In this paper, the bit error rate (BER) performance of a full-duplex (FD) overlay cognitive radio (CR) network with linear/nonlinear energy harvesting (EH) capability is investigated. The considered overlay CR network consists of a primary transmitter/receiver (PT/PR) pair, a secondary transmitter (ST) and an FD mode operated secondary receiver (SR) where ST harvests energy from both PT and SR during the first communication time slot. In the second communication time slot, SR receives its intended signal from ST while cooperating with PT by transmitting its signal to PR. The bit error probability (BEP) expressions for the primary/secondary users (PU/SU) are analytically derived and validated through Monte-Carlo simulations according to both linear and nonlinear EH models applied at ST. In addition, the optimum distance value between PT and ST is determined considering the objective of minimizing BER of both PU and SU. Moreover, corresponding system performances are obtained regarding a power allocation coefficient at SR to obtain the trade-off between EH and information processing. The results show that the proposed FD-CR system with nonlinear EH improves the PU BEP performance compared to the non-cooperative (direct transmission) case while the SU benefits from the spectrum of PU with a significant BER performance.