er Phase Amplitude Polarization driver driver driver Sa(t) So(t) Transm. Phase Amplitude Polarization laser FIGURE 9.17 Block scheme of the generic modulator for instantaneous multilevel modulation formats. Telecommunication Networks The power spectral density S+( and S_()) of the two polarization components of the transmitted signal (9.8) can be evaluated starting from the elements of the matrix S. In the hypothesis of instantaneous modulation, from Equation 9.13 it is deduced that S is always a diagonal matrix SO that (+)()) = = (9.14) S_(w) = S3,3(w)+S4,4(W)=So_G(w,T) where So+=(six)+(s2k) T = n/R, where R is the bit rate and n is defined by Equation 9.11 In the particularly important case of NRZ modulation, g(t) is a square pulse and (9.14) becomes (9.15) This is quite a common form of an NRZ signal, whose spectrum width is equal to B = 2R/n thus confirming the rule anticipated in Section 9.1 for the spectral width of an instanta- neous multilevel modulation. 9.3.2 Practical Multilevel Transmitters Almost in any practical case, the transmitter depicted in Figure 9.18 has a too high inser- tion loss and practical modulation formats are also selected on the ground of the possibil- ity of designing a low loss-high efficiency modulator. In this section, we will present a few particular modulation formats that are important in practice. 9.3.2.1 Multilevel Differential Phase Modulation (M-DPSK) This is probably one of the simpler cases that generalize to multilevel transmission binary differential phase shift keying (DPSK) that we have introduced in Chapter 6: the phase of the transmitted signal is modulated using multilevel differential modulation. Let us call W; the jth world of n transmitted bits and = 2/2 The M-DPSK signal transmitted in the kth symbol interval and modulated with Wi writes (9.16) where nT(k,k) is the Heaviside function that is equal to one for t E ((k-1)T,kT) and zero else- where and O(k)-O(k-1)=jA0 As in the binary case, the name differential comes from the fact that the transmitted symbol is 