Chapter

Wireless Communications

Volume 143 of the series The IMA Volumes in Mathematics and its Applications pp 297-330

Fair Allocation of A Wireless Fading Channel: An Auction Approach

  • Jun SunAffiliated withLaboratory for Information and Decision Systems, Massachusetts Institute of Technology
  • , Eytan ModianoAffiliated withLaboratory for Information and Decision Systems, Massachusetts Institute of Technology

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Abstract

We study the use of auction algorithm in allocating a wireless fading channel among a set of non-cooperating users in both downlink and uplink communication scenarios. For the downlink case, we develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the all-pay auction mechanism whereby user bid for the channel, during each time-slot, based on the fade state of the channel, and the user that makes the higher bid wins use of the channel. Under the assumption that each user has a limited budget for bidding, we show the existence of a unique Nash equilibrium strategy. We show that the strategy achieves a throughput allocation for each user that is proportional to the user’s budget and 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 scheme that does not take fairness into account.

For the uplink case, we present a game-theoretical model of a wireless communication system with multiple competing users sharing a multiaccess fading channel. With a specified capture rule and a limited amount of energy available, a user opportunistically adjusts its transmission power based on its own channel state to maximize the user’s own individual throughput. We derive an explicit form of the Nash equilibrium power allocation strategy. Furthermore, this Nash equilibrium power allocation strategy is unique under certain capture rule. We also quantify the loss of efficiency in throughput due to user’s selfish behavior. Moreover, as the number of users in the system increases, the total system throughput obtained by using a Nash equilibrium strategy approaches the maximum attainable throughput.

Key words

Stochastic processes Mathematical programming/optimization

AMS(MOS) subject classifications

Primary 91A80 91A10 93E03 93A14