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On the determination of the worst sampling error in a communication system for pulse‐amplitude‐modulated signals. I: The general model
Author(s) -
Kerber Dirk
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150706
Subject(s) - minimax , mathematics , subspace topology , impulse (physics) , dimension (graph theory) , mathematical optimization , mathematical analysis , pure mathematics , physics , quantum mechanics
Abstract We present a mathematical model of a communication system perturbed by statistical sampling errors (timing jitter). The aim is to find an ‘optimal’ impulse response for the system, the optimization problem actually being a minimax problem. that is we put the model into a game‐theoretical framework. The basic game turns out to be a statistical game similar to those arising from estimation problems in statistics. Earlier results concerning least‐favourable sampling error distributions published by Krabs and Vogel are supplemented by estimations of the number of support points of the least‐favourable distribution. Furthermore, we state the existence of the saddle points of our game, which formerly has only been proved for some special cases. In the first part we treat the general situation, where one strategy set for the game—the set of all feasible impulse responses—forms a vector space with infinite dimension. In the second part we discuss the problem in the case that the impulse responses are restricted to a finite‐dimensional subspace of the whole infinite‐dimensional subspace.