 10 times shorter than the typical polarization fluctuations time Tp and at least 106 M times longer than the symbol interval. The interval Tp is defined as the minimum time interval needed to change at least one of the output quadratures of 1% when the field at the system input is constant. Telecommunication Networks The requirement Tu > 106 M assures that, since the symbols are assumed statistically independent and equally probable, averaging over this interval the quadratures of the received field, the obtained value has a Gaussian distribution with a standard deviation about three orders of magnitude smaller that the average [52]. The requirement Tp > 10 Tu assures that the fluctuations of M are tracked by the algo- rithm with a small tracking error. In real 100 Gbit/s transmission systems, the symbol interval is generally smaller than 100 ps, while Tp ranges from hundreds of milliseconds to minutes [53-55] depending on the type and collocation of the fiber cable, on the season, and similar factors. An update time Tu of the order of 100 us is thus suitable to assure independency from the modulation and very precise JMT. The update algorithm works as follows. The constellation points are divided in three categories C1, C2, and C3 constituted by almost the same number of points. At every point of the category Cj (j = 1, 2, 3) let it call Pji (i = 1, n1) a rotation matrix is associated, let it call R which rotates the reference frame in the quadrature space to transform the coordinates of Pji in the reference point II The coordinates of the reference points are II 1=010,0) = II2 = (0,1,0,0) (9.38) II3 = (0,0,1,0) These matrixes depend only on the chosen constellation and are stored in a look-up table. Every time a symbol is received, a quadrature vector [51, S2, S3, S4] is present at the input of JMT. In correspondence to these quadratures, the DC produces an estimate of the trans- mitted symbol and passes it to the JMT. The JMT uses this estimate to associate to the received quadrature vector a matrix Rki At th