In this paper, we investigate a two-hop communication system in which the source utilizes radio frequency (RF) energy harvesting for the transmission of information. An intermediate relay works in a half-duplex (HD) mode in the energy harvesting (EH) phase to provide energy to the source. In the information transmission phase, the relay works in a full-duplex (FD) mode to receive information signals from the source and simultaneously transmit information signals to the destination in the same frequency band. The paper provides the analysis of outage probability and throughput of a FD relaying system and two HD relaying systems. The first HD system ( HD_1 ) has the same EH duration as the FD system while the second HD one ( HD_2 ) has the same transmitting power from the source as the FD one. The results show that the throughput with respect to the time split between the EH phase and the information transmission one is a concave function and the optimal time split can be calculated numerically. Besides, the polarization dissimilarity factor of the antennas used has an influence on the system throughput, which is maximized when polarization states are orthogonal. The FD system can double the system throughput while having the outage probability as low as that of the HD_1 system, at a cost of adopting the extra polarization-enabled digital cancellation (PDC) scheme. Meanwhile, the FD system can nearly double the system throughput while having the outage probability superior to that of the HD_2 system. Simulations are run to confirm the above analyses.