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In this paper, we analyze the performance of underlay communication between full-duplex capable device-to-device (D2D) nodes transmitting in the cellular band. The D2D nodes use peak interference type of power control to restrict the overall interference at the cellular base station below a statistically determined interference temperature limit (ITL), thereby ensuring its quality of service for uplink cellular users. From the derived analytical expressions, sum-throughput optimal strategies are evolved to choose between full-duplex and half-duplex modes of operation for the D2D nodes. Since both D2D nodes transmit simultaneously in full-duplex mode, the ITL needs to be apportioned between the D2D terminals. A closed-form expression is presented for the optimum ITL apportioning that maximizes D2D sum-throughput. It is shown that switching to half-duplex mode is advantageous when the target rate is above a …