Analytical upper bounds for noisy phase optical communication invoking Gaussian quadratic functionals

The impact of laser phase noise on lightwave communication systems is governed by certain exponential functionals (EFs) of the phase trajectory, which apparently prohibit the exact derivation of the decision statistics. In contrast, phase noise quadratic functionals (QFs) feature tractable statistics. The fundamental limitations imposed by simple replacement of the exponential nonlinearity by a quadratic one are explored in the presence of additive noise, and it is shown analytically that this may yield bit-error-rate (BER) approximations only. A novel class of upper bounds on the BER with envelope detection is presented. The bounds and the approximations are both given by easily computable closed-form algebraic expressions and are based on the moment generating function inherited by the QF.<>