TABLE OF CONTENTS This section presents several examples that demonstrate the analysis of interactions of cognitive radio networks. Specifically, we consider and analyze the (distributed) scenarios of ad hoc power control, DFS, and general waveform adaptation for adaptive interference avoidance. For each scenario, we briefly overview the algorithm under study, present a game model for the algorithm, and analyze the algorithm for steady states, optimality, convergence, and stability.
Many of these examples make extensive use of game theoretic techniques to provide the most generalizable results, but the analyses are not limited to only game theoretic techniques. When appropriate, traditional analysis techniques refine the results of our analysis.
Neel et al. [29] present an analysis of a distributed power control algorithm on an ad hoc network in which each link, j, varies its transmit power in an attempt to achieve a target SINR, g j, measured in dB at the receiving end of the link. This scenario can be thought of as analogous to the fixed assignment scenario presented by Yates [12] and presented in section Standard Interference Function Model. Indeed, this analysis can be considered an extension of that scenario to ad hoc networks with additional consideration given to stability.
Using the notation presented in section Standard Interference Function Model, in a network, N, of cognitive radios the SINR of the signal transmitted by j and received by its node of interest measured in dB is given by:
where g
