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Fifth-generation mobile networks (5G) are the solution for the demanding mobile traffic requirements, providing technologies that fulfill the requisites of different type of services. The utilization of the millimeter-wave (mm-wave) band is the straightforward technique to achieve high bit rates. Moreover, analog radio-over-fiber (ARoF) brings outstanding benefits such as low cost, low power consumption, and high spectral efficiency, among others. Thereby, mm-wave ARoF is a strong candidate to pave the way for common public radio interface (CPRI) in the fronthaul for the future 5G architecture. As orthogonal frequency-division multiplexing (OFDM) is the adopted waveform in the 5G standard, it should be also utilized in mm-wave ARoF systems for 5G. However, phase noise is one of the most degrading factors in mm-wave OFDM ARoF systems. Therefore, in this work, an analysis of the phase noise is carried out through an experimental setup up. The configuration of this setup enables to gradually modify the final phase noise level of the system. Furthermore, an original and novel algorithm to compensate the phase noise in OFDM receivers is proposed. The performance of this algorithm is experimentally evaluated through the setup for different phase noise levels and different subcarrier spacings. The obtained results show the effectiveness of the proposed algorithm under those conditions, highlighting the viability of mm-wave OFDM ARoF for 5G and beyond.