Future extragalactic sub-millimetre and millimetre surveys have the potential to provide a sensitive census of the level of obscured star formation in galaxies at all redshifts. While in general there is good agreement between the source counts from existing SCUBA (850um) and MAMBO (1.25mm) surveys of different depths and areas, it remains difficult to determine the redshift distribution and bolometric luminosities of the sub-millimetre and millimetre galaxy population. This is principally due to the ambiguity in identifying an individual sub-millimetre source with its optical, IR or radio counterpart which, in turn, prevents a confident measurement of the spectroscopic redshift. Additionally, the lack of data measuring the rest-frame FIR spectral peak of the sub-millimetre galaxies gives rise to poor constraints on their rest-frame FIR luminosities and star formation rates. In this paper we describe Monte-Carlo simulations of ground-based, balloon-borne and satellite sub-millimetre surveys that demonstrate how the rest-frame FIR-sub-millimetre spectral energy distributions (250-850um) can be used to derive photometric redshifts with an r.m.s accuracy of +/- 0.4 over the range 0 < z < 6. This opportunity to break the redshift deadlock will provide an estimate of the global star formation history for luminous optically-obscured galaxies [L(FIR) > 3 x 10^12 Lsun] with an accuracy of 20 per cent.
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