Effect of Nonlinear Phase Noise on the Performance of $M$-Ary PSK Signals in Optical Fiber Links

The effects of amplified spontaneous emission (ASE) noise and nonlinear phase (NLP) noise on the symbol error rate performance of
M
-ary coherent phase shift keying (CPSK) and differential phase shift keying (DPSK) are analyzed. Expressions for the symbol error probability (SEP) are derived for the two cases of independent ASE and NLP noises and dependent ASE and NLP noises. Numerical results are presented for 2-, 4-, 8-, and 16-level signaling to demonstrate the applicability of the SEP expressions. Our results indicate that the SEPs for DPSK for the two cases are approximately the same except for
M
=2. The SEPs for CPSK differ significantly for the two cases for all
M
, implying that independent phase noise assumption is not valid for CPSK.