This paper investigates approaches that can cancel nonlinear phase noise effectively for the phase-conjugate pair diversity transmission of 16-QAM WDM signals through multi-core fiber. The geometric mean is introduced for the combination of the phase-conjugate pair. A numerical simulation suggests that span-by-span chromatic dispersion compensation is more effective at cancelling phase noise in long distance transmission than lumped compensation at the receiver. Simulations suggest the span-wise compensation described herein yields Q-value enhancement of 7.8 and 6.8dB for CD values of 10 and 20.6ps/nm/km, respectively, whereas the lumped compensation equivalent attains only 3.5dB. A 1050km recirculating loop experiment confirmed a Q-value enhancement of 4.1dB for 20.6ps/nm/km, span-wise compensation transmission.