improving transmission rate and spectral density has become a hotspot in optical communication research.To use advanced modulation formats is the key for achieving these two aims and quadrature modulation format is one of them.This article presents a study method for calculating the BER of multi-dimensional and multi-level quadrature modulation signals and derives for the first time the analytical expression for multi-level phase-modulated signals and the simulation results by this method.In addition
it discusses the effects of such parameters as extinction ratio on BER.