he symbol transmitted in the kth symbol interval e is the normalized field polarization vector Next Generation Transmission Systems Delay Ts M-DPSK field Lowpass Hybrid filter Delay Ts Sampler Decision device FIGURE 9.32 Block scheme of a balanced M-DPSK receiver. (From Yamazaki, H. et al., Photon. Technol. Lett., 22(5), 2010.) the ASE noise contribution is represented with "ASE(t) (while it is to remember that NT represents the function equal to one in the symbol interval and zero elsewhere) The field on the upper branch of the receiver, after splitting, delay, and recombination, writes as )aaA(t) (9.43) where a is the optical chain loss, and an analogous expression holds for the field in the lower branch and (9.44) Detecting the fields with a balanced receiver gives the following photocurrent c(t) = where ng(t) is the shot noise term. In equation (9.45) the symbol transmitted in the k-th symbol interval is represented by j, that determines the phase of the cosine function. The photocurrent is then sampled after low pass filtering and the samples are sent to the decision device. The receiver we have described is much simpler than the whole quadrature receiver: no LO and no polarization tracking are needed due to the use of signal self-beating. This is one of the reasons that qualify M-DPSK modulation as a good candidate for long haul 100 Gbit/s systems, where limiting the system cost is frequently much more impor- tant to push performances up to the limit. 9.3.3.3 M-PolSK Receivers As in the case of M-DPSK, in the case of polarization modulation also, the quadrature receiver is not optimum and a direct detection receiver offering better performances can be designed [37,36]. Telecommunication Networks The possibility to perform direct detection also contributes to simplify the receiver structure eliminating the need of the LO, but polarization tracking is needed since the transmitted information is coded in the polarization itself. The idea on which optimum receivers, both coherent and direct detection, are desig