As LoRaWAN networks are actively being deployed in the field, it is important to comprehend the limitations of this Low Power Wide Area Network technology. Previous work has raised questions in terms of the scalability and capacity of LoRaWAN networks as the number of end devices grows to hundreds or thousands per gateway. Some works have modeled LoRaWAN networks as pure ALOHA networks, which fails to capture important characteristics such as the capture effect and the effects of interference. Other works provide a more comprehensive model by relying on empirical and stochastic techniques. This work uses a different approach where a LoRa error model is constructed from extensive complex baseband bit error rate simulations and used as an interference model. The error model is combined with the LoRaWAN MAC protocol in an ns-3 module that enables to study multi channel, multi spreading factor, multi gateway, bi-directional LoRaWAN networks with thousands of end devices. Using the lorawan ns-3 module, a scalability analysis of LoRaWAN shows the detrimental impact of downstream traffic on the delivery ratio of confirmed upstream traffic. The analysis shows that increasing gateway density can ameliorate but not eliminate this effect, as stringent duty cycle requirements for gateways continue to limit downstream opportunities.
@cite_5 , Georgiou and Raza provide a stochastic geometry framework for modeling the performance of a single channel LoRa network. Two independent link-outage conditions are studied, one which is related to SNR (i.e. range) and another one which is related to co-spreading factor interference. The authors argue that LoRa networks will inevitably become interference-limited, as end device coverage probability decays exponentially with increasing number of end devices. The authors report that this is mostly caused by co-spreading factor interference and that the low duty cycle and chirp orthogonality found in LoRa do little to mitigate this. Finally, the authors note that the lack of a packet-level software simulation is hindering the study into the performance of LoRa. It would be interesting to combine the authors' modeling of co-spreading factor interference with our ns-3 error model, as in the SINR approach all interference is treated as noise.
@cite_5
2750647255 2126158338 2081450055 2740650368
In this paper we study the impact of imperfect-orthogonality in LoRa spreading factors (SFs) in simulation and real-world experiments. First, we analyze LoRa modulation numerically and show that collisions between packets of different SFs can indeed cause packet loss if the interference power received is strong enough. Second, we validate such findings using commercial devices, confirming our numerical results. Third, we modified and extended LoRaSim, an open-source LoRa simulator, to measure the impact of inter-SF collisions and fading (which was not taken into account previously in the simulator). Our results show that non-orthogonality of the SFs can deteriorate significantly the performance especially of higher SFs (10 to 12) and that fading has virtually no impact when multiple gateways are available in space diversity. This paper addresses the following question, which is of interest in the design of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W N should the band be partitioned into in order to maximize the number of simultaneous links in the network? Dividing the available spectrum results in two competing effects. On the positive side, a larger N allows for more parallel, non- interfering communications to take place in the same area. On the negative side, a larger N increases the SINR requirement for each link because the same information rate must be achieved over less bandwidth. Exploring this tradeoff and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, the optimal SINR threshold - which directly corresponds to the optimal spectral efficiency - is derived for both the low SNR (power-limited) and high SNR (interference-limited) regimes. This leads to the optimum choice of the number of frequency bands N in terms of the path loss exponent, power and noise spectral density, desired rate, and total bandwidth. Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-of-cell interferers outside a guard region, and cross-tier interferers are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and large-scale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge. We consider a single cell wireless uplink in which randomly arriving devices transmit their payload to a receiver. Given SNR per user, payload size per device, a fixed latency constraint T, total available bandwidth W, i.e., total symbol resources is given by N = TW. The total bandwidth W is evenly partitioned into B bins. Each time slot of duration T is split into a maximum number of retransmission attempts M. Hence, the N resources are partitioned into N MB resources each bin per retransmission. We characterize the maximum average rate or number of Poisson arrivals that can successfully complete the random access procedure such that the probability of outage is sufficiently small. We analyze the proposed setting for i) noise-limited regime and ii) interference-limited regime. We show that in the noise-limited regime the devices share the resources, and in the interference-limited regime, the resources split such that devices do not experience any interference. We then incorporate Rayleigh fading to model the channel power gain distribution. Although the variability of the channel causes a drop in the number of arrivals that can successfully complete the random access phase, similar scaling results extend to the Rayleigh fading case.