Radio frequency on free-space optical (RoFSO) technology is regarded as a new universal platform for enabling seamless convergence of fiber and FSO communication networks, thus extending broadband connectivity to underserved areas. In this paper, we investigate the performance to characterize the transmission of code division multiple access (CDMA) based wireless signals over RoFSO system using aperture averaging (AA) technique under strong turbulence conditions. An analytical model including a modified carrier-to-noise-plus- interference ratio (CNIR) form and a novel closed-form expression for the bit-error rate (BER) is derived. Unlike earlier work, our model takes into consideration the effect of using the AA technique modeled by the gamma-gamma distribution, the optical noises, the intermodulation distortion term due to the laser diode non-linearity and the multiple interference access. By investigating the impact of AA on our model in the strong turbulence regime, we show that there is a design trade-off between the receiver lens aperture and the number of users to achieve a required CNIR ensuring a substantial scintillation fade reduction. The presented work can be used as baseline for the design and performance evaluation of the RoFSO system's ability to transmit different broadband wireless services signals over turbulent FSO links in real scenarios.