© 2017 IOP Publishing Ltd and Sissa Medialab srl . The Dark Energy Spectroscopic Instrument (DESI), a multiplexed fiber-fed spectrograph, is a Stage-IV ground-based dark energy experiment aiming to measure redshifts for 29 million Emission-Line Galaxies (ELG), 4 million Luminous Red Galaxies (LRG), and 2 million Quasi-Stellar Objects (QSO). The survey design includes a pattern of tiling on the sky, the locations of the fiber positioners in the focal plane of the telescope, and an observation strategy determined by a fiber assignment algorithm that optimizes the allocation of fibers to targets. This strategy allows a given region to be covered on average five times for a five-year survey, with a typical variation of about 1.5 about the mean, which imprints a spatially-dependent pattern on the galaxy clustering. We investigate the systematic effects of the fiber assignment coverage on the anisotropic galaxy clustering of ELGs and show that, in the absence of any corrections, it leads to discrepancies of order ten percent on large scales for the power spectrum multipoles. We introduce a method where objects in a random catalog are assigned a coverage, and the mean density is separately computed for each coverage factor. We show that this method reduces, but does not eliminate the effect. We next investigate the angular dependence of the contaminated signal, arguing that it is mostly localized to purely transverse modes. We demonstrate that the cleanest way to remove the contaminating signal is to perform an analysis of the anisotropic power spectrum P(k,μ) and remove the lowest μ bin, leaving μ > 0 modes accurate at the few-percent level. Here, μ is the cosine of the angle between the line-of-sight and the direction of K→. We also investigate two alternative definitions of the random catalog and show that they are comparable but less effective than the coverage randoms method.