Optical single side-band (SSB) signal modulation combined with direct-detection (DD) is favorable for data center interconnections and short-reach metro networks, because it alleviates the power fading and improves the spectrum efficiency (SE). However, in addition to the transmitted baseband signal, both its Hilbert transform and the signal-signal beat interference (SSBI) can be generated and hence introduce the interference. We analyze the generation of the linear and nonlinear interference in theory and experimentally demonstrate the interference mitigation schemes in an optical single side-band Nyquist-pulse shaping PAM-4 (NPAM-4) system.