Simple Asymptotic BER Expressions for LoRa System over Rice and Rayleigh Channels

This paper deals with the bit error rate (BER) of LoRa signal over Rayleigh and Rice channels. Exact analytical expressions of the BER in LoRa systems have been proposed in the literature, but they are not tractable and raise problems of computation precision. This is mainly due to the fact that these expressions involve sums of binomial coefficients, leading to extremely large numbers and leading to problem of precision. We then hereby suggest asymptotic expressions of the BER, which are at the same time tractable and accurate over a wide BER range. These expressions do not involve sums of binomial coefficients anymore, but only closed-form functions, and can then be easily obtained through computer simulations.