Spectrally Factorized Optical OFDM

A novel bandwidth efficient method to implement orthogonal frequency division multiplexing (OFDM) on intensity modulated direct detection (IM/DD) channels is presented and termed spectrally factorized optical OFDM (SFO-OFDM). It is shown that a necessary and sufficient condition for a bandlimited periodic signal to be positive for all time is that the frequency coefficients form an autocorrelation sequence. Instead of sending data directly on the subcarriers, the autocorrelation of the complex data sequence is performed before transmission to guarantee non-negativity. In $z$-domain, the average optical power is linked to the position of the zeros and used for the design of signal sets. In contrast to previous approaches, SFO-OFDM is able to use the entire bandwidth for data transmission and does not require reserved subcarriers. Using a sub-optimal design technique with 9 subcarriers and 8 bits per symbol, SFO-OFDM has a 0.5 dB gain over ACO-OFDM at a BER of $10^{-5}$ and a reduction in peak-to-average ratio of more than 30%.