Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers

A description is given of a relatively simple derivation of the bit-error probability for a lightwave communications system using an amplitude-shift-keying (ASK) pulse modulation format and employing optical amplifiers such that amplified spontaneous emission noise dominates all other noise sources. Mathematically, this noise is represented as a Fourier series expansion with Fourier coefficients that are assumed to be independent Gaussian random variables. The bit-error probability is given in a closed analytical form that is derived by the approximate evaluation of several integrals appearing in the analysis. The author uses the theory to derive the Gaussian approximation and finds that it overestimates the bit-error rate by one to two orders of magnitude