[Paper Review] Rate Analysis of Ultra-Reliable Low-Latency Communications in Random Wireless Networks

Jeonghun Park|arXiv (Cornell University)|Oct 30, 2019

Wireless Communication Security Techniques9 references4 citations

TL;DR

This paper analyzes the achievable rate of ultra-reliable low-latency communications (URLLC) in random wireless networks using stochastic geometry and finite block-length analysis. It derives an integral expression and a tight closed-form approximation for decoding error probability, showing that improving signal-to-interference ratio (SIR) yields significantly greater rate gains than increasing channel coding length, and fractional frequency reuse enhances spectral efficiency by reducing interference.

ABSTRACT

In this letter, we analyze the achievable rate of ultra-reliable low-latency communications (URLLC) in a randomly modeled wireless network. We use two mathematical tools to properly characterize the considered system: i) stochastic geometry to model spatial locations of the transmitters in a network, and ii) finite block-length analysis to reflect the features of the short-packets. Exploiting these tools, we derive an integral-form expression of the decoding error probability as a function of the target rate, the path-loss exponent, the communication range, the density, and the channel coding length. We also obtain a tight approximation as a closed-form. The main finding from the analytical results is that, in URLLC, increasing the signal-to-interference ratio (SIR) brings significant improvement of the rate performance compared to increasing the channel coding length. Via simulations, we show that fractional frequency reuse improves the area spectral efficiency by reducing the amount of mutual interference.

Motivation & Objective

• To analyze the achievable rate of URLLC in large-scale random wireless networks where node locations are randomly distributed.
• To address the limitations of classical Shannon capacity in short-packet URLLC by incorporating finite block-length analysis.
• To model interference and spatial randomness using stochastic geometry, particularly homogeneous Poisson point processes (PPP).
• To quantify the impact of key system parameters—path-loss exponent, communication range, density, and coding length—on decoding error probability.
• To evaluate the effectiveness of interference mitigation techniques such as fractional frequency reuse in improving URLLC performance.

Proposed method

• Models transmitter locations as a homogeneous Poisson point process (PPP) with density λ to capture spatial randomness in large-scale networks.
• Uses finite block-length information theory to model the achievable rate Rε as a function of decoding error probability ε, signal-to-interference ratio (SIR), and channel coding length n.
• Derives an integral-form expression for the decoding error probability based on the SIR distribution and the finite block-length approximation from [3].
• Develops a tight closed-form approximation of the decoding error probability by simplifying the integral expression using asymptotic and numerical techniques.
• Applies Slivnyak’s theorem to focus on a typical receiver at the origin, enabling tractable analysis of network-wide performance.
• Validates the analytical approximation through numerical comparison with the exact integral expression and simulations.

Experimental results

Research questions

• RQ1 How does the achievable rate of URLLC scale with network density and channel coding length in a random wireless network?
• RQ2 What is the relative impact of improving signal-to-interference ratio (SIR) versus increasing channel coding length on URLLC rate performance?
• RQ3 How effective is fractional frequency reuse in improving area spectral efficiency by reducing mutual interference in URLLC?
• RQ4 To what extent does the finite block-length regime affect the accuracy of rate predictions compared to classical Shannon capacity?
• RQ5 Can a closed-form approximation accurately represent the decoding error probability in URLLC under stochastic geometry assumptions?

Key findings

• Improving the signal-to-interference ratio (SIR) leads to significantly greater gains in achievable rate than increasing the channel coding length, especially in dense networks.
• The achievable rate $ R_{ ext{ε}} $ sharply increases as network density $ ext{λ} $ decreases, indicating that interference mitigation is more effective than coding gain for URLLC.
• Fractional frequency reuse improves area spectral efficiency by reducing interference, with the optimal reuse factor $ ext{η}^* $ increasing under higher reliability requirements (e.g., $ ext{ε} = 10^{-4} $).
• The proposed closed-form approximation of the decoding error probability closely matches the exact integral expression, validating its accuracy and practicality.
• For a given target rate and error probability, the rate degradation term in finite block-length analysis becomes dominant when coding length $ n $ is small (e.g., ~100 channel uses).
• The analysis confirms that classical Shannon capacity is inadequate for URLLC due to the non-negligible gap in short-packet regimes, necessitating finite block-length modeling.