[Paper Review] Achievable Data Rate for URLLC-Enabled UAV Systems with 3-D Channel Model

Hong Ren, Cunhua Pan+4 more|arXiv (Cornell University)|Jul 15, 2019

UAV Applications and Optimization10 references4 citations

TL;DR

This paper proposes a closed-form lower bound for the average achievable data rate (AADR) in ultra-reliable low-latency communication (URLLC)-enabled UAV systems using a 3D channel model with short packet transmission. By applying Gaussian-Chebyshev quadrature (GCQ), the authors derive a tight analytical approximation of AADR, enabling accurate packet size design under stringent reliability and latency constraints.

ABSTRACT

In this paper, we investigate the average achievable data rate (AADR) of the control information delivery from the ground control station (GCS) to unmanned-aerial-vehicle (UAV) under a 3-D channel, which requires ultra-reliable and low-latency communications (URLLC) to avoid collision. The value of AADR can give insights on the packet size design. Achievable data rate under short channel blocklength is adopted to characterize the system performance. The UAV is assumed to be uniformly distributed within a restricted space. We first adopt the Gaussian-Chebyshev quadrature (GCQ) to approximate the exact AADR. The tight lower bound of AADR is derived in a closed form. Numerical results verify the correctness and tightness of our derived results.

Motivation & Objective

• To address the lack of performance analysis for control information delivery in UAV systems under ultra-reliable and low-latency communication (URLLC) requirements.
• To model the GCS-to-UAV link using a realistic 3D channel model that accounts for elevation-dependent LoS probability and path loss.
• To characterize the average achievable data rate (AADR) under short channel blocklength, where Shannon’s capacity formula is no longer valid.
• To provide engineering insights into optimal packet size design by deriving a tight, closed-form lower bound for AADR.

Proposed method

• Adopts a 3D channel model where LoS probability increases with elevation angle, based on the expression $ P_{\text{LoS}} = \frac{1}{1 + a \exp(-b(\theta - a))} $.
• Models the UAV's position as uniformly distributed within an annular inverted cone, with distance $ d $ having CDF $ F_d(x) = \frac{x^3 - r^3}{D^3 - r^3} $ and PDF $ f_d(x) = \frac{3x^2}{D^3 - r^3} $.
• Uses the finite-blocklength achievable rate formula $ R = \frac{1}{1 + \frac{1}{M}} \left( C - \sqrt{\frac{V}{M}} Q^{-1}(\varepsilon) \right) $, where $ C $ is the Shannon capacity, $ V $ is the channel dispersion, and $ \varepsilon $ is the decoding error probability.
• Applies Gaussian-Chebyshev quadrature (GCQ) to numerically approximate the AADR over the 3D spatial distribution of the UAV.
• Derives a tight closed-form lower bound for AADR using convexity and monotonicity analysis of the rate function.
• Validates results via Monte Carlo simulations, comparing the GCQ approximation and lower bound against simulated AADR.

Experimental results

Research questions

• RQ1 What is the average achievable data rate (AADR) for control information delivery from a ground control station (GCS) to a UAV under short packet transmission in a 3D channel model?
• RQ2 How does the 3D spatial distribution of the UAV—constrained within an annular inverted cone—affect the AADR?
• RQ3 Can a tight closed-form lower bound be derived for AADR under finite blocklength and stringent reliability constraints?
• RQ4 How accurate is the Gaussian-Chebyshev quadrature (GCQ) method in approximating the exact AADR in this scenario?
• RQ5 What is the impact of decoding error probability $ \varepsilon $ on the achievable data rate, and how does it compare to Shannon capacity?

Key findings

• The Gaussian-Chebyshev quadrature (GCQ) method provides a highly accurate approximation of the exact AADR, closely matching Monte Carlo simulation results.
• The derived closed-form lower bound for AADR is tight, especially at low decoding error probabilities $ \varepsilon $, validating its use in practical system design.
• AADR increases with $ \varepsilon $, confirming that higher error tolerance allows higher data rates, but the gap between Shannon capacity and AADR remains significant at low $ \varepsilon $.
• For ultra-reliable communications (e.g., $ \varepsilon \leq 10^{-5} $), the finite-blocklength model is essential, as Shannon capacity overestimates achievable rates.
• The AADR is sensitive to both distance $ d $ and elevation angle $ \theta $, with higher reliability requiring careful trade-offs in packet size and power allocation.
• The 3D channel model, which accounts for elevation-dependent LoS probability, leads to a more accurate AADR estimation than traditional free-space models.