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Joint Uplink and Downlink Resource Configuration for Ultra-reliable and Low-latency Communications

Changyang She, Chenyang Yang, Tony Q. S. Quek

arXiv:1801.00988v1cs.IT

TL;DR

The paper asks how to support stringent URLLC delay and reliability requirements while reducing bandwidth usage. It proposes statistical multiplexing and broadcast downlink delivery, then jointly optimizes uplink and downlink resources and delay components. The reported results show that joint configuration can save half the total bandwidth compared with non-joint optimization.

  • Problem

    URLLC demands strict end-to-end delay and packet-loss guarantees, while spectrum is scarce and bandwidth-efficient resource allocation is needed.

  • Method

    The paper combines statistical multiplexing queueing, broadcast downlink transmission, and joint optimization of uplink, downlink, delay components, and bandwidth.

  • Results

    Joint resource configuration requires half of the total bandwidth of non-joint optimization.

  • Takeaways & Limitations

    Jointly configuring uplink and downlink resources can substantially reduce bandwidth while maintaining the specified URLLC delay and reliability requirements.

Abstract

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Supporting ultra-reliable and low-latency communications (URLLC) is one of the major goals for the fifth-generation cellular networks. Since spectrum usage efficiency is always a concern, and large bandwidth is required for ensuring stringent quality-of-service (QoS), we minimize the total bandwidth under the QoS constraints of URLLC. We first propose a packet delivery mechanism for URLLC. To reduce the required bandwidth for ensuring queueing delay, we consider a statistical multiplexing queueing mode, where the packets to be sent to different devices are waiting in one queue at the base station, and broadcast mode is adopted in downlink transmission. In this way, downlink bandwidth is shared among packets of multiple devices. In uplink transmission, different subchannels are allocated to different devices to avoid strong interference. Then, we jointly optimize uplink and downlink bandwidth configuration and delay components to minimize the total bandwidth required to guarantee the overall packet loss and end-to-end delay, which includes uplink and downlink transmission delays, queueing delay and backhaul delay. We propose a two-step method to find the optimal solution. Simulation and numerical results validate our analysis and show remarkable performance gain by jointly optimizing uplink and downlink configuration.

I. INTRODUCTION

URLLC requires stringent delay and reliability while using spectrum efficiently. The paper addresses this by jointly configuring uplink and downlink resources, delay components, and packet delivery modes.

  • I. INTRODUCTION: URLLC is difficult to optimize because short packets require finite-blocklength reliability modeling, whose approximations are neither convex nor concave in power or bandwidth.These properties make resource allocation more challenging than in traditional human-to-human communications.
  • I. INTRODUCTION: Joint uplink–downlink configuration minimizes total bandwidth while satisfying URLLC end-to-end delay and packet-loss requirements.The optimization covers bandwidth assignment and delay components, including transmission and queueing effects.
  • I. INTRODUCTION: The proposed delivery mechanism uses statistical multiplexing for downlink queueing, allowing packets for different users to share a common queue and downlink bandwidth.Broadcast transmission is used for downlink delivery, while uplink bandwidth is assigned to requesting devices.
  • I. INTRODUCTION: For the same queueing-delay bound and violation probability, a statistical multiplexing queue requires less service rate than the sum required by separate individual queues.This motivates sharing packets across users in one queue to reduce bandwidth requirements.
  • I. INTRODUCTION: The paper proposes a two-step optimization that first optimizes bandwidth for fixed delay components and then configures uplink and downlink resources jointly.The objective is to minimize the total bandwidth needed to meet QoS constraints.
  • I. INTRODUCTION: Numerical results show that joint configuration requires half the total bandwidth of non-joint optimization.This result is reported under the paper’s URLLC resource-configuration comparison.

II. SYSTEM MODEL

The system models local FDD communication among sensors, users, and base stations, with URLLC QoS defined by stringent packet-loss and end-to-end delay requirements. Event-driven packet delivery accounts for control signaling, uplink and downlink transmission, queueing, and backhaul delays.

  • A. Local Communication Scenarios: The local network contains K users, M sensors, and three multi-antenna base stations connected by one-hop backhaul.Sensors upload packets, which base stations deliver to users; packets may require inter-base-station forwarding.
  • A. Local Communication Scenarios: Frequency-reuse factor 1/3 and frequency-division multiple access are used to avoid interference among adjacent base stations and devices.The model assumes FDD operation and notes that TDD can be extended by adjusting uplink and downlink transmission durations.
  • B. QoS Requirement: URLLC QoS is characterized by an ultra-short end-to-end delay Dmax and an overall packet-loss probability εmax imposed on each packet.End-to-end delay includes uplink and downlink transmission, queueing, and backhaul components, while packet loss includes decoding errors and queueing-delay violations.
  • B. QoS Requirement: Short frames are used because LTE's 1 ms transmission time interval cannot support the considered URLLC end-to-end delay.The frame duration Tf is the system's minimum time granularity, determining transmission and queueing-delay components.
  • B. QoS Requirement: Event-driven uplink delivery uses scheduling requests, bandwidth assignment and grants, and data transmission, with reserved control resources preventing scheduling collisions.Periodic packets instead use reserved data-transmission resources and therefore require no control signaling.

III. PACKET DELIVERY MECHANISM

The packet delivery mechanism reduces bandwidth through statistical multiplexing and shared downlink transmission while separating concurrent uplink transmissions across subchannels. It combines queueing analysis, frequency diversity, and reliability constraints to support URLLC delivery.

  • A. Queueing Mode: Packets for different users share one base-station queue, and broadcast downlink transmission shares bandwidth across multiple devices.The mechanism is designed to reduce the total bandwidth required for the URLLC QoS constraints.
  • A. Queueing Mode: The queueing guarantee applies to packets from any of the M sensors when the statistical multiplexing queue satisfies (Dmax, εq).Each packet's probability of exceeding Dmax is then smaller than εq.
  • A. Queueing Mode: Statistical multiplexing requires less effective bandwidth than separate queues while satisfying the same per-packet queueing-delay requirement.For Poisson arrivals, Proposition 1 states that if λ̃ = λ/L, then L EB̃ > EB.
  • 1) Subchannel assignment for UL transmission:: Uplink packets are repeatedly transmitted over Nu_m separated subchannels so one successful transmission can provide packet reception and frequency diversity.Different concurrent sensors receive different subchannels to avoid severe interference, with subchannel separation exceeding the coherence bandwidth Wc.
  • 1) Subchannel assignment for UL transmission:: Spectrum sharing with common-spectrum transmission remains unresolved because finite-blocklength achievable rates under strong random interference are unavailable.The paper therefore separates concurrent uplink transmissions across subchannels rather than treating interference as additive noise.
  • 1) Subchannel assignment for UL transmission:: Subchannel bandwidth is quantized in units of B0 and assigned to active sensors immediately after their scheduling requests.The number of bandwidth units controls each subchannel's bandwidth.

2) Subchannel assignment for DL transmission:

Downlink uses broadcast transmission with repeated packet copies over independent subchannels, while reliability is analyzed through finite-blocklength decoding errors and packet-loss bounds.

  • 2) Subchannel assignment for DL transmission:: Downlink broadcasts packets to all associated users, sharing transmissions across users and supporting multicast extensions for clustered sensor requests.The paper notes that multicast can be applied separately within clusters when users request packets from fewer than all sensors.
  • 2) Subchannel assignment for DL transmission:: Each packet is repeatedly transmitted over N_d subchannels of bandwidth B_d, with different packets assigned to different subchannels.Users can receive signals on all downlink subchannels, and each subchannel has bandwidth below the coherence bandwidth.
  • 2) Subchannel assignment for DL transmission:: Independent channel coding makes decoding errors across subchannels uncorrelated, so other packets may still decode when one packet is lost.This independence supports repeated transmission across subchannels for reliability.
  • 2) Subchannel assignment for DL transmission:: The analysis uses finite-blocklength rate approximations rather than Shannon capacity because Shannon capacity does not characterize decoding error probability.The resulting error probability depends on channel conditions and is used to derive packet-loss constraints.
  • 2) Subchannel assignment for DL transmission:: An upper-bound approximation converts channel-gain thresholds into tractable packet-loss constraints, but may be loose below the threshold and cause conservative allocation.The paper explicitly evaluates the impact of this looseness numerically.

2) Constraint on DL transmission packet loss probability:

The downlink packet-loss constraint is determined by the weakest average-channel user, using a threshold-based reliability bound and adjustable transmission duration.

  • 2) Constraint on DL transmission packet loss probability:: Downlink transmission duration can be adjusted because it is shorter than the end-to-end delay budget.This flexibility enters the design of the downlink threshold and achievable rate.
  • 2) Constraint on DL transmission packet loss probability:: The downlink threshold is selected so the bounded packet-loss probability satisfies the required reliability constraint.The threshold-based expression increases with the threshold parameter, linking channel conditions to packet-loss control.
  • 2) Constraint on DL transmission packet loss probability:: The user with the lowest average channel gain has the highest downlink packet-loss probability, so reliability analysis can focus on that user.The downlink constraint is therefore imposed using the worst large-scale channel condition.
  • 2) Constraint on DL transmission packet loss probability:: The rate analysis uses lower bounds under typical high-SNR URLLC conditions, where multiple base-station antennas can support the required SNR.The approximation is justified by the stated closeness of the dispersion term to one above 10 dB.

B. Total Bandwidth of the System

The system bandwidth combines uplink and downlink requirements while accounting for active-sensor uncertainty, delay budgets, packet-loss allocations, and coherence-bandwidth constraints.

  • B. Total Bandwidth of the System: Active-sensor variability requires repeated resource updates, so the paper upper-bounds the active population to reduce computational complexity.The resulting allocation needs updating when large-scale channel gains change rather than whenever the active count changes.
  • B. Total Bandwidth of the System: Using all sensors as simultaneously active is conservative for large networks, where that event is extremely unlikely.A high-probability threshold M_a^th limits occasional losses from insufficient bandwidth, with little overall impact when ε_M is much smaller than ε_max.
  • B. Total Bandwidth of the System: The total-bandwidth optimization jointly accounts for uplink and downlink transmission, queueing delay, end-to-end delay, and packet-loss constraints.The formulation also constrains subchannel bandwidth so repeated copies experience flat fading.
  • B. Total Bandwidth of the System: The total bandwidth increases without bound as any uplink, queueing, or downlink loss probability approaches zero.This motivates allocating the overall loss budget across components instead of driving one component’s loss probability arbitrarily low.
  • B. Total Bandwidth of the System: Equal allocation ε_u = ε_q = ε_d = ε_max/3 produces nearly the same total bandwidth as optimizing these component loss allocations.The paper uses equal division in its formulation and compares it with optimized values in simulation.

V. JOINT UL AND DL RESOURCE CONFIGURATION

The paper solves joint uplink–downlink resource configuration in two steps: optimize subchannel assignments for fixed delays, then optimize delay components, with an optimality proof.

  • V. JOINT UL AND DL RESOURCE CONFIGURATION: The two-step method first minimizes bandwidth through subchannel assignment for fixed delays, then minimizes bandwidth by optimizing the delay components.The paper states that this decomposition provides the optimal solution.
  • V. JOINT UL AND DL RESOURCE CONFIGURATION: With delay and packet-loss components fixed, uplink and downlink bandwidth assignments decouple, allowing sequential optimization of uplink and downlink subchannels.The uplink assignment is optimized first, followed by the downlink assignment.
  • V. JOINT UL AND DL RESOURCE CONFIGURATION: The proposed search identifies an uplink solution by evaluating candidate subchannel counts and solving the associated bandwidth subproblems.The paper reports the resulting solution as an optimal solution of the fixed-delay uplink problem.
  • V. JOINT UL AND DL RESOURCE CONFIGURATION: Independent sensor constraints decompose the uplink problem into M single-sensor problems, reducing the joint search structure.The resulting per-sensor solutions are combined to solve the uplink assignment problem.
  • V. JOINT UL AND DL RESOURCE CONFIGURATION: For each uplink subchannel count, the method searches bandwidth and decoding-error thresholds using binary or exact linear search, exploiting established properties.Convexity and monotonicity properties support low-complexity search in the relevant regions.

2) DL subchannel assignment:

The section develops uplink and downlink subchannel-assignment analyses and derives how delay components affect required bandwidth. It shows that increasing uplink transmission delay reduces average uplink bandwidth, while queueing delay reduces downlink bandwidth.

  • The downlink bandwidth decreases as queueing delay D_q increases.
  • The analysis compares systems with different uplink transmission delays while accounting for control-signaling delay and sensor activity probabilities.
  • The uplink bandwidth expression is difficult to analyze directly, so the analysis studies average uplink bandwidth for useful insights.
  • Increasing D_u can reduce the required average bandwidth for uplink transmission.
  • The section notes that average bandwidth does not directly reflect the bandwidth requirement, although simulations validate the decrease in minimal uplink bandwidth with D_u.

3) Increasing DL transmission time:

The section analyzes how increasing downlink transmission time and reallocating delay components affect bandwidth, then validates the resulting two-step optimization numerically and by simulation. Joint delay optimization can save nearly half of the total bandwidth relative to an existing policy.

  • If constraint (19a) is inactive, the minimal downlink bandwidth does not change with D_d, although fixed subchannel allocation makes B_d increase as D_d decreases.
  • The two-step method is globally optimal when both bandwidth assignment and delay-component solutions are globally optimal.
  • The required bandwidth increases with sensor–base-station distance, while CSIT does not help save bandwidth for short distances or many active antennas.
  • For cell radius 100 m, B_d* < W_c when N_t ≥ 4, while for radius 250 m this holds when N_t ≥ 8.
  • Numerical total bandwidth is only slightly higher than simulation bandwidth, indicating that the objective is a tight upper bound.
  • Nearly half of the total bandwidth can be saved by optimizing the delay components instead of using the existing policy.

VII. CONCLUSION

The paper proposes a URLLC packet-delivery mechanism and jointly optimizes uplink, downlink, queueing delays, and bandwidth assignment under end-to-end delay and reliability constraints. The resulting joint configuration saves half of the total bandwidth compared with an existing policy.

  • The packet-delivery mechanism assigns uplink bandwidth to active sensors, uses broadcast downlink transmission, and applies statistical multiplexing at the base-station queue.
  • The mechanism minimizes bandwidth by jointly optimizing uplink and downlink transmission delays, queueing delay, and bandwidth assignment.
  • The two-step method first optimizes bandwidth assignment for fixed delays and packet-loss components, then optimizes transmission and queueing delays under the end-to-end delay requirement.
  • The analysis identifies a tradeoff between uplink and downlink bandwidth, making delay-component optimization necessary for minimizing total bandwidth.
  • Joint resource configuration can save half of the total bandwidth compared with an existing policy without optimized uplink and downlink transmission delays.

APPENDIX A

The appendix provides mathematical proofs for bandwidth and reliability properties used by the optimization analysis. It establishes monotonicity, convexity, and related structural results for the resource-allocation functions.

  • For Poisson arrivals, the required minimal constant service rate is derived from the queueing expression used in the analysis.
  • The appendix proves the relevant logarithmic inequality by showing f_L(x) > 0 for all x > 0 and L > 1.
  • The proofs establish monotonic behavior of uplink resource functions with respect to bandwidth and decoding-error thresholds.
  • The appendix establishes convexity through composition rules for the relevant uplink functions and their error-threshold terms.
  • The Gaussian-tail inverse is used as a decreasing convex function, supporting convexity claims in the resource-allocation analysis.

APPENDIX E

Appendix E proves properties of the downlink bandwidth optimization and the two-step solution procedure. The arguments establish feasibility, contradiction-based optimality, and consistency between the two optimization problems.

  • Bandwidth relationship: The proof uses monotonicity of the relevant expression with respect to uplink bandwidth to establish the required inequality under typical operating conditions.It fixes decoding error-related quantities, invokes their relationship from the earlier equation, and notes decreasing behavior over the stated range.
  • Proposition 3: The appendix shows that the solution of Problem A is feasible for Problem B, supporting equality of their optimal downlink bandwidths.The proof verifies the relevant constraints and derives a contradiction from assuming unequal optimal bandwidths.
  • Problem formulation: Problem A and Problem B differ in downlink transmission duration, with their optimal solutions and thresholds explicitly related.The appendix denotes the two durations and corresponding optimal solutions separately before comparing them.
  • Two-step method: Given delay components, the first step produces an optimal subchannel assignment, while the second step determines the optimal delay components.The appendix represents the assignment as Φ*(D̃u, D̃d, D̃q) and refers to the second-step optimization for the delay solution.
  • Proposition 4: The appendix concludes the proposition from the relationships established in equations (G.1) and (G.2).This final statement closes the proof of Proposition 4.
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