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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&#x2019; 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 <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-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.

Spectrum Sharing Among Multiple-Seller and Multiple-Buyer Operators of a Mobile Network: A Stochastic Geometry Approach