2 The Coherent Optical DFT-spread OFDM System with PDM 2.1 System Descriptions A block diagram for the optical DFT-spread OFDM system with PDM is shown in Fig. 1. We transmit and receive signals on both polarizations which effectively results in a 2 × 2 multiple-input multiple-output (MIMO) system. Consider one of the two data streams at the transmitter. The bit sequence is first mapped to the quadrature amplitude modulation (QAM) symbols. In the traditional OFDM system, an inverse discrete Fourier trans- form (IDFT) is directly applied to the QAM symbols. In the DFT-spread OFDM system, on the other hand, a DFT is first applied to the QAM sym- bols, and then followed by the IDFT operation. After inserting the cyclic prefix (CP) symbols, the electrical signal is passed through the digital-to- analog converter and the low-pass filter, and then upconverted to the optical signal. The optical signal traverses in the long-haul fiber link comprising of multiple spans to reach the destination. At the receiver the optical sig- nal is downconverted to the electrical signal, which is then low-pass filtered and passed through the analog-to-digital converter. After removing the CP and performing the DFT on the signals at each polarization, the two cou- pled frequency-domain received signals over M subcarriers are obtained. We then perform a tone-by-tone MIMO equalization to decouple the two signal 4