  In this paper, the problem of distributed power allocation is considered for
the downlink of a cloud radio access network (CRAN) that is coexisting with a
heterogeneous network. In this multi-tier system, the heterogeneous network
base stations (BSs) as well as the CRAN remote radio heads seek to choose their
optimal power to maximize their users' rates. The problem is formulated as a
noncooperative game in which the players are the CRAN's cloud and the BSs.
Given the difference of capabilities between the CRAN and the various BSs, the
game is cast within the framework of cognitive hierarchy theory. In this
framework, players are organized in a hierarchy in such a way that a player can
choose its strategy while considering players of only similar or lower
hierarchies. Using such a hierarchical design, one can reduce the interference
caused by the CRAN and high-powered base stations on low-powered BSs. For this
game, the properties of the Nash equilibrium and the cognitive hierarchy
equilibrium are analyzed. Simulation results show that the proposed cognitive
hierarchy model yields significant performance gains, in terms of the total
rate, reaching up to twice the rate achieved by a classical noncooperative
game's Nash equilibrium.
