 distortions are already reviewed in Chapter 6, and nothing more has to be added here for this particular case, while Decision Strategies in the general case of a multilevel signal will be discussed in Section 9.4. 9.3.3.1.1 Jones Matrix Tracking Circuit Since propagation is assumed linear, Equation 4.8 describes the fiber propagation SO that the transmitted and the received quadratures are related by the following equation: (9.36) where the fiber link length has been indicated with L and the residual dispersion after the online dispersion compensation is indicated with S(@). The elements Mij(L, ()) of the Jones matrix are random complex numbers that fluctuates very slowly with respect to the modulation rate and that are related one with the other by the property of the Jones matrix to be unitary. Exploiting the property that the square norm of an optical field is invariant after a transformation with the matrix M, that is, the optical energy is invariant to polarization rotations, it is easy to demonstrate that M depends only on three independent parameters and that it can be rewritten as follows (35): M = Mxx(L,w) Myx(L,w) Eeiv (9.37) cos(a)e iv sin(a)e -sin(a)e-is cos(a)e-in The third expression of the Jones matrix, depending on three independent angles (x, I, Q) clearly express the fact that linear polarization evolution can be represented as a rotation in the quadrature space. The polarization rotation compensation algorithm implemented in the block JMI simply multiplies the input filed quadrature vector by the inverse of M (i.e., equal to M+ since it is a unitary matrix). The first estimate of the matrix M is performed during the system initialization phase by transmitting a field periodically switching among two orthogonal polarizations and observing the field at the output of the receiver. Once the Jones matrix estimate is initialized, it is updated every Tu seconds by the algo- rithm implemented in the block JMT. The update interval is also determined in the initialization phase and it has to be at least