At T = 1 ms, increasing repetitions helps under light load but hurts under high load, while Proactive with up to 8 repetitions can match 4-repetition performance.When λD/λB ≥ 40000, additional repetitions increase collisions and waste time-frequency resources; 8-repetition K-repetition is infeasible within 1 ms.
  • Density and SINR: At lower SINR thresholds and high density, repetition interference can outweigh the combining gain, whereas power boosting improves K-repetition more than Proactive.With power boosting, K-repetition failure probability becomes much lower than Proactive in the reported example.
  • Operating boundary: When λD/λB ≥ 1.5 × 10^6, no scheme succeeds under the 1 ms constraint because the network is very crowded.The results indicate that active-UE access must be limited below such density levels.

V. CONCLUSION

The paper develops and evaluates a spatio-temporal model for grant-free URLLC access with three HARQ schemes. Proactive is best under shorter latency, K-repetition under longer latency when K is optimized, and power boosting especially benefits K-repetition.

  • Conclusion: The paper develops a spatio-temporal model comparing latent access failure probabilities for Reactive, K-repetition, and Proactive grant-free HARQ schemes.The model targets a randomly chosen UE under URLLC requirements.
  • Conclusion: Under shorter latency constraints T ≤ 8 TTIs, Proactive provides the lowest latent access failure probability.The conclusion identifies Proactive as the preferred scheme in this latency range.
  • Conclusion: Under longer latency constraints, K-repetition provides the lowest latent access failure probability, provided K is optimized.If K is overestimated, Proactive performs better than K-repetition.
  • Conclusion: Power boosting improves latent access failure probability, especially for K-repetition, including K = 1.The analytical model can also be applied to other grant-free HARQ schemes in cellular networks.

APPENDIX A A PROOF OF THEOREM 1

Appendix A derives latent access failure probabilities for Reactive grant-free HARQ by combining HARQ-round-trip timing with transmission and interference probabilities. The derivation uses stochastic-geometry interference transforms and a path-loss assumption.

  • Reactive scheme: For latency constraint T, the derivation sets M = ⌊(T − 1)/T_RTT,Reac⌋ as the number of Reactive HARQ round trips.The failure probability is then formulated for successive values of M.
  • Reactive scheme: For M = 1, 2, and 3, latent access failure is expressed as failure across the corresponding number of HARQ round trips.For M > 3, the probability follows an iterative process based on the M = 2 and M = 3 cases.
  • Interference analysis: The transmission success probability is derived by conditioning on intra-cell interferers and calculating intra-cell and inter-cell interference Laplace transforms.The derivation uses averaging, the PPP probability generating functional, and a variable transformation.
  • Assumption: The analysis assumes general fading with path-loss exponent α = 4 to simplify the resulting expressions.This assumption is stated in the derivation of the transmission success probability.

APPENDIX C A PROOF OF LEMMA 2

Appendix C derives the K-repetition transmission success probability by modeling success across repeated transmissions and evaluating the associated intra-cell and inter-cell interference.

  • K-repetition derivation: For K-repetition, one HARQ round trip succeeds if any of the K repetitions succeeds.The success probability is conditioned on the number of intra-cell interfering UEs.
  • K-repetition derivation: The conditional success expression is rewritten using the Binomial theorem before evaluating interference terms.The derivation explicitly introduces the binomial expansion and coefficient.
  • Interference analysis: The intra-cell and inter-cell aggregate interference are represented through their Laplace transforms.These transforms are substituted into the conditional success expression to obtain the K-repetition result.

APPENDIX D A PROOF OF LEMMA 3

The proof distinguishes two repetition regimes according to whether feedback is available and when the number of interfering users changes.

  • For l ≤4, the UE cannot receive feedback, so the number of interfering users remains unchanged in each repetition.
  • The displayed derivation includes a factor written as (1 + γth)n.
  • For l ≥5, feedback is received from the fourth repetition, and the number of interfering users changes starting with the fifth repetition.
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