Power moment derivation for noisy phase lightwave systems

The distribution law of the Brownian motion exponential functional: ε=|f_[0,1]exp[j√(2βW_t]dt|² ), where {W_t,t∈ℛ⁺} is a standard Brownian motion, modeling the laser´s phase noise, plays a key role in many of the proposed heterodyne lightwave systems. The exact analytic derivation of these statistics appears to be, however, a formidable mathematical task. We present a closed form formula for the kth power moment Eε^k induced by the unknown distribution law. The results are useful in assessing the performance of noisy phase lightwave systems