Analog radio over fiber (ARoF) is an candidate to construct mobile optical backhaul and fronthaul network that connects between wireless radio transceiver and remote antenna unit (RAU) because of its centralized signal processing capability and heterogeneous property of the optical fiber communication technologies. Its broad bandwidth for transmitting heterogeneous radio signal enables us to share single optical fiber infrastructure even if the light source has single wavelength resource. There were some reports on the method for sharing the 10Gbps optical Ethernet infrastructure to transmit radio frequency (RF) signal without introducing extra light source. Previous paper has reported on the probability density function (pdf) of RF signal amplitude that modulates an optical OOK signal, and derived the bit error rate (BER) performance for the OOK signal. However, only the continuous wave (CW) was assumed as an RF signal in the last work. This paper proposes an application of frequency shift for transmitting the RF orthogonal frequency division multiplexing (OFDM) signal over fiber with optical On-Off Keying (OOK) in order to avoid serious interference. In this paper, the error vector magnitude (EVM) performance is evaluated by using computer simulation.