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This paper proposes a theoretical and experimental performance study to characterize the transmission of code-division-multiple-access-based wireless signals over a radio frequency on free-space optical (RF-FSO) system using an aperture averaging (AA) technique. First, we propose an analytical model including the carrier-to-noise-plus-interference ratio (CNIR) and outage probability expressions taking into consideration the use of the AA technique, the laser diode nonlinear distortion, and the multiple-access interference. Furthermore, we show that there is a design trade-off between an optimum optical modulation index in the transmitter side and the receiver aperture size to achieve a required average CNIR ensuring a substantial scintillation fade reduction. We thus provide preliminary criteria for optimizing both the transmitter and the receiver design of our RF-FSO system. Using an experimental RF-FSO system, we conduct investigations to characterize the deployment environment influencing the transmission of wideband code division multiple access (W-CDMA) signals over a 1 km free-space optical communication (FSO) link. Important performance metric parameters like the CNIR and adjacent channel leakage ratio are measured and analyzed to quantify the influence of atmospheric effects. We then validate the proposed mathematical model by performing a comparison with the experimental results obtained from the W-CDMA signal transmission over RF-FSO experiments. The presented work can be used as a baseline for the design and performance evaluation of FSO systems able to transmit different broadband wireless services signals.