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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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. This paper addresses non-Gaussian statistical modeling of interference as a superposition of a large number of small effects from terminals scatterers distributed in the plane volume according to a Poisson point process. This problem is relevant to multiple access communication systems without power control and radar. Assuming that the signal strength is attenuated over distance r as 1 r m, we show that the interference clutter could be modeled as a spherically symmetric spl alpha -stable noise. A novel approach to stable noise modeling is introduced based on the LePage series representation. This establishes grounds to investigate practical constraints in the system model adopted, such as the finite number of interferers and nonhomogeneous Poisson fields of interferers. In addition, the formulas derived allow us to predict noise statistics in environments with lognormal shadowing and Rayleigh fading. The results obtained are useful for the prediction of noise statistics in a wide range of environments with deterministic and stochastic power propagation laws. Computer simulations are provided to demonstrate the efficiency of the spl alpha -stable noise model in multiuser communication systems. The analysis presented will be important in the performance evaluation of complex communication systems and in the design of efficient interference suppression techniques. Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control as well as the maximum power limitations for UEs. More specifically, for interference mitigation and robust uplink communication, each UE is required to control its transmit power such that the average received signal power at its serving base station (BS) is equal to a certain threshold ρ o . Due to the limited transmit power, the UEs employ a truncated channel inversion power control policy with a cutoff threshold of ρ o . We show that there exists a transfer point in the uplink system performance that depends on the following tuple: BS intensity λ, maximum transmit power of UEs P u , and ρ o . That is, when P u is a tight operational constraint with respect to (w.r.t.) λ and ρ o , the uplink outage probability and spectral efficiency highly depend on the values of λ and ρ o . In this case, there exists an optimal cutoff threshold ρ o *, which depends on the system parameters, that minimizes the outage probability. On the other hand, when P u is not a binding operational constraint w.r.t. λ and ρ o , the uplink outage probability and spectral efficiency become independent of λ and ρ o . We obtain approximate yet accurate simple expressions for outage probability and spectral efficiency, which reduce to closed forms in some special cases. We investigate spatial interference statistics for multigigabit outdoor mesh networks operating in the unlicensed 60-GHz "millimeter (mm) wave" band. The links in such networks are highly directional: Because of the small carrier wavelength (an order of magnitude smaller than those for existing cellular and wireless local area networks), narrow beams are essential for overcoming higher path loss and can be implemented using compact electronically steerable antenna arrays. Directionality drastically reduces interference, but it also leads to "deafness," making implicit coordination using carrier sense infeasible. In this paper, we make a quantitative case for rethinking medium access control (MAC) design in such settings. Unlike existing MAC protocols for omnidirectional networks, where the focus is on interference management, we contend that MAC design for 60-GHz mesh networks can essentially ignore interference and must focus instead on the challenge of scheduling half-duplex transmissions with deaf neighbors. Our main contribution is an analytical framework for estimating the collision probability in such networks as a function of the antenna patterns and the density of simultaneously transmitting nodes. The numerical results from our interference analysis show that highly directional links can indeed be modeled as pseudowired, in that the collision probability is small even with a significant density of transmitters. Furthermore, simulation of a rudimentary directional slotted Aloha protocol shows that packet losses due to failed coordination are an order of magnitude higher than those due to collisions, confirming our analytical results and highlighting the need for more sophisticated coordination mechanisms.