We discuss about digital signal processing approaches that can enable coherent links based on semiconductor lasers. A state-of-the art analysis on different carrier-phase recovery (CPR) techniques is presented. We show that these techniques are based on the assumption of lorentzian linewidth, which does not hold for monolithically integrated semiconductor lasers. We investigate the impact of such lineshape on both 3 and 20 dB linewidth and experimentally conduct a systematic study for 56-GBaud DP-QPSK and 28-GBaud DP-16QAM systems using a decision directed phase look loop algorithm. We show how carrier induced frequency noise has no impact on linewidth but a significant impact on system performance; which rises the question on whether 3-dB linewidth should be used as performance estimator for semiconductor lasers.