  In this paper, we consider device-to-device (D2D) communications as an
underlay to the cellular networks over both licensed and unlicensed spectrum,
where Long Term Evolution (LTE) users utilize the spectrum orthogonally while
D2D users share the spectrum with LTE users. In the system, each LTE and D2D
user can access the licensed or unlicensed band for communications. To maximize
the total throughput of the system, we leverage stochastic geometry to derive
the throughput for each kind of users by modeling the deployment of users as
Poisson point processes (PPPs), and investigate the spectrum access problem for
these users. Since the problem is NP-hard, we propose a sequential quadratic
programming (SQP) based algorithm to obtain the corresponding suboptimal
solutions. Theoretically, we evaluate the system performance by analyzing the
throughput regions. Simulation results validate the accuracy of the geometric
analysis and verify the effectiveness of the proposed algorithm.
