Competitive spectrum management with incomplete information

An important issue in wireless communication is the interaction between selfish independent wireless communication systems operating in the same frequency band. Due to the selfish nature of each system, this interaction is well modeled as a strategic game where each player (system) behaves to maximize its own utility. This paper studies an interference game where each system (player) has incomplete information about the other player's channel conditions. Using partial information, players choose between frequency division multiplexing (FDM) strategy and full spread (FS) strategy where power is spread across the transmission band. An important notion in game theory is the Nash equilibrium (NE) which represents a steady point in the game; that is, each player can only lose by unilaterally deviating from it. A trivial Nash equilibrium point in this game is where players mutually choose FS and interfere with each other. This point may lead to poor spectrum utilization from a global network point of view and even for each user individually. In this paper, we provide a closed form expression for a nonpure-FS ε-Nash equilibrium point; i.e., an equilibrium point where players choose FDM for some channel realizations and FS for the others. To reach this point, the only instantaneous channel state information (CSI) required by each user is its own interference-to-signal ratio. We show that operating in this nonpure-FS-Nash equilibrium point increases each user's throughput and therefore improves the spectrum utilization, and demonstrate that this performance gain can be substantial. Finally, important insights are provided into the behavior of selfish and rational wireless users as a function of the channel parameters such as fading probabilities, the interference-to-signal ratio.