We present a simple and efficient method for generating regular pulse trains with GHz pulse repetition rates in lasers based on semiconductor optical amplifiers (SOAs). This method enables pulse formation without active modulation or saturable absorption of the generated radiation. The method relies upon the self-sustaining cross-gain modulation which is achieved by adding the negative optical feedback (NOF) to a ring laser configuration. The resulting modulation of laser gain is shown to be restricted to the frequencies which match both the spacing of longitudinal laser modes and the highest peaks in the NOF-induced instability gain spectrum. This enables the reproducible stationary pulse generation at the strictly defined repetition rates. The feasibility of the method was confirmed by the stable generation of sub-nanosecond pulses at repetition rates up to 1.79 GHz in a SOA-based laser with a simple fiber cavity.