Individual and Mass Behaviour in Large Population Stochastic Wireless Power Control Problems: Centralized and Nash Equilibrium Solutions
نویسندگان
چکیده
We consider uplink power control for lognormal fading channels in the large population case. First, we examine the structure of the control law in a centralized stochastic optimal control setup. We analyze the effect of large populations on the individual control inputs. Next, we split the centralized cost to approach the problem in a game theoretic framework. In this context, we introduce an auxiliary LQG control system and analyze the resulting ε-Nash equilibrium for the control law; subsequently we generalize the methodology developed for the LQG problem to the wireless power control problem to get an approximation for the collective effect of all other users on a given user. The obtained state aggregation technique leads to highly localized control configurations in contrast to the full state based optimal control strategy.
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