encoded into the phase difference between signals in two consecutive symbol intervals. Next Generation Transmission Systems Multilevel encoder Phase Transm. laser Phase FIGURE 9.18 Dual driver Mach-Zehnder modulator Dual driver mach-zehnder phase modulator used to obtain a multilevel DPSK signal. In terms of quadrature components, (9.16) writes e2(t) = sin[0(k-1)+jA0]n-(t,k) (9.17) e3(t)=e4(t)=0 Equation 9.17 shows that the points representing the transmitted symbols in the quadrature space are all distributed on a circle on the l3, e4 plane whose center is in the origin and whose square radius is the transmitted power, which is constant due to the pure phase modulation. A typical characteristic of a multilevel constellation is the minimum distance d in the quadrature space between a couple of symbols. It is quite intuitive that this distance will be related to the noise robustness of the modulation format. Considering for example binary IM, the constellation is done by two points and the distance is d = JP, SO that we can write SNo = d2/PASE! where PASE is the ASE power. In this case, we have simply d=vFsin(MM) (9.18) A practical transmitter for the M-DPSK signal is presented in Figure 9.18, conceptually, this is simply a phase modulator, in practice almost only dual drive integrated modulators are used to reduce distortions (see Chapter 5). 9.3.2.2 Multilevel Quadrature Amplitude Modulation (M-QAM) This modulation format is widely used in radio applications and consists in the amplitude modulation of the two complex quadratures of one of the field polarizations. The points representing the states of the transmitted field in the quadratures space are comprised in one coordinate plane and form a square lattice: a few examples are provided in Figure 9.19. Telecommunication Networks 4-QAM 8-QAM-1 FIGURE 9.19 Examples of squared QAM constellations. 8-QAM-2 16-QAM In terms of quadrature, the components of the transmitted field can be written as e1(t) = Pos1,knT(t,k) e2(t) = ,(t,k) (9.19) e3(t)=e4(t)=0 where Sj,k is t