## 2 Laser Phase Noise and Equalization Enhanced Phase Noise  
As shown in Figure 1, the origin of equalization enhanced phase noise in the coherent optical communication systems using electronic dispersion compensation and carrier phase recovery is schematically illustrated. In such systems, the transmitter laser phase noise goes through both the transmission fiber and the EDC module, and therefore the net dispersion experienced by the transmitter laser phase noise is close to zero. However, the LO laser phase noise only goes through the EDC module, where the transfer function is heavily dispersed in the transmission system without using any optical dispersion compensation (ODC) techniques. As a result, the LO laser phase noise will interplay with the dispersion equalization module, and will significantly degrade the performance of the long-haul high-speed coherent optical fiber communication systems, with the increment of fiber dispersion, laser linewidths, modulation formats, and symbol rates [33; 34; 36]. In coherent optical communication systems, the variance of the phase noise coming from the transmitter laser and the LO laser follows a Lorentzian distribution and can be described using the following equation [4; 5]:  
\[\sigma_{Laser}^{2}=2\pi\left(\Delta f_{Tx}+\Delta f_{LO}\right)\cdot T_{S}, \tag{1}\]  
where \(\Delta f_{Tx}\) and \(\Delta f_{LO}\) are the 3-dB linewidths (assuming the Lorentzian distribution) of the transmitter laser and the LO laser, respectively, and \(T_{S}\) is the symbol period of the coherent transmission system. It can be found that the variance of the laser phase noise decreases with the increment of the signal symbol rate \(R_{S}=1/T_{S}\). Considering the interplay between the electronic dispersion compensation module and the LO laser phase noise, the noise variance of the equalization enhanced phase noise in the long-haul high-speed optical fiber communication systems can be expressed as follows [33; 37; 40]:  
Figure 1: Principle of equalization enhanced phase noise in electronic dispersion compensation based \(n\)-PSK coherent optical transmission system. PRBS: pseudo random bit sequence, N(t): additive white Gaussian noise (AWGN), e.g., amplified spontaneous emission (ASE) noise from optical amplifiers, ADC: analog-to-digital convertor. \[\sigma_{EEPN}^{2}=\pi\lambda^{2}D\cdot L\cdot\Delta f_{LO}/2 cT_{S}, \tag{2}\]  
where \(f_{LO}\) is the central frequency of the LO laser, which is equal to the central frequency of the transmitter laser \(f_{Tx}\) in the homodyne optical communication systems, \(D\) is the CD coefficient of the transmission fiber, \(L\) is the length of the transmission fiber, \(R_{S}\) is the signal symbol rate of the communication system, and \(\lambda=c/f_{Tx}=c/f_{LO}\) is the central wavelength of the optical carrier wave. When the equalization enhanced phase noise is taken into account in the carrier phase recovery, the total noise variance (or effective phase noise variance) in the long-haul high-speed \(n\)-PSK optical fiber transmission systems can be calculated and described using the following expression [37; 40]:  
\[\sigma_{T}^{2}\approx\sigma_{Laser}^{2}+\sigma_{EEPN}^{2}=2\pi T_{S}\left(\Delta f _{Tx}+\Delta f_{LO}\right)+\pi\lambda^{2}D\cdot L\cdot\Delta f_{LO}/2 cT_{S} \tag{3}\]  
The equalization enhanced phase noise differs from the laser phase noise, and the noise variance in Equation (2) has two-thirds contribution in the phase noise and one-third contribution in the amplitude noise [33; 37; 40]. Therefore, Equation (3) is only valid for \(n\)-PSK communication systems, and the performance of \(n\)-QAM transmission systems has to be assessed based on the evaluation of error vector magnitudes [52].