where there is only one such plane), three dimensions (where each rotation "axis" defines the rotation plane by coinciding with the normal vector to that plane), and with four dimensions. Defining rotations in this way evidences also the fact that, since in a four dimensional space there is a plane completely orthogonal to the rotation plane, the points on this plane are not affected by the rotation, SO that, coming back to our case, if both our reference points belongs to that plane they are not able to individuate the rotation matrix. Thus, it is not possible to eliminate a priori some equations from the system (9.39); it has to be simplified every time isolating three independent equations and solving them to obtain the parameters of the matrix AM+. Once evaluated, this matrix is added to the run- ning estimate of the inverse Jones matrix without any disruption of the detection process. 9.3.3.1.2 Local Oscillator Frequency Lock The scope of the LO control loop is to stabilize the LO frequency to maintain the photocur- rent in baseband while the wavelength of the transmitting laser fluctuates. Different systems have been devised to perform this operation, but the greater num- ber of them can be divided into two categories: electronically driven and injection locking based. In the first case, the LO is tuned to track the incoming signal via a decision driven elec- tronic feedback circuit that modulates the laser current, in the second case, part of the incoming optical signal, in case suitably filtered, is directly injected into the LO. The scheme of an electronic LO circuit is reported in Figure 9.31, where it is evidenced that the loop has to be driven by a signal somehow related to the frequency different from the LO and the signal. Frequency Laser tracking signal Laser driver Local oscillator FIGURE 9.31 field Block scheme of a LO control circuit. Telecommunication Networks This signal is derived in the block FCC of Figure 9.29b. As a matter of fact, modulation can be interpreted as a rotation of the quadrat