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Register a new userLimitations of Stochastic Geometry Modelling for Estimating the Performance of CSMA Networks
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Andra Voicu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This letter considers stochastic geometry modelling (SGM) for estimating the signal-to-interference-and-noise ratio (SINR) and throughput of CSMA networks. We show that, despite its compact mathematical formulation, SGM has serious limitations in terms of both accuracy and computational efficiency. SGM often severely underestimates the SINR versus ns-3 simulations, yet as it neglects the sensing overhead when mapping SINR to throughput, SGM usually overestimates the throughput substantially. We propose our hybrid model for CSMA, which we argue is a superior modelling approach due to being significantly more accurate and at least one order of magnitude faster to compute than SGM.
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In this paper, we study the transport capacity of large multi-hop wireless CSMA networks. Different from previous studies which rely on the use of centralized scheduling algorithm and/or centralized routing algorithm to achieve the optimal capacity scaling law, we show that the optimal capacity scaling law can be achieved using entirely distributed routing and scheduling algorithms. Specifically, we consider a network with nodes Poissonly distributed with unit intensity on a $sqrt{n}timessqrt{n}$ square $B_{n}subsetRe^{2}$. Furthermore, each node chooses its destination randomly and independently and transmits following a CSMA protocol. By resorting to the percolation theory and by carefully tuning the three controllable parameters in CSMA protocols, i.e. transmission power, carrier-sensing threshold and count-down timer, we show that a throughput of $Thetaleft(frac{1}{sqrt{n}}right)$ is achievable in distributed CSMA networks. Furthermore, we derive the pre-constant preceding the order of the transport capacity by giving an upper and a lower bound of the transport capacity. The tightness of the bounds is validated using simulations.
This work characterises the effect of mutual interference in a planar network of pulsed-radar devices. Using stochastic geometry tools and a strongest interferer approximation, we derive simple closed-form expressions that pinpoint the role played by key system parameters on radar detection range and false alarm rate in the interference-limited region. The fundamental tradeoffs of the system between radar performance, network density and antenna directivity are captured for different path-loss exponents in the no-fading and Rayleigh-fading cases. The discussion highlights practical design hints for tuning the radar parameters. The accuracy of the model is verified through network simulations, and the role of random noise on detection in sparse, non interference-limited networks is characterised.
This work started out with our accidental discovery of a pattern of throughput distributions among links in IEEE 802.11 networks from experimental results. This pattern gives rise to an easy computation method, which we term back-of-the-envelop (BoE) computation, because for many network configurations, very accurate results can be obtained within minutes, if not seconds, by simple hand computation. BoE beats prior methods in terms of both speed and accuracy. While the computation procedure of BoE is simple, explaining why it works is by no means trivial. Indeed the majority of our investigative efforts have been devoted to the construction of a theory to explain BoE. This paper models an ideal CSMA network as a set of interacting on-off telegraph processes. In developing the theory, we discovered a number of analytical techniques and observations that have eluded prior research, such as that the carrier-sensing interactions among links in an ideal CSMA network result in a system state evolution that is time-reversible; and that the probability distribution of the system state is insensitive to the distributions of the on and off durations given their means, and is a Markov random field. We believe these theoretical frameworks are useful not just for explaining BoE, but could also be a foundation for a fundamental understanding of how links in CSMA networks interact. Last but not least, because of their basic nature, we surmise that some of the techniques and results developed in this paper may be applicable to not just CSMA networks, but also to other physical and engineering systems consisting of entities interacting with each other in time and space.
We study algorithms for carrier and rate allocation in cellular systems with distributed components such as a heterogeneous LTE system with macrocells and femtocells. Existing work on LTE systems often involves centralized techniques or requires significant signaling, and is therefore not always applicable in the presence of femtocells. More distributed CSMA-based algorithms (carrier-sense multiple access) were developed in the context of 802.11 systems and have been proven to be utility optimal. However, the proof typically assumes a single transmission rate on each carrier. Further, it relies on the CSMA collision detection mechanisms to know whether a transmission is feasible. In this paper we present a framework for LTE scheduling that is based on CSMA techniques. In particular we first prove that CSMA-based algorithms can be generalized to handle multiple transmission rates in a multi-carrier setting while maintaining utility optimality. We then show how such an algorithm can be implemented in a heterogeneous LTE system where the existing Channel Quality Indication (CQI) mechanism is used to decide transmission feasibility.
We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.
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