Spectrum is a critical yet scarce resource and it has been shown that dynamic spectrum access can significantly improve spectrum utilization. To achieve this, it is important to incentivize the primary license holders to open up their under-utilized spectrum for sharing. In this paper we present a secondary spectrum market where a primary license holder can sell access to its unused or under-used spectrum resources in the form of certain fine-grained spectrum-space-time unit. Secondary wireless service providers can purchase such contracts to deploy new service, enhance their existing service, or deploy ad hoc service to meet flash crowds demand. Within the context of this market, we investigate how to use auction mechanisms to allocate and price spectrum resources so that the primary license holder's revenue is maximized. We begin by classifying a number of alternative auction formats in terms of spectrum demand. We then study a specific auction format where secondary wireless service providers have demands for fixed locations (cells). We propose an optimal auction based on the concept of virtual valuation. Assuming the knowledge of valuation distributions, the optimal auction uses the Vickrey-Clarke-Groves (VCG) mechanism to maximize the expected revenue while enforcing truthfulness. To reduce the computational complexity, we further design a truthful suboptimal auction with polynomial time complexity. It uses a monotone allocation and critical value payment to enforce truthfulness. Simulation results show that this suboptimal auction can generate stable expected revenue.
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