Unbiased clustering estimates with the DESI fibre assignment

The Emission Line Galaxy survey made by the Dark Energy Spectroscopic Instrument (DESI) survey will be created from five passes of the instrument on the sky. On each pass, the constrained mobility of the ends of the fibres in the DESI focal plane means that the angular distribution of targets that can be observed is limited. Thus, the clustering of samples constructed using a limited number of passes will be strongly affected by missing targets. In two recent papers, we showed how the effect of missing galaxies can be corrected when calculating the correlation function using a weighting scheme for pairs. Using mock galaxy catalogues we now show that this method provides an unbiased estimator of the true correlation function for the DESI survey after any number of passes. We use multiple mocks to determine the expected errors given one to four passes, compared to an idealized survey observing an equivalent number of randomly selected targets. On BAO scales, we find that the error is a factor of 2 worse after one pass, but that after three or more passes, the errors are very similar. Thus, we find that the fibre assignment strategy enforced by the design of DESI will not affect the cosmological measurements to be made by the survey, and can be removed as a potential risk for this experiment.