We report on the observation of the self-excited dust density waves in the dc discharge complex plasma. The experiments were performed under microgravity conditions in the Plasmakristall-4 facility on board the International Space Station. In the experiment, the microparticle cloud was first trapped in an inductively coupled plasma, then released to drift for some seconds in a dc discharge with constant current. After that the discharge polarity was reversed. DC plasma containing a drifting microparticle cloud was found to be strongly non-uniform in terms of microparticle drift velocity and plasma emission in accord with [Zobnin et.al., Phys. Plasmas 25, 033702 (2018)]. In addition to that, non-uniformity in the self-excited wave pattern was observed: In the front edge of the microparticle cloud (defined as head), the waves had larger phase velocity than in the rear edge (defined as tail). Also, after the polarity reversal, the wave pattern exhibited several bifurcations: Between each of the two old wave crests, a new wave crest has formed. These bifurcations, however, occurred only in the head of the microparticle cloud. We show that spatial variations of electric field inside the drifting cloud play an important role in the formation of the wave pattern. Comparison of the theoretical estimations and measurements demonstrate the significant impact of the electric field on the phase velocity of the wave. The same theoretical approach applied to the instability growth rate, showed agreement between estimated and measured values.