nition of Figure 9.24, the position on the Poincare sphere of any SOP can be individuated. Up to now we have supposed the field completely polarized, as an M-PolSK signal at the output of the modulator. During propagation however, ASE is added to the field. The noise is randomly distrib- uted among the two polarizations, thus introducing a field depolarization. In this case, the polarization degree can be defined as (9.24) Where P is the overall field power and the definition of the Stokes parameters becomes S = Po, cos(20)cos(20) S2=Po,sin(20)cos(20) = (9.25) S3=Po,sin(20) If the light is composed of a fraction of perfectly polarized light and a fraction of perfectly depolarized light (like a PolSK signal plus ASE noise), the power of the polarized compo- nent Pp and the power of the unpolarized component Pu are given by (9.26) Pu(t)[p(t)-Pp(t)]p(t)(1-op (9.27) FIGURE 9.24 Relations between the angular coordinates in the Stokes space and the angles defining the polarization ellipse in the physical space. Next Generation Transmission Systems SO that, if the Optical SN coincides with the ratio between the polarized and the unpolar- ized part of the field, it can be written as (9.28) The general instantaneous multilevel Polarization modulation format (M-PolSK: Multilevel Polarization Shift Keying) is obtained by choosing a constellation on the Poincare sphere and associating to each of the constellation points a transmitted symbol. We will introduce in the following a Stokes parameters receiver for the M-PolSK [35] that can be demonstrated to be the optimum receiver for this type of modulation format [36]. We will see that, also in this case, what is relevant to evaluate the effectiveness of the constellation is the minimum distance in the Stokes space. Limiting our analysis to constant power modulation, the problem of determining the best possible constellation can be formulated as the problem of distributing M points on a sphere SO that the minimum distance between two of them is maximized. This problem is not ea