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Cross-layer Optimization for Ultra-reliable and Low-latency Radio Access Networks

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

arXiv:1703.09575v2cs.IT

TL;DR

URLLC resource allocation must handle finite-blocklength transmission, random queueing, and delay bounds shorter than channel coherence time. The paper develops a cross-layer framework with proactive packet dropping and jointly optimized power and bandwidth, obtaining an optimal channel- and queue-aware policy. Simulations and numerical results validate the analysis and show that equalizing the three packet-loss probabilities is near optimal.

  • Problem

    Short finite-blocklength transmissions and randomly arriving packets make Shannon-capacity-based allocation inadequate, while short coherence-time queueing constraints can require unbounded power even with spatial diversity.

  • Method

    The paper jointly optimizes proactive packet dropping, power allocation, and bandwidth allocation using channel and queue state information.

  • Results

    Equal transmission-error, queueing-delay-violation, and packet-dropping probabilities cause only minor power loss and are near optimal.

  • Takeaways & Limitations

    Proactive packet dropping enables the required QoS with finite transmit power while accounting for transmission and queueing delay in overall reliability.

Abstract

from arXiv · show

In this paper, we propose a framework for cross-layer optimization to ensure ultra-high reliability and ultra-low latency in radio access networks, where both transmission delay and queueing delay are considered. With short transmission time, the blocklength of channel codes is finite, and the Shannon Capacity cannot be used to characterize the maximal achievable rate with given transmission error probability. With randomly arrived packets, some packets may violate the queueing delay. Moreover, since the queueing delay is shorter than the channel coherence time in typical scenarios, the required transmit power to guarantee the queueing delay and transmission error probability will become unbounded even with spatial diversity. To ensure the required quality-of-service (QoS) with finite transmit power, a proactive packet dropping mechanism is introduced. Then, the overall packet loss probability includes transmission error probability, queueing delay violation probability, and packet dropping probability. We optimize the packet dropping policy, power allocation policy, and bandwidth allocation policy to minimize the transmit power under the QoS constraint. The optimal solution is obtained, which depends on both channel and queue state information. Simulation and numerical results validate our analysis, and show that setting packet loss probabilities equal is a near optimal solution.

I. INTRODUCTION

URLLC requires jointly controlling transmission and queueing delays under stringent packet-loss constraints. Finite blocklength, short coherence-time regimes, and random arrivals make conventional capacity, retransmission, and diversity-based approaches insufficient, motivating cross-layer optimization with proactive packet dropping.

  • URLLC targets ultra-high reliability and ultra-low latency for mission-critical applications using short packets.Applications include exoskeleton control, remote driving, tactile internet, autonomous vehicles, and factory automation.
  • Existing analyses often omit queueing delay, although randomly arriving packets can wait in the base-station buffer and violate QoS.The paper argues that both queueing and transmission delay must be included in the reliability and latency requirements.
  • Finite blocklength makes Shannon capacity inapplicable and the achievable rate nonconvex or nonconcave in transmit power and bandwidth.This complicates optimal radio-resource allocation compared with traditional communications.
  • When delay bounds are shorter than channel coherence time, retransmission and time diversity are ineffective, while spatial diversity alone cannot guarantee QoS with finite power.The paper identifies unbounded required power in this regime and motivates a proactive packet-dropping mechanism.
  • The proposed framework jointly optimizes packet dropping, power allocation, and bandwidth allocation for downlink RANs.It considers transmission error, queueing-delay violation, and proactive packet-dropping probabilities in overall reliability, using channel and queue information.
  • Effective bandwidth remains applicable for the short-delay regime across Poisson, IPP, and SPP traffic models, and equal packet-loss probabilities are near optimal for minimizing transmit power.Simulation and numerical results support both the queueing analysis and the practical equal-allocation heuristic.

B. Channel Model

The model uses short frames and finite-blocklength coding over block-fading channels, with queue evolution driven by randomly arriving packets. Transmission resources and achievable packet service depend on channel conditions, bandwidth, and frame duration.

  • Channel Model: The channel is modeled as block fading, remaining constant within coherence intervals and varying independently between intervals.Typical URLLC operation assumes Tc > Dmax > Dqmax, with the short frame duration below the coherence time.
  • Channel Model: The TTI equals the short frame duration Tf, and each frame contains data transmission and control-signaling phases.Uplink and downlink transmission of each short packet are completed within one frame; retransmission is unavailable when a packet fails in that frame.
  • Channel Model: Finite transmission duration and limited bandwidth determine the channel-coding blocklength as ns_k = φW_k.Because φ is short and bandwidth is limited, only a small number of symbols can be transmitted in one frame.
  • Channel Model: The maximal packet service uses a finite-blocklength approximation based on transmit power, channel gain, bandwidth, and target error probability.The paper notes that Shannon capacity is not adequate for this short-blocklength regime and uses a normal approximation instead.
  • Queueing Model: The BS queue aggregates packets from nearby nodes, and departures in each frame equal either the queued packets or the frame service capacity.Packets can arrive from multiple nearby nodes, making nonzero queueing delay relevant under stringent reliability targets.

III. ENSURING THE QUEUEING DELAY REQUIREMENT

The queueing-delay requirement is represented with effective bandwidth and a QoS exponent, then translated into a sufficient service condition. The paper also identifies limitations of constant-service and asymptotic approximations in short-delay fading scenarios.

  • III. ENSURING THE QUEUEING DELAY REQUIREMENT: Effective bandwidth represents the queueing-delay requirement for stationary packet arrival processes.The paper validates its use in the short-delay regime and extends discussion beyond Poisson arrivals to IPP and SPP.
  • III. ENSURING THE QUEUEING DELAY REQUIREMENT: A larger QoS exponent θk indicates a smaller queueing-delay bound for a given queueing-delay violation probability.The QoS exponent parameterizes the effective-bandwidth requirement for each user.
  • III. ENSURING THE QUEUEING DELAY REQUIREMENT: Meeting the effective-bandwidth service rate over fading channels requires channel inversion, which is not always feasible in practical fading channels.With finite resources, setting the achievable service equal to effective bandwidth makes Pk(n)gk constant.
  • III. ENSURING THE QUEUEING DELAY REQUIREMENT: The queueing-delay approximation is accurate under stated asymptotic conditions, but the required delay bound for accurate approximation is unclear.The exact queueing-delay distribution is difficult to obtain, and a numerical validation is used for the upper bound.
  • III. ENSURING THE QUEUEING DELAY REQUIREMENT: A constant service rate no smaller than the effective bandwidth can satisfy the queueing-delay requirement.The departure-process condition can also guarantee the requirement without requiring a constant service process, for example when the queue is empty.

1) Representative arrival processes:

The paper considers Poisson, bursty IPP, and autocorrelated SPP arrivals, then develops packet dropping and resource-allocation policies for finite-power QoS. The effective-bandwidth upper bound is numerically validated in short-delay settings.

  • Representative arrival processes: Poisson, IPP, and SPP model progressively different traffic characteristics, including burstiness and autocorrelation.IPP represents event-driven ON/OFF arrivals, while SPP represents event-driven and periodic traffic through a two-state process.
  • Representative arrival processes: The effective-bandwidth queueing-delay upper bound remains applicable for Poisson, IPP, and SPP arrivals even when the delay bound is extremely short.IPP is described as more bursty than Poisson, while SPP is an autocorrelated two-phase Markov-modulated Poisson process.
  • Representative arrival processes: Proactive packet dropping discards packets before their queueing deadline to satisfy QoS with finite transmit power.The overall loss budget includes transmission errors, queueing-delay violations, and proactive or reactive packet drops.
  • Representative arrival processes: The proposed cross-layer policy jointly controls power allocation and packet dropping using channel gain and queue length.A per-user power threshold bounds allocated power; packets that cannot be conveyed under that threshold are dropped.
  • Representative arrival processes: When Dqmax < Tc, deep fading can make the required finite transmit power unbounded even with spatial diversity.The channel gain can approach zero during a coherence interval, preventing the required service rate from being achieved with finite power.
  • Representative arrival processes: The proactive dropping policy adds negligible processing delay because the BS discards packets through a few comparisons when channel gain is low.The paper defines reactive loss as loss from queueing-delay violation or unsuccessful decoding.

B. A Framework for Cross-layer Transmission Optimization

The framework jointly optimizes power, proactive packet dropping, and bandwidth allocation to minimize transmit power while satisfying reliability and delay constraints.

  • The cross-layer strategy jointly optimizes transmit power, proactive packet dropping, and, for multiple users, bandwidth allocation.
  • The objective is to minimize required transmit power under a total-bandwidth constraint while ensuring the QoS requirement.
  • Power allocation depends on channel gain, required SNR, and the threshold transmit power.
  • The packet-dropping policy determines how many packets are discarded based on the queue state and threshold transmit power.
  • The analysis first treats a single user and then extends the framework to multiple users.

1) Single-user Scenario:

For a single user, the paper decomposes the optimization into error-probability allocation and threshold-power selection, obtaining a globally optimal solution under the stated conditions.

  • Single-user Scenario: The single-user QoS constraint allocates total packet-loss probability among transmission error, queueing violation, and packet dropping.
  • Single-user Scenario: The proposed two-step method first minimizes required SNR over transmission and queueing error probabilities, then selects the threshold power through search over packet-dropping probability.
  • Single-user Scenario: For Poisson arrivals, the first optimization is strictly convex and has a unique solution under stringent QoS requirements.
  • Single-user Scenario: The resulting two-step solution is globally optimal when both component searches return global optima.
  • Single-user Scenario: For IPP traffic, increasing burstiness from C2 = 1 to ∞ increases the effective bandwidth by 1 + δ times, while SPP service demand remains bounded by a Poisson-process upper bound.

2) Multi-user Scenario:

In the multi-user case, bandwidth allocation is integrated with per-user power and packet-dropping optimization, producing a mixed-integer problem solved through decomposition and heuristic subcarrier allocation.

  • Multi-user Scenario: The multi-user strategy jointly optimizes bandwidth allocation, power allocation, and packet dropping.
  • Multi-user Scenario: The allocation respects the system's maximum number of downlink subcarriers and assigns each subcarrier to at most one user.
  • Multi-user Scenario: Because subcarrier counts are integer variables, the bandwidth-allocation problem is a mixed-integer program.
  • Multi-user Scenario: Fixing each user's subcarrier count decomposes the problem into K single-user subproblems solved by the two-step method.
  • Multi-user Scenario: The heuristic allocation assigns one subcarrier per step to the user producing the steepest total-transmit-power descent.

V. APPLYING THE FRAMEWORK TO FREQUENCY-SELECTIVE CHANNEL

For frequency-selective channels, the framework partitions users' bandwidth into flat-fading subchannels and compares joint coding with independent per-subchannel coding under finite blocklength.

  • V. APPLYING THE FRAMEWORK TO FREQUENCY-SELECTIVE CHANNEL: The proposed QoS constraints extend to frequency-selective channels by replacing the flat-channel bandwidth term with the corresponding subchannel allocation.
  • V. APPLYING THE FRAMEWORK TO FREQUENCY-SELECTIVE CHANNEL: Each user’s bandwidth is divided into subchannels of width Wc, with flat fading within subchannels and frequency-selective fading across them.
  • V. APPLYING THE FRAMEWORK TO FREQUENCY-SELECTIVE CHANNEL: Joint coding can lose all packets in a frame when one block fails, whereas independent coding allows successful blocks to remain decoded.
  • V. APPLYING THE FRAMEWORK TO FREQUENCY-SELECTIVE CHANNEL: Independent coding across subchannels is easier to analyze for proactive dropping but requires more resources than joint coding for the same QoS.
  • V. APPLYING THE FRAMEWORK TO FREQUENCY-SELECTIVE CHANNEL: The gap between the optimal and suboptimal achievable rates increases with the number of subchannels, while the suboptimal rate approaches a constant.

VI. SIMULATION AND NUMERICAL RESULTS

Simulations validate the effective-bandwidth analysis and show that equalizing the three packet-loss probabilities is near-optimal, while proactive dropping reduces losses and spatial diversity lowers power requirements.

  • Effective-bandwidth validation: Effective bandwidth accurately upper-bounds queueing-delay behavior for Poisson, IPP, and SPP traffic when the maximal queue length or delay is short.The bound works for short maximal queue length, and prior observations support its use when TTI is much shorter than the delay bound.
  • Probability allocation: The optimized transmission-error, queueing-violation, and packet-dropping probabilities remain in the same order of magnitude across antenna configurations.The optimal transmission-error probabilities are reported as having the same order of magnitude with different Nt values.
  • Probability allocation: 2–5% maximal-transmit-power reduction for Nt ≥8 makes equal division of packet-loss probability a near-optimal heuristic.Compared with the optimized allocation, equalizing the three probabilities causes only minor performance loss.
  • Traffic and antennas: Bursty IPP arrivals produce higher optimal queueing-delay violation probabilities than Poisson arrivals, while increasing Nt rapidly decreases required maximal transmit power.The reduction is attributed to spatial diversity.
  • Algorithm comparison: The proposed algorithm is near-optimal relative to exhaustive search, whose complexity becomes extremely high for large Nc max and K.The comparison is reported using small Nc max values because exhaustive search is computationally expensive.
  • Packet dropping: Proactive packet dropping reduces dropped packets compared with dropping all packets under the stated deep-fading threshold policy.The dropped-packet evaluation uses Nakagami-m fading and varies m and Nt.

VII. CONCLUSIONS

The paper develops cross-layer resource allocation for URLLC when both queueing and transmission affect QoS, including proactive dropping to avoid unbounded power. Results support effective-bandwidth optimization and near-equal loss-probability allocation.

  • Conclusions: The framework minimizes BS maximal transmit power by jointly optimizing channel- and queue-state-dependent power and packet-dropping policies, with bandwidth allocation added for multiple users.The QoS reliability accounts for transmission errors, queueing-delay violations, and packet dropping.
  • Conclusions: Unbounded transmit power occurs when the queueing-delay bound is shorter than channel coherence time, motivating proactive packet dropping for finite-power QoS.The conclusion explicitly identifies the shorter-than-coherence-time regime.
  • Conclusions: Effective bandwidth is validated for Poisson, IPP, and SPP traffic, and the three packet-loss probabilities are numerically found to be of the same order of magnitude.The conclusion summarizes both the queueing-analysis validation and the reliability allocation result.
  • Conclusions: Equalizing the three packet-loss probabilities is a near-optimal allocation according to the numerical results.This conclusion concerns transmission error, queueing-delay violation, and packet-dropping probabilities.

APPENDIX A EFFECTIVE BANDWIDTH OF SEVERAL RELEVANT ARRIVAL

The appendix derives effective-bandwidth expressions or bounds for Poisson, IPP, and SPP arrivals and establishes convexity properties used in the optimization analysis.

  • Poisson process: For Poisson arrivals, the effective bandwidth is substituted into the QoS relation to obtain θk and express it as a function of Dq max.The appendix presents the Poisson-specific effective-bandwidth route.
  • IPP: For IPP arrivals, substituting the effective bandwidth yields the QoS exponent θk, which is obtained numerically from the stated relation.The derivation uses the IPP effective-bandwidth expression.
  • SPP: For SPP arrivals, an upper bound on effective bandwidth is introduced because autocorrelated-process derivation is harder than for renewal processes.The bound is related to a Poisson process with a corresponding arrival-rate substitution.
  • Convexity analysis: Convexity arguments establish that the relevant inverse Gaussian-tail term and objective components are strictly convex under the stated reliability regime.The proof uses εc < 0.5 and εq < 10^-5 assumptions, alongside derivative-based positivity arguments.

APPENDIX D PROOF OF THE OPTIMALITY OF THE TWO-STEP METHOD

The appendix proves optimality of the two-step method by first minimizing power for fixed packet-dropping probability and then optimizing that probability globally.

  • Two-step proof: For any feasible allocation, fixing εh allows problem (24) to produce a global minimum no greater than the associated feasible transmit power.This establishes the first inequality in the two-step comparison.
  • Two-step proof: Optimizing εh in the second step yields a solution whose maximal transmit power is no greater than that of any feasible candidate.The proof concludes P max* ≤ P̃ max.
  • Frequency-selective channels: In frequency-selective channels, each user’s subchannel gains are represented through channel-vector eigenvalues before determining packets transmitted per frame.The eigenvalues of H H^H are substituted into the packet-transmission expression.
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