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Multilevel M-ary amplitude-shift-key (M-ASK) intensity modulation formats have been proposed and experimentally demonstrated in millimeter-wave radio-over-fiber (mm-wave RoF) system. In order to demonstrate multilevel intensity modulation for spectrally efficient implementation, return-to-zero (RZ) and non-RZ (NRZ) implementations for both 4-ASK and 8-ASK modulation formats are utilized in full-duplex RoF link. Hence, for downlink, two different signal generation schemes are utilized in this paper for optical mm-wave generation and transport using optical heterodyning of two unlocked lasers. For uplink, similar RF self-homodyning technique is applied at the base station (BS) to simplify the signal translation process. Theoretical analyses and experimental results using the proposed technique for M-ASK modulation formats confirm the system's performance. Apart from the bandwidth-efficient realization of the proposed schemes, demonstrated full-duplex RoF techniques avoid most of the high-speed electrooptic and RF devices from both the central station (CS) and BSs keeping the optical mm-wave generation, optical transport, and BSs simpler in both directions.