Rate Analysis of Ultra-Reliable Low-Latency Communications in Random Wireless Networks

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.