Decoding performance in low-power wide area networks with packet collisions

This paper proposes an analytical framework for the prediction of decoding error probabilities in heterogeneous wireless environments, where transmissions from various radio nodes with distinct Poisson-arrival rates and packet lengths populate the channel. Random channel access without feedback is assumed, where partial packet collisions can lead to the loss of packets. The analysis is based on the modeling of the collision length distribution between competing nodes. With recent results from information theory in the finite block length regime, we provide bounds on achievable decoding error probabilities for a given interference scenario. The new framework enables jointly considering inter- and intra-system interference, which is an important aspect in unlicensed radio bands. The framework's applicability to optimize system designs is demonstrated for a typical low-power wide area network scenario. We study the tradeoff between reliability and code rate for a point-to-point link and present achievable throughput regions. The analysis reveals the superior performance of coded time-hopping spread spectrum systems. They reach very low error probability even under strong interference for wide ranges of practically relevant load regions.