The continuous increase of the worldwide data traffic demands new concepts for data transmission in the optical fiber-based backbone networks. One promising way to increase the capacity of the existing fiber infrastructure is to use quadrature amplitude modulation (QAM) in combination with polarization-multiplexing and coherent detection. In this book all necessary algorithms are presented that are required for the realization of such a system using digital signal processing at the receiver. The main focus thereby lies on the algorithms for polarization control and carrier recovery. But also clock recovery, intermediate frequency control and compensation of intersymbol interference are considered. The performance of the algorithms is studied in extensive simulations. Additionally the results of the real-time implementation of selected algorithms in a single polarization and a polarization-multiplexed synchronous optical QPSK transmission system are presented. Both systems are the worldwide first that are realized with a real-time coherent digital receiver and standard DFB lasers.