Analysis and Design of Cognitive Radio Networks Using Game Theory
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Modeling and
Problem Formalization

A General Model of Cognitive Radio Interactions

example : Modeling a Cognitive Radio

Consider two cognitive radios, {1,2}, with actions (waveforms) :

respectively, that are communicating with a common receiver which reports to each cognitive radio that radio’s signal-to-interference ratio (SIR).In this case, the passive operating environment is defined by the gains from each
cognitive radio to the common receiver, g1 and g2. We’ll consider the interference that one waveform induces on the other to be given by the absolute value of the correlation of their signal space representations,

where wj is the waveform chosen by radio j and w−j is the waveform chosen by the other radio. In such a system, the observed outcome for each radio j is given by the SIR equation given in :

where gj is the link budget gain of radio j to the common receiver, and g−j is the gain of the other radio to the common receiver.A reasonable goal or a utility function for a cognitive radio operating in this system would be to maximize oj so that the greater the SIR the radio achieves, the higher the value the radio assigns to the outcome. Note that this goal incorporates both the relevant information from the passive operating environment (in this case, the link gains), the potential actions that could be taken by the radios, and the interactive nature of those actions.

Based on this discussion, these various modeling parameters can be compactly summarized as shown in Table 2.1.

Table 2.1 : Parameters for Example Model