  In this paper, we present a framework for resource allocations for multicast
device-to-device (D2D) communications underlaying a cellular network. The
objective is to maximize the sum throughput of active cellular users (CUs) and
feasible D2D groups in a cell, while meeting a certain
signal-to-interferenceplus- noise ratio (SINR) constraint for both the CUs and
D2D groups. We formulate the problem of power and channel allocation as a mixed
integer nonlinear programming (MINLP) problem where one D2D group can reuse the
channels of multiple CUs and the channel of each CU can be reused by multiple
D2D groups. Distinct from existing approaches in the literature, our
formulation and solution methods provide an effective and flexible means to
utilize radio resources in cellular networks and share them with multicast
groups without causing harmful interference to each other. A variant of the
generalized bender decomposition (GBD) is applied to optimally solve the MINLP
problem. A greedy algorithm and a low-complexity heuristic solution are then
devised. The performance of all schemes is evaluated through extensive
simulations. Numerical results demonstrate that the proposed greedy algorithm
can achieve closeto- optimal performance, and the heuristic algorithm provides
good performance, though inferior than that of the greedy, with much lower
complexity.
