In this paper, we present a framework for resource allocations for multicastdevice-to-device (D2D) communications underlaying a cellular network. Theobjective is to maximize the sum throughput of active cellular users (CUs) andfeasible D2D groups in a cell, while meeting a certainsignal-to-interferenceplus- noise ratio (SINR) constraint for both the CUs andD2D groups. We formulate the problem of power and channel allocation as a mixedinteger nonlinear programming (MINLP) problem where one D2D group can reuse thechannels of multiple CUs and the channel of each CU can be reused by multipleD2D groups. Distinct from existing approaches in the literature, ourformulation and solution methods provide an effective and flexible means toutilize radio resources in cellular networks and share them with multicastgroups without causing harmful interference to each other. A variant of thegeneralized bender decomposition (GBD) is applied to optimally solve the MINLPproblem. A greedy algorithm and a low-complexity heuristic solution are thendevised. The performance of all schemes is evaluated through extensivesimulations. Numerical results demonstrate that the proposed greedy algorithmcan achieve closeto- optimal performance, and the heuristic algorithm providesgood performance, though inferior than that of the greedy, with much lowercomplexity.
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