A simple bidirectional radio over fiber (RoF) design based on orthogonal frequency division multiplexing (OFDM)-based millimeter wave (mm-wave) signal generation and transmission with compensation of linear and non-linear impairment with the aid of sparse second-order Volterra non-linear equalizer (S2-VNLE) is proposed. At the central station (CS), an optical 60 GHz OFDM-based mm-wave downlink signal is generated by a 16-QAM downlink radio frequency (RF) signal. The generated OFDM-based downlink mm-wave signal is transmitted to the base station (BS) via bidirectional single-mode fiber (SMF) of length 75 km. At BS, the downlink signal is photo detected and transmitted via an antenna to the user end. The 16-QAM uplink RF signal, obtained via a receiving antenna from the user end, is modulated on the unused carrier of the downlink mm-wave signal. The modulated uplink signal is transmitted to the CS through the same bidirectional fiber. The carrier reuse and fiber reuse reduce the system complexity. However, the simultaneous signal co-propagation may induce linear and non-linear impairment, further degrading the system performance and has to be compensated. The compensation of linear and non-linear impairment is done by full Volterra non-linear equalization (FVNLE). However, pruning the insignificant Volterra filter coefficient enables a reduction in computational complexity. The sparse second-order Volterra non-linear equalization (S2-VNLE) is obtained by l₁-regularization to cut off the kernels with a moderate contribution. The weights of the tap coefficient are updated by the RLS algorithm. The transmission performance of compensated bidirectional RoF system is investigated. The performance analysis of the bidirectional RoF system shows improved efficiency, having performance closer to FVNLE with reduced system and computational complexity.