On the Error Rate of the LoRa Modulation With Interference

Abstract

LoRa is a chirp spread-spectrum modulation developed for the Internet of Things. In this work, we examine the performance of LoRa in the presence of both additive white Gaussian noise and interference from another LoRa user. To this end, we extend an existing interference model, which assumes perfect alignment of the signal of interest and the interference, to the more realistic case where the interfering user is neither chip-nor phase-aligned with the signal of interest and we derive an expression for the error rate. We show that the existing aligned interference model overestimates the effect of interference on the error rate. Moreover, we prove two symmetries in the interfering signal and we derive low-complexity approximate formulas that can significantly reduce the complexity of computing the symbol and frame error rates compared to the complete expression. Finally, we provide numerical simulations to corroborate the theoretical analysis and to verify the accuracy of our proposed approximations. ). layer, which uses an ALOHA-based channel access scheme in which collisions are not explicitly avoided. These collisions lead to same-technology inter-user interference which may ultimately become the capacity-limiting factor in massive IoT scenarios [13]. For this reason, it is of great interest and importance to study the performance of LoRa under sametechnology interference.The authors of [14] present a mathematical network model for LoRa that includes the capture effect, i.e., the fact that a LoRa packet can be correctly decoded even under interference from another LoRa packet. A stochastic geometry framework for modeling the performance of a single gateway LoRa network is used in [15]. An investigation of the latency, collision rate, and throughput for LoRaWAN under duty-cycle restrictions is performed in [16]. Several real-world deployments of LoRa have been tested, but in order to assess the network scalability of LoRaWAN to future network densities that are expected to be orders of magnitude larger, evaluations through network simulators need to be performed. For this reason, the works of [17], [18] added LoRa functionality to the well-known ns-3 network simulator. A simpler Python-based network simulator for the LoRa uplink was first described in [19], and later extended for the LoRa downlink in [20]. The impact of the downlink feedback on LoRa capacity was also studied in [21]. A general overview and performance evaluations of LoRaWAN can be found in [13], [22].The impact of interference coming from different technologies on the performance of the LoRa modulation has received some attention in the literature. Specifically, [23] studies the co-existence of LoRa with IEEE 802.15.4g, while [24] studies the co-existence of LoRa with ultra-narrowband technologies, such as Sigfox. The impact of interference coming from other LoRa nodes has also received some attention. Specifically, the work of [25] extended the simulator of [19] in order to study the impact of imperfect orthogonality between different LoRa spr...

A Study of LoRa Performance in Monitoring of Patient’s SPO2 and Heart Rate based IoT

“…Bit error rate or bit error ratio is the number of digital bits in the transmission network, in this case, LoRa 915 MHz where the total number of error bits is divided by the number of bits sent in a certain time (t), e.g, Bits sent 0110001011, while those received are 0010101001, from 10 data bits sent, there are 3 error bits, so the percentage is 3/10 or 0.3 or 30% BER, BER can be showed by equation 11 [23]. (11)…”

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

“…The accurateness of the suggested BER expressions compared with the exact one is very interesting in practice, especially since (7) is not tractable, and raises some computing precision problems. In fact, to give an idea of the required precision, the binomial coefficient N −1 k in (7) with full AWGN+channel coding approximation [7] AWGN+interferences approximation [6] Rayleigh, Rice, Nakagami exact precision needs to be stored over up to 150 bits in SF7, and even up to 4000 bits in SF12 (e.g. 2047 200 is of order 9.10 282 ), which can be achieved only with the use of the package gmpy2 in python.…”

“…model and the approach (exact or approximated BER expression) is provided in Table 1. Note that we have added [7] and [8] to enlarge the scope of this overview. In fact, even if these paper does not deal with BER of LoRa signal over specific channel model, but their BER analysis consider the effect of the channel coding and the impact of interference on the BER performance, respectively.…”

Analysis of the reliability of LoRa

“…Perfect orthogonality for LoRa network, i.e. frames that are set with different spreading factors (SF) are orthogonal to each other and do not cause interference, has been assumed considering that there is at least 16dB co-channel rejection between any different SF couples [4], [5], [6], [7]. This assumption however, has not been taken by others when analyzing the performance of LoRa networks [8], [9], [10], [11].…”