  Sharing the spectrum among mobile network operators (MNOs) is a promising
approach to improve the spectrum utilization and to increase the monetary
income of MNOs. In this paper, we model a nonorthogonal spectrum sharing system
for a large-scale cellular network where multiple seller MNOs lease their
licensed sub-bands to several buyer MNOs. We first analyze the per-user
expected rate and the per-MNO expected profit using stochastic geometry. Then,
we formulate the joint problem of power control and licensed sub-band sharing
to maximize the expected profit of all MNOs as a multiobjective optimization
problem (MOOP) under the users' quality of service requirement and the
nonnegative return on investment constraints. To transform the MOOP into a
single objective form, we use a combination of the $\epsilon$-constraint and
weighted sum methods. However, the transformed problem is nonconvex because of
the presence of binary variables and nonconvex rate functions in the objective
function and constraints. We address this problem by using a penalty function
and approximating the nonconvex rate functions by a constrained stochastic
successive convex approximation method. Finally, the numerical results show the
correctness and performance of the proposed algorithm under various conditions.
