Four-wave mixing model for centrosymmetric constellation shaping in twin-wave-based coherent OFDM system including intersymbol interference

The four-wave-mixing (FWM) noises are modeled when walk-off and intersymbol interference (ISI) are taken into account for any centrosymmetric constellation shaped signal in orthogonal frequency-division multiplexed (OFDM) with phase-conjugated twin waves (PCTW) scheme. Bit error rate (BER) and the equivalent Q-factor for any constellation shaped signal are also modeled when the FWM and amplified spontaneous emission (ASE) noises are taken into account as additive white Gaussian noise. By using the newly derived semi-analytic models, example calculations are carried out for 16-ary signal in PCTW OFDM system with four cases classified according to some proposed constellation shaping schemes adopted or not. A hybrid constellation shaping scheme consisted of Huffman-coded probabilistic shaping and radius-optimized geometric shaping is proposed. The performance gain in terms of the equivalent Q-factor is calculated to be about 0.563 dB for 16-ary signal in PCTW OFDM system with the proposed hybrid constellation shaping scheme over the square conventional 16QAM signal. The performance degradation for such system due to the effects of ISI on the FWM noise is also evaluated by using the semi-analytic calculation models.