Modeling four-wave mixing noises for any signal constellation in twin-wave-based coherent OFDM system

Semi-analytic models of four-wave-mixing (FWM) noise for any possible signal constellation, called as general FWM models, are derived in this paper for coherent orthogonal frequency-division multiplexed (OFDM) system with three kinds of phase-conjugated twin waves (PCTW) schemes. The PCTW scheme, used to reduce the impact of FWM noise by co-propagating a signal with its phase-conjugated copy along optical fiber link, can be implemented in polarization, time or subcarrier domains. Based on the derived general FWM models, example calculations are carried out to evaluate the performance of OFDM system with polarization-domain PCTW scheme for 16-ary signal with several kinds of signal constellations when the FWM and the amplified spontaneous emission (ASE) noises are included. Three kinds of 16-ary signal constellations are defined here. The first kind, written as (N1, N2), has N1 signal points on the inner circle and N2 points on the outer circle. The second kind, written as (1, N1, N2), has N1 signal points on the inner circle, N2 points on the outer circle and a signal point in the center. The third kind, written as (N1, N2, N3), has N1 signal points on the innermost circle, N2 signal points on the media circle and N3 points on the outermost circle. Among all 16-ary signal constellations discussed here, the performance of (5, 11) is best and that of the 16-ary phase-shift keying (PSK) is worst. The performance of (5, 11) is close to that of (1, 5, 10) and 16-ary quadrature amplitude modulation (QAM).