In LoRa (Long Range), when a collision occurs in the network, each end-device has to retransmit its colliding frame, which reduces the throughput, and increases the energy consumption of the end-devices and the delay of the frames. In this paper, we propose an algorithm to decode colliding synchronized LoRa signals and thus improve the overall performance of the network. Indeed, we use successive transmissions of bitmaps by the end-devices to determine the correct symbols of each colliding frame, instead of retransmitting the whole frames. Simulation results show that our algorithm is able to significantly improve the overall throughput of LoRaWAN, and to decrease the energy consumption and the delay of the transmitters.
In @cite_3 , the author proposed an analysis of packet collision and packet loss probabilities in LoRaWAN, and developed theoretical expressions for both of them. The author showed that his theoretical expressions are more accurate than a Poisson distributed process to describe the collisions.
@cite_3
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Internet of things (IoT) is considered as the next technological revolution. Therefore, many solutions are developed either in free, i.e. ISM bands or in non free bands with the ultimate aim of affording connectivity over several kilometers. Based on this feature, in urban environment the density of IoT devices will be extremely high. In this paper we propose to analyze the collision and packet loss when LoRaWAN is considered. Based on the LoRaWAN features, we develop closed-form expressions of collision and packet loss probabilities. Simulation results confirm our theoretical developments. We also show that our theoretical expressions are more accurate than the Poisson distributed process to describe the collisions. The authors present an exact analysis of framed ALOHA for the case of a finite number of users. This analysis, which is based on the use of a novel combinatorial technique, does not require any restrictive assumptions on channel traffic. This model can accommodate a general model for capture, in which the probability that one packet is received successfully depends on the number of packets involved in the collision. Performance results are presented for both uncontrolled and dynamically controlled systems. > In this paper, the performance of the ALOHA and CSMA MAC protocols are analyzed in spatially distributed wireless networks. The main system objective is correct reception of packets, and thus the analysis is performed in terms of outage probability. In our network model, packets belonging to specific transmitters arrive randomly in space and time according to a 3-D Poisson point process, and are then transmitted to their intended destinations using a fully-distributed MAC protocol. A packet transmission is considered successful if the received SINR is above a predefined threshold for the duration of the packet. Accurate bounds on the outage probabilities are derived as a function of the transmitter density, the number of backoffs and retransmissions, and in the case of CSMA, also the sensing threshold. The analytical expressions are validated with simulation results. For continuous-time transmissions, CSMA with receiver sensing (which involves adding a feedback channel to the conventional CSMA protocol) is shown to yield the best performance. Moreover, the sensing threshold of CSMA is optimized. It is shown that introducing sensing for lower densities (i.e., in sparse networks) is not beneficial, while for higher densities (i.e., in dense networks), using an optimized sensing threshold provides significant gain. Current 802.11 networks do not typically achieve the maximum potential throughput despite link adaptation and cross-layer optimization techniques designed to alleviate many causes of packet loss. A primary contributing factor is the difficulty in distinguishing between various causes of packet loss, including collisions caused by high network use, co-channel interference from neighboring networks, and errors due to poor channel conditions. In this paper, we propose a novel method for estimating various collision type probabilities locally at a given node of an 802.11 network. Our approach is based on combining locally observable quantities with information observed and broadcast by the access point (AP) in order to obtain partial spatial information about the network traffic. We provide a systematic assessment and definition of the different types of collision, and show how to approximate each of them using only local and AP information. Additionally, we show how to approximate the sensitivity of these probabilities to key related configuration parameters including carrier sense threshold and packet length. We verify our methods through NS-2 simulations, and characterize estimation accuracy of each of the considered collision types. Carrier Sense Multiple Access Collision Detection (CSMA CD) is the protocol for carrier transmission access in Ethernet networks (international standard IEEE 802.3). On Ethernet, any Network Interface Card (NIC) can try to send a packet in a channel at any time. If another NIC tries to send a packet at the same time, a collision is said to occur and the packets are discarded. The CSMA CD protocol was designed to avoid this problem, more precisely to allow a NIC to send its packet without collision. This is done by way of a randomized exponential backoff process. In this paper, we analyse the correctness of the CSMA CD protocol, using techniques from probabilistic model checking and approximate probabilistic model checking. The tools that we use are PRISM and APMC. Moreover, we provide a quantitative analysis of some CSMA CD properties. This paper presents an analytic model for evaluating the MAC layer queueing delays at wireless nodes using the distributed coordination function of IEEE 802.11 MAC specifications. Our model is valid for finite loads and can account for arbitrary arrival patterns, packet size distributions and number of nodes. Each node is modeled as a discrete time G G 1 queue and we obtain closed form expressions for the delay and queue length characteristics at each node. We derive the service time distribution for the packets at each node while accounting for a number of factors including the channel access delay due to the shared medium, impact of packet collisions, the resulting backoffs as well as the packet size distribution. Our analytical results are verified through extensive simulations and are more accurate than existing models. Hidden nodes are a fundamental problem that can potentially affect any wireless network where nodes cannot hear each other. Although the hidden node problem is well known, so far only few papers have quantified its effects in a comprehensive manner. This paper represents a first step towards getting a quantitative insight into the impact of hidden nodes on the performance of wireless networks. We first carry out an exact queuing-theoretic analysis for a 4-node segment and derive analytical expressions for the probability of packet collision, the mean packet delay, and the maximum throughput, based on a model that closely follows the IEEE 802.11 standard. We then extend the analysis and provide an approximation for a general linear topology that is asymptotically exact at low load. Finally, we perform detailed simulations to validate our analytical results and show their applicability to predict the performance of IEEE 802.11 networks with hidden nodes. The simulation and analysis closely match. Moreover, they reveal that the impact of hidden nodes propagates through the network causing some nodes to saturate at load as low as 15 of the capacity. We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show that systematic network coding outperforms conventional network coding. We also develop an algorithm based on Gaussian elimination that allows progressive decoding of source packets. Simulation results show that the proposed decoding algorithm can achieve the theoretical optimal performance. Furthermore, we demonstrate that systematic network codes equipped with the proposed algorithm are good candidates for progressive packet recovery owing to their overall decoding delay characteristics. In this paper, a random access scheme is introduced, which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes through a density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed, and component code distributions tightly approaching the bound are derived. In this paper, we consider the problem of modelling the average delay in an IEEE 802.11 DCF wireless mesh network with a single root node under light traffic. We derive expression for mean delay for a co-located wireless mesh network, when packet generation is homogeneous Poisson process with rate λ. We also show how our analysis can be extended for non-homogeneous Poisson packet generation. We model mean delay by decoupling queues into independent M M 1 queues. Extensive simulations are conducted to verify the analytical results. The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered. This channel is a generalization of the usual collision channel, in that it allows the correct reception of one or more packets involved in a collision. The number of successfully received packets in each slot is modeled as a random variable which depends exclusively on the number of simultaneously attempted transmissions. This general model includes as special cases channels with capture, noise, and code-division multiplexing. It is shown by drift analysis that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity. The properties of the backlog in the nonergodicity region are examined. > Wireless LANs (WLANs) have been deployed at a remarkable rate at university campuses, office buildings, airports, hotels, and malls. Providing efficient and reliable wireless communications is challenging due to inherent lossy wireless medium and imperfect packet scheduling that results in packet collisions. In this paper, we develop an efficient retransmission scheme (ER) for wirless LANs. Instead of retransmitting the lost packets in their original forms, ER codes packets lost at different destinations and uses a single retransmission to potentially recover multiple packet losses. We develop a simple and practical protocol to realize the idea and implement it in both simulation and testbed, and our results demonstrate the effectiveness of this approach. We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks. In this paper, we address the problem of computing the probability that r out of n interfering wireless signals are "captured," i.e., received with sufficiently large Signal to Interference plus Noise Ratio (SINR) to correctly decode the signals by a receiver with multi-packet reception (MPR) and Successive Interference Cancellation (SIC) capabilities. We start by considering the simpler case of a pure MPR system without SIC, for which we provide an expression for the distribution of the number of captured packets, whose computational complexity scales with n and r. This analysis makes it possible to investigate the system throughput as a function of the MPR capabilities of the receiver. We then generalize the analysis to SIC systems. In addition to the exact expressions for the capture probability and the normalized system throughput, we also derive approximate expressions that are much easier to compute and provide accurate results in some practical scenarios. Finally, we present selected results for some case studies with the purpose of illustrating the potential of the proposed mathematical framework and validating the approximate methods. We present an analytic model for evaluating the queueing delays at nodes in an IEEE 802.11 MAC based wireless network. The model can account for arbitrary arrival patterns, packet size distributions and number of nodes. Our model gives closed form expressions for obtaining the delay and queue length characteristics. We model each node as a discrete time G G 1 queue and derive the service time distribution while accounting for a number of factors including the channel access delay due to the shared medium, impact of packet collisions, the resulting backoffs as well as the packet size distribution. The model is also extended for ongoing proposals under consideration for 802.11e wherein a number of packets may be transmitted in a burst once the channel is accessed. Our analytical results are verified through extensive simulations. The results of our model can also be used for providing probabilistic quality of service guarantees and determining the number of nodes that can be accommodated while satisfying a given delay constraint. We evaluate the end-to-end delay of a multihop transmission scheme that includes a source, a number of relays, and a destination, in the presence of interferers located according to a Poisson point process. The medium access control (MAC) protocol considered is a combination of TDMA and ALOHA, according to which nodes located a certain number of hops apart are allowed to transmit with a certain probability. Based on an independent transmissions assumption, which decouples the queue evolutions, our analysis provides explicit expressions for the mean end-to-end delay and throughput, as well as scaling laws when the interferer density grows to infinity. If the source always has packets to transmit, we find that full spatial reuse, i.e., ALOHA, is asymptotically delay-optimal, but requires more hops than a TDMA-ALOHA protocol. The results of our analysis have applications in delay-minimizing joint MAC routing algorithms for networks with randomly located nodes.We simulate a network where sources and relays form a Poisson point process, and each source assembles a route to its destination by selecting the relays closest to the optimal locations. We assess both theoretically and via simulation the sensitivity of the end-to-end delay with respect to imperfect relay placements and route crossings. Most medium access control (MAC) mechanisms discard collided packets and consider interference harmful. Recent work on Analog Network Coding (ANC) suggests a different approach, in which multiple interfering transmissions are strategically scheduled. Receiving nodes collect the results of collisions and then use a decoding process, such as ZigZag decoding, to extract the packets involved in the collisions. In this paper, we present an algebraic representation of collisions and describe a general approach to recovering collisions using ANC. To study the effects of using ANC on the performance of MAC layers, we develop an ANC-based MAC algorithm, CMAC, and analyze its performance in terms of probabilistic latency guarantees for local packet delivery. Specifically, we prove that CMAC implements an abstract MAC layer service, as defined in [14, 13]. This study shows that ANC can significantly improve the performance of the abstract MAC layer service compared to conventional probabilistic transmission approaches. We illustrate how this improvement in the MAC layer can translate into faster higher-level algorithms, by analyzing the time complexity of a multi-message network-wide broadcast algorithm that uses CMAC. We study the biased random-walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to study the efficiency of different routing protocols in communication networks. We derive exact expressions for the stationary occupation probability and for the mean transit time between two nodes. The effect of the cyclic search on transit times is also explored. Results presented in this paper provide the basis for a theoretical treatment of transport-related problems in complex networks, including quantitative estimation of the critical value of the packet generation rate. Low power wide area networks are gaining interest to connect thousands of nodes to the internet of things. However, because the link budget in these networks is huge, nodes suffer from a near-far effect. Nodes far from the base station cannot send to the base station succesfully when closer nodes are transmitting, causing destructive collisions. LoRa, the considered technology in this paper, is a spread spectrum technology. It is known that spread spectrum is also sensitive to this effect. This paper presents a scheme to efficiently optimize the packet error rate fairness inside a LoRaWAN cell. This is achieved by optimizing the power and spreading factor for each node while avoiding near-far problems by allocating distant users to different channels. Simulations show that the packet error rate can be decreased up to 50 for edge nodes in a moderate contention scenario where 1 node per 1000m2 transmits every 10 minutes. In this letter, we focus on the evaluation of link-level performance of LoRa technology, in the usual network scenario with a central gateway and high-density deployment of end-devices. LoRa technology achieves wide coverage areas, low power consumption and robustness to interference thanks to a chirp spread-spectrum modulation, in which chirps modulated with different spreading factors (SFs) are quasi-orthogonal. We focus on the performance analysis of a single receiver in presence of collisions. First, we analyze LoRa modulation numerically and show that collisions between packets modulated with different SFs can indeed cause packet loss if the interference power received is strong enough. Second, we validate such findings in experiments based on commercial devices and software-defined radios. Contradicting the common belief that SFs can be considered orthogonal, our results demonstrate that inter-SF collisions are indeed an issue in LoRa networks and, thus, allocating higher SFs to users far from the gateway might not necessarily improve their link capacity, in case of congested networks.