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Resource Allocation and HARQ Optimization for URLLC Traffic in 5G Wireless Networks

Arjun Anand, Gustavo de Veciana

arXiv:1804.09201v2cs.NI

TL;DR

URLLC requires very low latency and high reliability, making wireless downlink system design challenging. The paper uses analytical and queuing-network models to study capacity, resource allocation, and HARQ; it finds that preferred transmission and retransmission designs depend on load regime.

  • Problem

    Downlink wireless systems must support URLLC packets with latency below 1 msec and reliability of 99.999%.

    Source: §I · p. 1

  • Method

    An analytical queuing-network framework evaluates downlink URLLC capacity across system parameters, OFDMA resource allocation, and HARQ designs.

    Source: §I · p. 1, 2) Impact of system parameters · p. 2

  • Results

    Wide one-shot transmissions increase supported load, while optimal HARQ uses one-shot transmission in the variance-dominated regime and retransmissions in the mean-utilization-dominated regime.

    Source: 1) Resource allocation in OFDMA systems · p. 2, 2) Impact of system parameters · p. 3

  • Takeaways & Limitations

    The framework can help evaluate retransmission limits and per-transmission reliability targets for URLLC system design.

    Source: §I · p. 1

    The analysis focuses on downlink transmissions in an FDD-based system.

    Source: §I · p. 1

Abstract

from arXiv · show

5G wireless networks are expected to support Ultra Reliable Low Latency Communications (URLLC) traffic which requires very low packet delays ( < 1 msec.) and extremely high reliability ($\sim$99.999\%). In this paper we focus on the design of a wireless system supporting downlink URLLC traffic. Using a queuing network based model for the wireless system we characterize the effect of various design choices on the maximum URLLC load it can support, including: 1) system parameters such as the bandwidth, link SINR , and QoS requirements; 2) resource allocation schemes in Orthogonal Frequency Division Multiple Access (OFDMA) based systems; and 3) Hybrid Automatic Repeat Request (HARQ) schemes. Key contributions of this paper which are of practical interest are: 1) study of how the the minimum required system bandwidth to support a given URLLC load scales with associated QoS constraints; 2) characterization of optimal OFDMA resource allocation schemes which maximize the admissible URLLC load; and 3) optimization of a repetition code based HARQ scheme which approximates Chase HARQ combining.

I. INTRODUCTION

The paper analyzes downlink URLLC capacity under stringent QoS requirements, focusing on system parameters, OFDMA resource allocation, and HARQ. It uses an analytical framework to examine these interrelated design choices.

I. INTRODUCTION

  • The study examines how bandwidth, user SINR, delay and reliability requirements, OFDMA resource allocation, and HARQ affect maximum URLLC load.The bandwidth effect depends on the HARQ scheme used.Source: §I · p. 1

A. Related Work

  • Earlier work considered blocking but not decoding failures and retransmissions; HARQ studies, focused on mean rather than both mean and variance of resource use.The paper also distinguishes its scheduled downlink setting from the uplink random-access focus of.Source: A. Related Work · p. 2

1) Resource allocation in OFDMA systems:

  • Extending one-shot transmissions in time while reducing bandwidth usage, subject to deadlines, increases the supported URLLC load; thus, “wide” transmissions outperform “tall” ones.The allocation trade-off is between shorter transmission times and fewer concurrent transmissions versus longer transmission times and greater concurrency.Source: §I · p. 1, 1) Resource allocation in OFDMA systems · p. 2

2) Impact of system parameters:

The paper studies URLLC capacity under system-parameter and HARQ design choices, using a queuing-network model for downlink traffic. Its model starts with one-shot transmissions and characterizes the system under infinite bandwidth.

2) Impact of system parameters:

  • The analysis studies capacity scaling with bandwidth, SINR, latency, and reliability, then extends the one-shot model to retransmissions and HARQ optimization.The HARQ optimization minimizes the bandwidth needed for a given URLLC load.Source: 2) Impact of system parameters · p. 2
  • In the variance-dominated regime, one-shot transmission is optimal; in the mean-utilization-dominated regime, optimal HARQ uses retransmissions, with the maximum number non-increasing in SINR.The paper identifies the first regime with lower overall URLLC loads and the second with higher loads.Source: 2) Impact of system parameters · p. 3

C. Organization

  • The paper proceeds from the one-shot model to a retransmission model and then to HARQ optimization before concluding.Source: C. Organization · p. 3

A. System Model– One Shot Transmission

  • The system model considers a single base station, Poisson class-specific packet arrivals, and OFDMA allocations whose bandwidth and duration provide the required channel uses.Transmission duration is constrained by the packet deadline, and requests are scheduled immediately when spare bandwidth is available; otherwise they are lost.Source: §II · p. 3, A. System Model– One Shot Transmission · p. 3

B. Infinite System Bandwidth

  • With infinite bandwidth, active transmissions in each class are Poisson distributed with mean load ρ_c.The infinite-bandwidth system is modeled as a multi-class M/GI/∞ queue.Source: B. Infinite System Bandwidth · p. 3

C. Effect of Finite System Bandwidth

For finite bandwidth, the section examines how allocation duration and bandwidth affect blocking and required system bandwidth. Its main result favors spreading transmissions over more time while reducing bandwidth per transmission, within the deadline.

C. Effect of Finite System Bandwidth

  • For sufficiently large W, reducing class i's bandwidth by q and increasing its duration by q does not increase blocking for any class, provided ρ_i < 1.The result assumes one-shot transmission; the transformed duration and bandwidth are h′_i = h_i/q and s′_i = q s_i.Source: C. Effect of Finite System Bandwidth · p. 4
  • The scaling keeps mean bandwidth utilization unchanged but reduces its variance, making congestion events less frequent and allowing more traffic to be admitted.The theorem's ρ_i < 1 condition can be met by splitting a class into virtual subclasses with average load below one.Source: C. Effect of Finite System Bandwidth · p. 4
  • The recommended allocation extends transmission duration to the deadline while decreasing bandwidth per transmission, provided the deadline constraint is respected.The choice uses an integer q such that q s_i = d, under the stated assumption that d is an integer multiple of s_i.Source: C. Effect of Finite System Bandwidth · p. 4
  • The paper concludes that spreading packets as widely as possible is preferable to shorter “tall” transmissions in this setting.Source: C. Effect of Finite System Bandwidth · p. 4
  • A multi-class square-root staffing extension relates required bandwidth to URLLC load, reliability, and the resource requirement r.The rule is used to choose bandwidth so blocking probability is of the order of δ.Source: C. Effect of Finite System Bandwidth · p. 4

D. Finite Block Length Model

The finite-blocklength model relates packet size, decoding error probability, channel uses, and SINR to estimate the resources needed for URLLC transmission. Under the one-shot model, capacity scales strictly concavely with SINR, delay, and reliability, but grows linearly with bandwidth for large W.

D. Finite Block Length Model

  • The finite-blocklength model uses to relate packet size, decoding error probability, channel uses, and SINR, then derives required channel uses from δ, L, and SINR_c.Source: D. Finite Block Length Model · p. 4

E. Capacity Scaling

  • Single-class URLLC capacity is the maximum arrival rate supportable under QoS when only class c traffic is present, and it depends on W, d, δ, SINR_c, and L.Source: E. Capacity Scaling · p. 4
  • Under the one-shot model, capacity scales strictly concavely with SINR, delay, and reliability, while increasing linearly with W for large bandwidth.The concavity implies diminishing returns for increasing SINR and delay or decreasing δ.Source: E. Capacity Scaling · p. 5

III. PERFORMANCE ANALYSIS WITH MULTIPLE TRANSMISSIONS

The multi-transmission model permits packets to be retransmitted after decoding failures, with transmission resources and attempt limits specified by class and attempt. Immediate scheduling and feedback-delay assumptions determine how packets progress through the system.

A. System Model– Multiple Transmissions

B. Infinite System Bandwidth

With infinite bandwidth, the system models base-station transmissions and packets awaiting decoding feedback as two multi-class M/GI/∞ queues. Packets advance to another transmission subclass after decoding failure and leave after success or the attempt limit.

B. Infinite System Bandwidth

  • The infinite-bandwidth system is represented by separate multi-class M/GI/∞ queues for base-station transmissions and packets awaiting feedback.Source: B. Infinite System Bandwidth · p. 5
  • The base-station queue tracks each class by retransmission stage, and its infinite servers allow concurrent transmission of any number of packets.Source: B. Infinite System Bandwidth · p. 5
  • After transmission, a packet spends f_c seconds in the feedback queue; decoding failure routes it to the next subclass, while successful decoding or exhausting attempts removes it.Source: B. Infinite System Bandwidth · p. 6, Figure 1 · p. 6

C. Effect of Finite System Bandwidth

Finite bandwidth can cause blocking under stochastic load, so the system bandwidth must be dimensioned to meet a target blocking probability. The square-root staffing analysis separates mean and variance effects and motivates allocating transmission times across stages within the deadline.

C. Effect of Finite System Bandwidth

  • Finite-bandwidth congestion can block new packets or retransmissions, so W is selected to meet the target blocking probability δ.Source: C. Effect of Finite System Bandwidth · p. 6
  • The bandwidth requirement follows a square-root staffing rule: mean utilization depends on r and m, while the variance term also depends on stage durations s.For one attempt, increasing transmission time (and reducing bandwidth) helps blocking probability subject to the deadline; the text presents this as an insight for choosing durations with multiple attempts.Source: C. Effect of Finite System Bandwidth · p. 7
  • The design procedure chooses r and m to meet decoding reliability, chooses s so transmissions and feedback fit the deadline, then computes minimum W for the target arrival rate.Source: C. Effect of Finite System Bandwidth · p. 7

IV. URLLC CAPACITY MAXIMIZATION/ REQUIRED BANDWIDTH MINIMIZATION

The paper minimizes the bandwidth needed to support given URLLC arrival rates, then studies repetition coding with homogeneous transmissions as a tractable approximation to HARQ optimization. The optimal retransmission strategy differs by utilization regime: one shot at low loads, but multiple transmissions at high loads.

IV. URLLC CAPACITY MAXIMIZATION/ REQUIRED BANDWIDTH MINIMIZATION

  • The bandwidth-minimization formulation supports a given vector of URLLC arrival rates subject to QoS constraints and is used to study HARQ scheme structure.The alternative is to characterize a multi-class capacity region for a fixed system bandwidth.Source: §IV · p. 7

A. Repetition Coding– Homogeneous Transmissions

  • Because the general problem is non-convex and mixed-integer, repetition coding with homogeneous transmissions is analyzed as an upper bound on minimum bandwidth under commonly used Chase combining.The same codeword is retransmitted until decoding succeeds or the retransmission limit is reached; transmissions use the same rate, bandwidth, and duration.Source: §IV · p. 7, A. Repetition Coding– Homogeneous… · p. 7
  • The multi-class problem remains analytically intractable under finite blocklength and repetition coding, so the analysis separates variance-dominated and mean-utilization-dominated regimes.Low loads emphasize utilization variance, while high loads emphasize mean utilization; these simplifications allow optimization to decouple across classes.Source: A. Repetition Coding– Homogeneous… · pp. 7–8
  • In the variance-dominated regime, for SINRc ∈ [0, 20] dB and fc ≥ 0.1 msec., one-shot transmission is optimal (mc* = 1).The cited passage states that c is the smallest r such that pc(r) ≤ δ.Source: A. Repetition Coding– Homogeneous… · p. 8
  • For SINRc ∈ [0, 20] dB, the optimal value m*c is strictly more than one and is a non-increasing function of SINRc.The cited conditions specify fc ∈ [0.1, 0.25] msec.Source: A. Repetition Coding– Homogeneous… · p. 8
  • In the variance-dominated regime, the variance objective penalizes additional transmissions more sharply; in the mean-dominated regime, lower SINRc favors more attempts and a lower per-transmission reliability target.Figure 2 plots scaled bandwidth-utilization variance against retransmission count for different SINRc and L values.Source: A. Repetition Coding– Homogeneous… · p. 8, Figure 2 · p. 8

V. CONCLUSIONS

The conclusions link URLLC capacity to system parameters and resource allocation, and identify different bandwidth-minimizing HARQ strategies at low and high loads. The results favor longer, narrower transmissions within latency constraints and show that the optimal maximum transmission count falls as SINR rises.

V. CONCLUSIONS

  • Extending transmissions in time while reducing bandwidth use, subject to deadlines, increases the supportable URLLC load compared with tall transmissions.The conclusion describes this as favoring wide transmissions over tall transmissions.Source: §V · p. 8
  • The analysis develops a downlink URLLC model and scaling results for admissible load across system bandwidth, SINR, latency, and reliability requirements.It also examines resource allocation and HARQ scheme choices.Source: §V · p. 8
  • At low loads, one-shot transmissions minimize required bandwidth, whereas at high loads the optimal HARQ scheme uses retransmissions and its maximum transmission count is non-increasing with SINR.The paper characterizes URLLC capacity scaling with link SINR, system bandwidth, latency, and reliability requirements.Source: §V · pp. 8–9

A. Proof of Theorem 1

The proof compares blocking probabilities under two bandwidth-and-duration allocations by relating their feasible user-state sets. It uses a wide-band condition to establish the inequality needed for the comparison.

A. Proof of Theorem 1

  • The state-set argument defines S as feasible user configurations under the bandwidth constraint and relates configurations in S to corresponding configurations in S′.States in S1 represent configurations where class 1 users experience blocking; PASTA is used to express the blocking probability for a typical arrival.Source: A. Proof of Theorem 1 · p. 9
  • The proof targets the inequality that the blocking probability under h′ and s′ is no greater than under h and s.It compares expressions for the two blocking probabilities through their denominators.Source: A. Proof of Theorem 1 · p. 9
  • For wide-band systems with W large enough and ρi < 1, the denominator comparison establishes the desired blocking-probability ordering.The argument concludes that pb,1(h′, s′, λ, W) ≤ pb,1(h, s, λ, W).Source: A. Proof of Theorem 1 · p. 9

B. Approximate Expression for Blocklength

The appendix approximates the relation among blocklength, information bits, and decoding-failure probability by dropping smaller terms. Substituting the square root of blocklength yields a quadratic that can be solved for an approximate blocklength.

B. Approximate Expression for Blocklength

  • The blocklength approximation relates r, information bits L, and decoding-failure probability p after ignoring 0.5 log2(r) and o(1) terms.The passage describes this as an approximate expression.Source: B. Approximate Expression for… · p. 9
  • Setting √r = x turns the approximation into a quadratic in x, whose solution gives the approximate r in equation (6).The solved expression is used as an approximation for blocklength.Source: B. Approximate Expression for… · p. 10

C. Proof of Theorem 2

The proof derives asymptotic scaling of admissible load, treating bandwidth, SINR, distance, and reliability constraints through the preceding relationships.

C. Proof of Theorem 2

  • The cited passage says that scaling with respect to W follows directly from equation (35), without specifying a particular quantity or scaling relationship.Source: C. Proof of Theorem 2 · p. 10
  • For large SINR_c, the proof first studies r_c scaling, then uses equation (35) to obtain admissible-load scaling.Source: C. Proof of Theorem 2 · p. 10
  • The proof similarly uses equation (35) to derive admissible-load scaling with d.Source: C. Proof of Theorem 2 · p. 10
  • With square-root staffing and the normal approximation, r_c scales as Θ(−log(δ)), which is then used to derive admissible-load scaling.Source: C. Proof of Theorem 2 · p. 10
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