Union Bounds on the Symbol Error Probability of LoRa Modulation for Flat Rician Block Fading Channels

TL;DR

This paper derives exact and bounded symbol error probabilities for LoRa modulation over flat Rician block fading channels, providing insights into its performance and the accuracy of bounds versus exact calculations.

Contribution

It introduces exact symbol error probability derivation for LoRa in Rician fading and evaluates tightness of union bounds compared to exact and approximate results.

Findings

Upper bound is very tight to the exact probability.

Lower bound has approximately 2.5 dB gap from the exact probability.

Numerical results validate the bounds against exact and approximate calculations.

Abstract

In this paper the symbol error performance of LoRa modulation is addressed for flat Rician block fading channels. First the exact symbol error probability of the LoRa modulation on Rician fading is derived. Then the upper and lower union bounds are employed on the derived symbol error probability. The proposed bounds are compared against the exact symbol error probability, the numerical evaluation of the symbol error probability and the state-of-art approximation of the LoRa symbol error probability. Numerical results show that while the proposed upper bound is very tight to the exact symbol error probability, there is approximately a 2.5 dB gap for the lower bound.