We study the problem of interference management for device-to-device (D2D) communications where multiple D2D users may coexist with one cellular user. The problem is to optimize the transmit power levels of D2D users to maximize the cell throughput while preserving the signal-to-noise-plus-interference ratio (SINR) performance for the cellular user. This is the so-called multi rate power control problem. We investigate the problem under two assumptions, the availability of the instantaneous or average channel state information (CSI) at the base station. In the first case, D2D transmit power levels adapt to fast fading, whereas in the second case, they only adapt to slow fading. In the latter assumption, the cellular user has a maximum outage probability requirement. With numerical results, we study the trade-off between the signaling overhead, that is frequent CSI feedbacks, and the overall system performance, that is the maximum achievable cell capacity, for D2D communications underlying cellular networks.
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