  This paper studies the optimal investment and pricing decisions of a
cognitive mobile virtual network operator (C-MVNO) under spectrum supply
uncertainty. Compared with a traditional MVNO who often leases spectrum via
long-term contracts, a C-MVNO can acquire spectrum dynamically in short-term by
both sensing the empty "spectrum holes" of licensed bands and dynamically
leasing from the spectrum owner. As a result, a C-MVNO can make flexible
investment and pricing decisions to match the current demands of the secondary
unlicensed users. Compared to dynamic spectrum leasing, spectrum sensing is
typically cheaper, but the obtained useful spectrum amount is random due to
primary licensed users' stochastic traffic. The C-MVNO needs to determine the
optimal amounts of spectrum sensing and leasing by evaluating the trade off
between cost and uncertainty. The C-MVNO also needs to determine the optimal
price to sell the spectrum to the secondary unlicensed users, taking into
account wireless heterogeneity of users such as different maximum transmission
power levels and channel gains. We model and analyze the interactions between
the C-MVNO and secondary unlicensed users as a Stackelberg game. We show
several interesting properties of the network equilibrium, including threshold
structures of the optimal investment and pricing decisions, the independence of
the optimal price on users' wireless characteristics, and guaranteed fair and
predictable QoS among users. We prove that these properties hold for general
SNR regime and general continuous distributions of sensing uncertainty. We show
that spectrum sensing can significantly improve the C-MVNO's expected profit
and users' payoffs.
