  This paper presents a semi-analytical approximation of Symbol Error Rate
(SER) for the well known LoRa Internet of Things (IoT) modulation scheme in the
following two scenarios: 1) in multi-path frequency selective fading channel
with Additive White Gaussian Noise (AW GN) and 2) in the presence of a second
interfering LoRa user in flat-fading AW GN channel. Performances for both
coherent and non-coherent cases are derived by considering the common Discrete
Fourier transform (DF T) based detector on the received LoRa waveform. By
considering these two scenarios, the detector exhibits parasitic peaks that
severely degrade the performance of the LoRa receiver. We propose in that sense
a theoretical expression for this result, from which a unified framework based
on peak detection probabilities allows us to derive SER, which is validated by
Monte Carlo simulations. Fast computation of the derived closedform SER allows
to carry out deep performance analysis for these two scenarios.
