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We develop a flexible and accurate framework for device-to-device (D2D)communication in the context of a conventional cellular network, which allowsfor time-frequency resources to be either shared or orthogonally partitionedbetween the two networks. Using stochastic geometry, we provide accurateexpressions for SINR distributions and average rates, under an assumption ofinterference randomization via time and/or frequency hopping, for bothdedicated and shared spectrum approaches. We obtain analytical results inclosed or semi-closed form in high SNR regime, that allow us to easily explorethe impact of key parameters (e.g., the load and hopping probabilities) on thenetwork performance. In particular, unlike other models, the expressions weobtain are tractable, i.e., they can be efficiently optimized without extensivesimulation. Using these, we optimize the hopping probabilities for the D2Dlinks, i.e., how often they should request a time or frequency slot. This canbe viewed as an optimized lower bound to other more sophisticated schedulingschemes. We also investigate the optimal resource partitions between D2D andcellular networks when they use orthogonal resources.

Resource Optimization in Device-to-Device Cellular Systems Using Time-Frequency Hopping