The symbol decomposition technique aims to decompose Optical Orthogonal Frequency Division Multiplexing (O-OFDM) symbols into multiple symbols with a small Peak to Average Power Ratio (PAPR) to mitigate the non-linear effects of Light Emitting Diodes (LEDs). However, O-OFDM generates more decomposed symbols with a higher PAPR, thereby reducing the information rate and degrading the Bit Error Rate (BER) performance.

The proposed design of Precoding O-OFDM Adaptive Symbol Decomposition with Serial Transmission (PCO-OFDM-ASDST) system uses precoding scheme to reduce the PAPR of O-OFDM symbols. The proposed method can reduce the average number of symbol decompositions for adaptive symbol decomposition. The theoretical Signal-to-Noise Ratio (SNR) expressions are derived for multipath channels, and the performance of PAPR, BER, and information rate is analyzed using Monte Carlo BER simulations.

The results demonstrate that under 4 Quadrature Amplitude Modulation (QAM) modulation in Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing (ACO-OFDM) systems, the symbol power required for PCO-OFDM-ASDST is 7 dB less than that of Adaptive Symbol Decomposition with Serial Transmission (ASDST) when the BER is 10^-4. Moreover, under 64QAM, the information rate can be increased by 10 Mbit/s when the symbol power is 20 dBm.

The results indicate that the PCO-OFDM-ASDST outperforms ASDST systems in terms of BER and information transmission rate.