Abstract-We investigate the problem of optimal power allocation for energy recycling cooperative communications systems, employing full duplex relays, based on the criterion of maximizing the rate, or equivalently the Signal to Noise Ratio (SNR), of the system. A system model is investigated where each time slot is split into an information transmission phase, during which the Source (S) transmits information to the destination (D) and a full-duplex Relay (R), and an energy harvesting phase. During the energy harvesting phase, R relays information to D, while concurrently it performs energy harvesting, exploiting a signal transmitted by S and energy recycling, exploiting its own transmission. For this system model, we formulate a rate/SNR maximization problem, in order to compute the optimal source power levels for both information transfer and energy transfer phases. The cost function of this optimization problem is then substituted by a sharp approximation, which allows for obtaining an analytically tractable power allocation. The performance of the resulting power allocation is then assessed by means of Monte Carlo simulations, and it is found that it outperforms existing solutions. It is therefore shown that our proposed solution can contribute towards increasing the range of IoT networks.