ent from the polarimeter matrix A if the ASE noise is dominant The decision variable statistic is independent from the fiber polarization rotation; this property derives from the fact that the ASE power is uniformly distributed on the Poincare sphere among all the polarization states The last two properties, which are a key to evaluate the performance of various PolSK systems, deserve a comment. Let us consider the evolution of the M-PolSK signal under the polarization point of view representing it in the Stokes space. Let us indicate with S the Stokes vector having for com- ponents the three Stokes parameters that are coordinates in the Stokes space. If the Launched signal is represented with Si, after fiber propagation, the Stokes vector So in front of the receiver can be written as So=MSi+n (9.60) where M is the Muller matrix (the Stokes space version of the Jones matrix) n is the ASE noise vector in the Stokes space Both coherent and direct detection receivers have an optical front end constituted by a polarimeter generating a photocurrents vector Co whose elements are proportional to the Stokes parameters. This means that a nonsingular matrix A can be found SO that, neglect- ing distortions and the photodiode sensitivity, Co=AS, (9.61) The polarimeter is followed by an electronic processing section that has the role of invert- ing the matrix to obtain a set of photocurrent C1 proportional to the received field Stokes parameters. This means that, whatever be the polarimeter, coherent or incoherent, the currents in front of the electronic polarization compensation section have the following expression: C1=A-1Co==S. (9.62) Remembering that So does not depend on the receiver structure, we can conclude that the decision variable is exactly the same in every ideal Stokes parameters receiver and thus all these receivers have the same performances. At this point, it is useful to choose the receiver structure that makes easiest the evalua- tion of the BER, and it is for sure the coherent receiver. Due to the square l