Auction design for dynamic spectrum sharing

Abstract

Scarcity of the wireless spectrum has become a major problem as a result of the rapid growth in wireless communications. With the proliferation of smart phones and tablets, wireless data more than doubles every year. The limited nature of the wireless spectrum together with these demands, intensify the spectrum deficit problem. Several measurement studies indicate that current long-term spectrum licenses result in poor spectrum utilization. Therefore, a novel paradigm is needed to enable spectrum access in a short time scale. Dynamic spectrum sharing enables new methods of spectrum cooperation and competition where a Primary Owner (PO) can re-allocate its idle spectrum bands to unlicensed or Secondary Users (SUs). For this purpose, it is necessary to design mechanisms that provide incentives for both PO and SUs to participate in spectrum sharing.

Finally, we study the bidding problem of a budget constrained operator in repeated secondary spectrum auctions. In existing truthful auctions, truthful bidding is the optimal strategy of a bidder. However, budget limits impact bidding behaviors and make bidding decisions complicated, since bidders may behave differently to avoid running out of money. The auction model used in this work takes into account the interference relations among operators, which is an important consideration in wireless spectrum markets. We formulate the bidding problem as a dynamic auction game between operators, where knowledge of other operators is limited due to the distributed nature of wireless networks/markets. We first present a Markov Decision Process (MDP) formulation of the problem and characterize the optimal bidding strategy of an operator, provided that opponents' bids are i.i.d. Next, we generalize the formulation to a Markov game that, in conjunction with model-free reinforcement learning approaches, enables an operator to make inferences about its opponents based on local observations. Finally, we present a fully distributed learning-based bidding algorithm which relies only on local information. Our numerical results show that our proposed learning-based bidding results in a better utility and spectrum utilization than truthful bidding.

Third, we study spectrum auctions in a dynamic setting where SUs can change their valuations based on their experiences with the channel quality. Existing spectrum auctions assume that SUs have static and known values for the channels. However, in many real world settings, the SUs do not know the exact value of channel access at first, but they learn it and adapt it over time. We propose ADAPTIVE, a dynAmic inDex Auction for sPectrum sharing with TIme-evolving ValuEs that maximizes the social welfare of the SUs. ADAPTIVE is based on multi-armed bandit models where for each user an allocation index is independently calculated in polynomial time. Then we generalize ADAPTIVE to Multi-ADAPTIVE that auctions multiple channels at each time step. We provide a sufficient condition under which Multi-ADAPTIVE achieves the maximum social welfare. Both ADAPTIVE and Multi-ADAPTIVE have some desired proven economic properties. Also, we provide a numerical performance comparison between the proposed mechanisms and the well known static auctions, namely the Vickrey's second price auction and the VCG mechanism.

Second, we study revenue maximizing spectrum auctions for the general case of heterogeneous channels. We show that the problem is computationally complex. Thus, we approach the problem by utilizing reserve prices to approximate the optimal revenue. Reserve prices are minimum prices at which the PO is willing to sell channels, and setting reserve prices in an appropriate manner may be effective for increasing the PO's revenue. We first present a reserve price mechanism for auctioning heterogeneous channels that works for any arbitrary reserve prices. Next, we study optimal reserve prices that maximize the PO's revenue. We consider two cases, depending upon the available knowledge about distributions of SUs' valuations. In a prior-dependent setting, we present a 2-approximate reserve price scheme for the general case of heterogeneous channels and non-i.i.d SU valuations. In the case where no prior information is available about valuation distributions (i.e. prior-free), we present prior-free reserve prices that guarantee at least 1/4 of the optimal revenue for non-i.i.d. valuation distributions and heterogeneous channels. Finally, we present numerical results that investigate the effect of reserve prices on the performance of spectrum auctions.

First, we study the problem of heterogeneous spectrum sharing where the channels offered by the PO are of different qualities. In the model, SUs are allowed to express their preferences for each channel separately. That is, each SU submits a vector of bids, one for each channel. This model provides much more flexibility for SUs and is more practical compared to the existing spectrum auctions. We propose an efficient auction mechanism that maximizes the social welfare of the SUs.