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Abstract: We give new results about the set of all medians, the set of all first quartiles and the set of all third quartiles of a finite dataset. We also give new and interesting results about rela- tionships between these sets. We also use these results to provide an elementary correctness proof of the Langford's doubling method.
Keywords: statistic, probability, median, first quartile, third quartile, median set, first quartile set, third quartile set
Published in DKUM: 19.09.2022; Views: 538; Downloads: 15
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Abstract: Data transmission sent through wireless channel is usually affected by background noise, multipath fading and interference which cause data errors. Influence of such disturbances is the most commonly expressed in a form of error probability statistics. Effects of these disturbances on IEEE 802.15.4 wireless transmissions are previously studied, except influence of co-channel interference (CCI) which originates from collision between IEEE 802.15.4 devices which perform simultaneous radio transmission. Our thesis puts forward the assumption that it is possible to derive more accurate analytical error probability model for higher data level error probability parameters without the idealization of PN spreading sequences. Additionally, thesis is that is possible to derive an accurate analytical error probability model in the case of CCI influenced by background noise by consideration of constellation diagram. IEEE 802.15.4 standard uses CSMA/CA (Carrier Sense Multiple Access with Collision Detection) channel access mechanism to prevent collisions between devices, but this mechanism doesn't provide protection from hidden node problem which is primary source of co-channel interference. Using Monte Carlo simulations we determined frequency of hidden node collisions, which shown that co-channel interference frequently occur in parts of the network with high traffic load. Some prior works in this field tend to idealize these non-ideal spreading sequences in order to simplify calculations for error probability parameters. Our doctor thesis presents analytical model of data level error probability parameters (symbol, bit and packet) for IEEE 802.15.4, which uses original non-ideal spreading sequences without their idealization. Proposed error probability model consists of mutually dependent chip, symbol, bit and packet error probability models. Derived error probability models are linked together, so each of error probability parameters can be determined using error probability parameter from the previous stage. Error probability model for IEEE 802.15.4 wireless communication could be used in network simulation tools in order to accurately simulate energy efficient medium access protocols in realistic scenarios. Presented theoretical results are tested by independent numerical simulation of IEEE 802.15.4 transmission according to Monte Carlo method. Simulation results shows that derived models for error probability parameters were matched by two simulation scenarios in background noise, for multipath fading and co-channel interface, respectively Furthermore, the accuracy of derived mathematical models was tested in real-world experiment using IEEE 802.15.4 compliant wireless transceivers for creating co-channel interference. Packets were received by software defined radio platform, which enabled realization of coherent receiver in which all error probability statistics could be collected. The results of the experiment show consistency with proposed analytical error probability models, but some deviations are caused by poor preamble synchronization under low SNR (Signal to Noise Ratio) value. The thesis was proved with Monte Carlo simulations of the physical level of the IEEE 802.15.4 communication and experimental measurements on a real physical communication system.
Keywords: IEEE 802.15.4 standard, error probability model, co-channel interference, Rician fading channel, additive white Gaussian noise, wireless transmission, wireless sensor networks, numerical simulations, software defined radio
Published in DKUM: 14.10.2016; Views: 2502; Downloads: 147
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Keywords: statistics, statistical methods, commercial business, economy, probability, distributions, sampling, analysis of variance, experimental design, regression analysis, forecasting, analysis
Published in DKUM: 06.06.2012; Views: 1654; Downloads: 40
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Keywords: economics, economy, business operation, business operation of the enterprise, statistical methods, statistics, computer science, computer application, software, computer programmes, Excel, CD-ROM, compact disc, computer diskette, Internet, computer networks, data base, probability, realibility, distributions, hypotheses testing, data, sampling, regression analysis, correlations, time series, mistakes, problem solving, solution of problems, statistical analysis, application, business process, accounting, cas
Published in DKUM: 01.06.2012; Views: 2975; Downloads: 37
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Keywords: projects, project management, management, manager, project organization, planning, project planning, conflicts, bargaining, negotiation, budgeting, costs, information systems, information resources, allocation, monitoring, control, auditing, statistics, probability, case study, textbooks
Published in DKUM: 01.06.2012; Views: 2391; Downloads: 115
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