In this work a wireless power transfer (WPT) scheme for orthogonal frequency division multiple access (OFDMA) systems is proposed, with the objective of prolonging the battery life of the receiver. A novel receiver that capitalizes on the presence of a redundant portion of the OFDMA signal, i.e, the cyclic prefix (CP), to harvest energy that can be used to reduce the power consumption of the OFDMA digital signal processing at the receiver, is described. The concept of self-sustainability, a condition achieved when the amount of harvested energy from the received signal is sufficient to perform the digital signal processing at the receiver, is introduced. A parametric model to study the feasibility of several levels of self-sustainability, is provided and an analytical condition to ensure their achievability is derived. Numerical findings show that, under certain reasonable conditions, the full self-sustainability can be achieved for CP sizes compliant with the existing telecommunication standards.