Game Theory in Wireless Communications with an Application to Signal Synchronization

This paper is concerned with the general issue of game-theoretic techniques applied to the problem of resource allocation in wireless communication networks. Specifically, its first part is devoted to a tutorial explanation of game theory in the context of CDMA wireless networking, whilst the second part focuses on the particular issue of allocating power resources to optimize the receiver performance in terms of spreading code acquisition. The problem of initial signal acquisition is formulated as a noncooperative game in which each transmitter-receiver pair in the network seeks to maximize a specifically chosen utility function. For the problem at hand, the most significant utility function is represented by the ratio of the probability of signal detection to the transmitted energy per bit, and the game each receiver plays consists in setting its own transmit power and detection threshold, under a constraint on the maximum probability of spurious code locks. This formulation of the game captures the tradeoff between obtaining good code acquisition performance and saving as much energy as possible. Using the techniques introduced with the “toy examples” in the first part of the paper, the Nash solution of the proposed game is investigated and found. Closed-form expressions for the optimal transmit power and detection threshold at the Nash equilibrium are derived, and they are compared with simulation results for a decentralized resource control algorithm.