This paper looks into an energy harvesting (EH) relay-enabled cognitive radio wireless sensor network (CR-WSN) considering power splitting (PS) architecture. More specifically, a relay (RU) harvesting energy from the signals transmitted from a secondary user transmitter (ST,) and using the harvested energy to forward the resulting signals to another sensor node subsequently is being investigated. This scheme can be broken down into two components, i.e., a sensor node physically placed near the transmitter (SPNT) and a sensor node physically placed far from the transmitter (SPFT). The closed-form expressions for the successful transmission probability (STP) and the achievable data rate in both cases can be derived analytically. In order to quantify the energy consumption, the system energy efficiency (EE) is examined. Furthermore, the achievable data rate was optimized in three possible scenarios, i.e., the trade-off between the sum data rate and the sum harvested energy (R-E), the achievable data rate at RU, and the joint optimization of the power allocation and PS ratio in case of SPNT. A Monte Carlo simulation has been performed to verify the theoretical analysis obtained, and to show the impact of different parameters on system performance.