Wireless channel allocation using an auction algorithm

We develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the second-price auction mechanism whereby user bids for the channel, during each time slot, based on the fade state of the channel, and the user that makes the highest bid wins use of the channel by paying the second highest bid. Under the assumption that each user has a limited budget for bidding, we show the existence of a Nash equilibrium strategy, and the Nash equilibrium leads to a unique allocation for certain channel state distribution, such as the exponential distribution and the uniform distribution over [0, 1]. For uniformly distributed channel state, we establish that the aggregate throughput received by the users using the Nash equilibrium strategy is at least 3/4 of what can be obtained using an optimal centralized allocation that does not take fairness into account. We also show that the Nash equilibrium strategy leads to an allocation that is Pareto optimal (i.e., it is impossible to make some users better off without making some other users worse off). Based on the Nash equilibrium strategies of the second-price auction with money constraint, we further propose a centralized opportunistic scheduler that does not suffer the shortcomings associated with the proportional fair scheduler.