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Joint Blocklength and Location Optimization for URLLC-enabled UAV Relay Systems
Cunhua Pan, Hong Ren, Yansha Deng, Maged Elkashlan, Arumugam Nallanathan
TL;DR
The paper addresses joint UAV-location and blocklength optimization for finite-blocklength URLLC relay communication, where latency and weak direct links constrain command delivery. It proposes an alternating perturbation-based iterative method and reports performance matching exhaustive search while outperforming existing algorithms.
Problem
The paper seeks to minimize decoding error for a UAV relay serving URLLC command communication under latency and location constraints.
Method
The paper alternates optimization of UAV location and two-phase blocklength allocation using a low-complexity iterative algorithm with bisection-based subproblem solutions.
Results
The proposed algorithm achieves the same performance as exhaustive search and significantly outperforms existing algorithms.
Takeaways & Limitations
Jointly optimizing UAV location and blocklength is supported as an effective approach for the considered URLLC UAV relay system.
Abstract
from arXiv · showhide
This letter considers the unmanned aerial vehicle (UAV)-enabled relay system to deliver command information under ultra-reliable and low-latency communication (URLLC) requirements. We aim to jointly optimize the blocklength allocation and the UAV's location to minimize the decoding error probability subject to the latency requirement. The achievable data rate under finite blocklength regime is adopted. A novel perturbation-based iterative algorithm is proposed to solve this problem. Simulation results show that the proposed algorithm can achieve the same performance as the exhaustive search method, and significantly outperforms the existing algorithms.
I. INTRODUCTION
The paper targets URLLC relay communication where short packets make Shannon-capacity analysis unsuitable and prior UAV studies did not incorporate latency requirements. It jointly optimizes UAV location and blocklength allocation to reduce decoding error under latency and location constraints.
- URLLC supports applications including factory automation, autonomous driving, and remote surgery, requiring short-packet transmission for low latency.
- Shannon capacity is unsuitable for short packets, motivating finite-blocklength achievable-rate analysis.
- Prior UAV delay studies did not consider latency requirements and adopted Shannon’s capacity formula.
- The system uses a UAV relay because shelters make the direct controller-to-robot channel weak and negligible.
- The proposed perturbation-based iterative algorithm jointly optimizes UAV location and blocklength allocation for lower decoding error under constraints.
II. SYSTEM MODEL
The system models a fixed-altitude UAV relay serving a controller and robot separated by shelters, with two transmission phases and finite-blocklength decoding errors. The resulting joint optimization minimizes total error subject to blocklength and location feasibility constraints.
- The UAV hovers at (x, H) between controller location (0, 0) and robot location (D, 0), with fixed altitude H.
- The latency budget gives total blocklength M = BTmax, divided between controller-to-UAV and UAV-to-robot phases as m1 and m2.
- Free-space channel gains h1 and h2 depend on the UAV’s fixed altitude and horizontal location under a near-certain line-of-sight assumption.
- The study restricts the scenario to one UAV and one robot because larger configurations complicate error modeling and may increase discoverability.
- Finite-blocklength decoding errors are modeled separately for the UAV and robot links, with the UAV acting as a decode-and-forward relay.
- The optimization minimizes overall decoding error while satisfying latency and location constraints, but the objective is non-convex in the joint variables and in each variable separately.
III. LOW-COMPLEXITY ALGORITHM
The proposed low-complexity algorithm alternates between optimizing blocklength allocation for a fixed UAV location and optimizing location for fixed blocklengths until convergence.
- The algorithm first optimizes blocklength with fixed location, then optimizes location with fixed blocklength allocation, alternating until convergence.
- The two subproblems are solved iteratively rather than optimizing location and blocklength jointly in one step.
- The approach is designed as a low-complexity iterative procedure for the original joint optimization problem.
A. Optimize Blocklength Allocation with Fixed x
With UAV location fixed, the paper approximates the extremely low total error by the sum of two link errors, proves convexity in blocklength, and uses bisection to allocate symbols.
- A. Optimize Blocklength Allocation with Fixed x: With fixed location, the channel gains are fixed and the total error is approximated as ε(m1) ≈ ε1(m1) + ε2(m1).
- A. Optimize Blocklength Allocation with Fixed x: The approximation is justified for extremely low overall error probabilities, where each link error should also be sufficiently small.
- A. Optimize Blocklength Allocation with Fixed x: Theorem 1 states that the approximated error function is convex in continuous m1 for fixed channel gains.
- A. Optimize Blocklength Allocation with Fixed x: The proof establishes convexity for each link error and then uses their sum to establish convexity of the approximation.
- A. Optimize Blocklength Allocation with Fixed x: Bisection search finds the optimal blocklength allocation by solving the corresponding optimality equation.
1 Initialize mlb
The initialization procedure returns the optimal blocklength allocation after selecting the midpoint-based candidate.
- The procedure returns the optimal m1 as m1* after midpoint-based search.
- The corresponding optimal m2 is also returned.
B. Optimal Location Optimization with Fixed m1 and m2
With fixed blocklengths, the location subproblem is handled through a transformed objective and bisection search, supported by numerical evidence of a single minimum.
- B. Optimal Location Optimization with Fixed m1 and m2: The location objective is not convex, but numerical results indicate only one local minimum and one minimizing solution.
- B. Optimal Location Optimization with Fixed m1 and m2: The paper defines g(x) as the logarithm of the approximate overall error probability, preserving its monotonic behavior.
- B. Optimal Location Optimization with Fixed m1 and m2: The channel gains γ1(x) and γ2(x) depend on the UAV location through the controller-UAV and UAV-robot distances.
- B. Optimal Location Optimization with Fixed m1 and m2: Although g(x) changes between concave and convex regions, its derivative changes sign once, indicating a single minimum in the illustrated interval.
- B. Optimal Location Optimization with Fixed m1 and m2: Algorithm 2 uses endpoint checks and bisection on g′(x) to return the optimal location x*.
C. Overall Algorithm and Analysis
The overall method perturbs the blocklength during alternating optimization to avoid stagnation, while convergence follows from monotonic objective decrease.
- C. Overall Algorithm and Analysis: Conventional block coordinate descent can get stuck at its initial point, motivating a small blocklength perturbation in each iteration.
- C. Overall Algorithm and Analysis: Algorithm 3 alternates blocklength and location updates, with convergence guaranteed because the objective decreases and is bounded below by zero.
- C. Overall Algorithm and Analysis: The bottleneck link changes with UAV position: the UAV-robot link dominates for small x, while the other link dominates conversely.
- C. Overall Algorithm and Analysis: Algorithm 3 is the iterative procedure used to solve the joint optimization problem.
1 Initialize m(0)
The iterative algorithm evaluates perturbed blocklength candidates, selects the location with minimum approximate error, and achieves low-complexity convergence relative to exhaustive search.
- 1 Initialize m(0): The algorithm selects the candidate location with the minimum approximate error and iterates until the maximum iteration count.
- 1 Initialize m(0): The algorithm generally converges within ten iterations, with complexity O(nmax(Q1 + Q2)).
- 1 Initialize m(0): The exhaustive search complexity is O(M(d2 − d1)/ζ), which is significantly higher than Algorithm 3's complexity.
- 1 Initialize m(0): Because the original problem is non-convex, Algorithm 3 lacks a global-optimality guarantee but matches exhaustive-search performance in simulations.
IV. SIMULATION RESULTS
The simulations evaluate convergence and compare the proposed joint optimization algorithm with exhaustive search and fixed-variable baselines. The proposed algorithm converges rapidly and matches exhaustive search while outperforming the fixed-location and fixed-blocklength approaches.
- Simulation setup: The simulations use B = 1 MHz, D = 200 m, H = 120 m, L = 100 bits, and M = 100 symbols.The transmission delay is Tmax = 100 us, yielding M = BTmax = 100.
- Convergence: The proposed algorithm generally converges within ten iterations for all considered UAV altitudes H.The convergence behavior indicates low computational complexity in the tested settings.
- Performance comparison: The proposed algorithm achieves the same performance as exhaustive search and significantly outperforms the Fixedx and Fixedm baselines.Fixedx optimizes blocklength with x = (d1 + d2)/2, whereas Fixedm optimizes location with m1 = M/2.
V. CONCLUSIONS
The paper jointly optimizes UAV location and blocklength allocation for a URLLC-enabled relay system. A low-complexity iterative method matches exhaustive search and outperforms existing algorithms.
- The optimization jointly determines UAV location and blocklength allocation under a URLLC requirement.
- A low-complexity iterative algorithm solves the optimization problem by solving its subproblems with bisection search.
- The proposed algorithm achieves the same performance as exhaustive search and superior performance over existing algorithms.