No abstract

In this paper we consider different methods to design mathematical models for a satellite channel. These channel models, being based on homogeneous Markov chains, are used as a basis for evaluations of OSI layer 2 protocols. The parameter design of our models is based on measured block error probabilities, obtained by German Pl'T on the Olympus 20130 GHz channel. Since the block error rate is one of the most importaru issues for a satellite channel, our modeling will be based on block oriented data transfers. We compare block error probabilities of Gilbert's and Fritchman's models with two new generative time variant models. The first is a one dimensional Markov chain (called Time Variant model, TV) and the second one is a two layered Markov model (called Two Luyer Time Variant model, TLTV). Analyses and simulations show that the TLTV model exhibits the best results.In literature a number of models for telephone channels are presented, for example [Gil60], [Ell 631, [McC 681, [Fri 671. These probabilistic models studied in literature are either descriptive, i.e. based on empiric statistics, or generative, i.e. state models generate a sequence "similar" to that of the considered channel. We will tailor their parameters so that they can be applied to the modeling of satellite channels. In section 2 we briefly consider a descriptive model. In sections 3 Gilbert's and Fritchman's generative models will be reviewed, while in sections 4 and 5 we suggest two new satellite channel models termed the Time Variant model (TV) and the Two Layer Time Variant model (TLTV). Finally in section 6 the results are presented. A stochastical analysis of single bit and burst errors behaviour is not considered here, since the measurements which have been available to us were performed by recording bit errors in 1 second intervals. Therefore, our examinations refer to block error probabilities on satellite channels. We define BLER (block error rate) as the ratio of erroneous blocks to total number of transmitted blocks during a period of time. A Descubve ModelIt is not possible to comprise in a mathematical analysis the complete physical background for the induction of errors to transmissions over satellite channels. The simplest way for describing the process of error generation is based on the assumption that each error originates from an event statistically independent of preceding events. Thus the probability Q(m,n) that a block of length n contains m errors can be determined as follows Q(m,n)=(:)qm(l -q)"-m . .where q is the bit error probability. Then the block error probability for blocks of length n is a n ) = Q(m,n) = 1 -(1 -4)"This mgzee'l bases on the mathematical description of a static property of an error sequence. The models of Mandelbrot and Berger [Maly89] are also among the descriptive models. Genwative ModelsOften, the generative channel model is a Markov chain consisting of a finite or infinite number of states with defined transition probabilities. The transition among the states produce a state sequence. Such mode...

No abstract