Radio Frequency energy harvesting (EH) is one of the enabling technologies for the next genera- tion wireless communication systems. EH techniques are specifically used to improve energy efficiency of the system. Recently, the simultaneous wireless information and power transmission (SWIPT) protocol is adapted for EH. In this paper, we design a new receiver for joint carrier frequency offset (CFO) and channel estimation on single-carrier (SC) modulations with frequency-domain equalization (FDE) along with SWIPT implementation for EH by using the pilot signal. The pilot signal is a highly energized signal, which is superimposed with the information signal. The sumperimposed signal is used not only to transmit power for EH purposes, but also to estimate the CFO and channel conditions. The receiver is designed to accommodate the strong interference levels in the channel estimation and data detection. The proposed scheme offers a flexible de- sign method and efficient resource utilization. We validate our analytical results using simulations.