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This article analyzes and validates through simulation the influence of fiber nonlinearity, dispersion, and loss on the Relative Noise Intensity (RIN) spectrum at fiber output in externally modulated optical single side band (OSSB) systems. The analysis includes the RIN generated by the laser source, the effect of the OSSB modulator, and noise generated by the in-line optical amplifiers. The analysis takes into account conversion between phase noise and intensity noise introduced by fiber transmission. It is shown that, depending on the operating conditions, the system performance may be predominantly affected either by the laser RIN or by the noise generated by the in-line optical amplifiers. The impact of the OSSB modulator can be relevant when the RIN of the system is dominated by the laser noise and should therefore be considered.