Spectrum auctions provide a platform for licensed spectrum users to share their underutilized spectrum with unlicensed users. Existing spectrum auctions either use the protocol interference model to characterize interference relationship as binary, or do not allow the primary and secondary users to share channels simultaneously. To fill this void, we design SPA, a spectrum single-sided auction under the physical interference model, which considers the interference to be accumulative. We prove that SPA is computationally efficient, individualrational, and truthful. Results from extensive simulation studies demonstrate that, SPA achieves higher revenue, spectrum utilization and buyer satisfaction ratio, compared with the existing auctions modified with the physical interference model.