We consider a multipoint-to-point network in which sensors periodically send measurements to a gateway. The system uses Long Range (LoRa) communications in a frequency band with duty-cycle limits. Our aim is to enhance the reliability of the measurement transmissions. In this setting, retransmission protocols do not scale well with the number of sensors as the duty cycle limit prevents a gateway from acknowledging all receptions if there are many sensors. We thus intend to improve the reliability without acknowledgments by transmitting multiple copies of a measurement, so that the gateway is able to obtain this measurement as long as it receives at least one copy. Each frame includes the current and a few past measurements. We propose a strategy for redundancy allocation that takes into account the effects of fading and interference to determine the number of measurements to be included in a frame. Numerical results obtained using the simulation tool LoRaSim show that the allocation of redundancy provides up to six orders of magnitude decrease in the outage probability. Compared to a system that blindly allocates the maximum redundancy possible under duty-cycle and delay constraints of the gateway and memory constraints of the sensors, our technique provides up to 30 reduction in the average energy spent to successfully deliver a measurement to the gateway.
There is a wide range of results available on interference analysis based on tools from stochastic geometry @cite_8 @cite_9 . They consider the sum interference power as opposed to the power of the strongest interferer. Since only the latter is important for LoRa due to the capture effect @cite_2 , these results are not applicable for our purpose. Results on the outage probability of LoRa that take into account the capture effect are given in @cite_2 . The scenario analyzed in @cite_2 comprises a random number of nodes distributed over a circular region with the gateway at the center. In contrast, our work is motivated mainly by use cases pertaining to industrial monitoring in which a known number of sensors are placed over a small area. The area could be a production floor, a processing unit, a storage facility, or a collection of entities equipped with many sensors to periodically measure physical quantities of interest. The gateway could be located at an office building and wired to a computational unit where the sensor data are processed and monitored.
@cite_9 @cite_2 @cite_8
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We analyze the performance of an interference-limited decode-and-forward cooperative relaying system that comprises a source, a destination, and @math relays, arbitrarily placed on the plane and suffering from interference by a set of interferers placed according to a spatial Poisson process. In each transmission attempt, first, the transmitter sends a packet; subsequently, a single one of the relays that received the packet correctly, if such a relay exists, retransmits it. We consider both selection combining and maximal ratio combining at the destination, Rayleigh fading, and interferer mobility. We derive expressions for the probability that a single transmission attempt is successful, as well as for the distribution of the transmission attempts until a packet is successfully transmitted. Results provide design guidelines applicable to a wide range of systems. Overall, the temporal and spatial characteristics of the interference play a significant role in shaping the system performance. Maximal ratio combining is only helpful when relays are close to the destination; in harsh environments, having many relays is particularly helpful, and relay placement is critical; the performance improves when interferer mobility increases; and a tradeoff exists between energy efficiency and throughput. Low power wide area (LPWA) networks are making spectacular progress from design, standardization, to commercialization. At this time of fast-paced adoption, it is of utmost importance to analyze how well these technologies will scale as the number of devices connected to the Internet of Things inevitably grows. In this letter, we provide a stochastic geometry framework for modeling the performance of a single gateway LoRa network, a leading LPWA technology. Our analysis formulates the unique peculiarities of LoRa, including its chirp spread-spectrum modulation technique, regulatory limitations on radio duty cycle, and use of ALOHA protocol on top, all of which are not as common in today’s commercial cellular networks. We show that the coverage probability drops exponentially as the number of end-devices grows due to interfering signals using the same spreading sequence. We conclude that this fundamental limiting factor is perhaps more significant toward LoRa scalability than for instance spectrum restrictions. Our derivations for co-spreading factor interference found in LoRa networks enables rigorous scalability analysis of such networks. The temporal correlation of interference is a key performance factor of several technologies and protocols for wireless communications. A comprehensive understanding of interference correlation is especially important in the design of diversity schemes, whose performance can severely degrade in case of highly correlated interference. Taking into account three sources of correlation-node locations, channel, and traffic-and using common modeling assumptions-random homogeneous node positions, Rayleigh block fading, and slotted ALOHA traffic-we derive closed-form expressions and calculation rules for the correlation coefficient of the overall interference power received at a certain point in space. Plots give an intuitive understanding as to how model parameters influence the interference correlation.