Resource and power costs in dynamic spectrum allocation

We consider a network setting, where a single service provider (SP) provides wireless data services to a group of users in the downlink. The transmission model is similar to OFDMA and thus the SP allocates spectrum to the users. The SP transmits at specific power spectral density. A user applications are characterized by its received rate which is a function of the allocated spectrum, its link gain to the SP and the transmit power spectral density. The SP obtains the net spectrum requested by all the users from a central clearinghouse. The SP charges the users a two part tariff consisting of a fixed subscription fee and variable usage cost and pays the clearinghouse a spectrum cost. The SP also incurs a cost proportional to the power it transmits to all the users. We model this allocation scheme and characterize the trade-off between transmit power spectral density and net spectrum purchased by the SP as a function of the spectrum and power costs for different classes of concave user utilities.