A modification to the Asymmetrically-Clipped Optical Orthogonal Frequency-Division Multiplexing (ACO-OFDM) technique is proposed through unipolar encoding. A performance analysis of the Bit Error Rate (BER) is developed and Monte Carlo simulations are carried out to verify the analysis. Results are compared to that of the corresponding ACO-OFDM system under the same bit energy and transmission rate; an improvement of 1 dB is obtained at a BER of 10-4 . In addition, the performance of the proposed system in the presence of atmospheric turbulence is investigated using single-input multiple-output (SIMO) configuration and its performance under that environment is compared to that of ACO-OFDM. Energy improvements of 4 dB and 2.2 dB are obtained at a BER of 10-4 for SIMO systems of 1 and 2 photodetectors at the receiver for the case of strong turbulence, respectively.