Analysis and Design of Cognitive Radio Networks Using Game Theory
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Analysis and Design of Cognitive Radio Networks Using Game Theory |
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In this interaction problem, each radio reacts to observations of the outside world by choosing some adaptation (or waveform) that the radio believes will help bring it closer to its goal, whatever that goal may be. At any given point in time, the observation a cognitive radio makes will be a function of the passive operating environment of the network (the channel conditions and interference environmentthat would be observed if no cognitive radios were operating in the environment) andthe decision processes of the cognitive radios – decision processes that may beimplemented via procedures or via a reasoning engine. Regardless of the implementation of the decision process, by definition, the cognitive radios are guided in their adaptations by some goal.
the following presents a collection of symbols and conventions that captures
the general features of cognitive radio interaction and can be fashioned into a usable
model of cognitive radio interactions.
• N : The (finite) set of cognitive radios in the network where n is the number of
elements in N, |N| .
• i, j : Particular devices in N.
• Aj : The set of actions available to radio j. While these sets are quite limited for
many radios, they include all available adaptations to the radio. As the adaptations
can include a number of independent types of adaptations, e.g., power levels,
modulations, channel and source coding schemes, encryption algorithms, MAC
algorithms, center frequencies, bandwidths, and routing algorithms, Aj will
generally be a multidimensional set.
• A : The action space, i.e., set of all possible combinations of actions by the radios. Throughout, we assume that A is formed by the Cartesian product
of each radio’s action sets.
• a : A particular combination of actions where each radio in N has implemented a
particular action (waveform), i.e., a point in A or an action vector. Radio j’s
contribution to a is written as aj, and the choice of actions by all cognitive radios
other than j is written as a-j.
• O : The set of all possible observed outcomes of the outside world.
• oj : An observation made by or supplied to radio j. For instance, an SINR
measurement.
• o : A vector of observed outcomes where all radios have observed an outcome. For instance, o may represent a vector of SINR
measurements with each measurement associated with a particular cognitive
radio. Frequently, we refer to this as an outcome.
• dj : The decision rule which describes how radio j updates its decisions based on observations.
• uj(a) : The utility function which describes how much value radio j assigns to
action vector a. In general, the utility function expresses some goal that the radio
is working towards.
• Tj : The times at which radio j can update its decision
• T : The set of all times where decision updates can occur.
Summarizing this discussion, the basic model of cognitive radio interaction consists of a collection of cognitive radios, N, an action space A, a utility function for each cognitive radio j which is a function of the ctions of each radio and the passive operating environment, a decision rule for each cognitive radio, and a set of times at which these decisions occur. This can be compactly represented as the 5-tuple shown in :
Table 2.1 : Symbol summary |
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example
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