We propose a novel multi-user hybrid precoder design that imitates the bit error rate (BER) performance of a given fully digital precoder by minimizing the Frobenious norm between them. We show that the proposed design equivalently minimizes the chordal distance between the column spaces of the phase-only RF precoder and the given fully digital precoder. The proposed design, in the large antenna regime, has the same BER as that of an existing optimal hybrid precoder design but with much reduced complexity. Furthermore, the proposed design is also shown to approach the BER of a given fully digital precoder. © 1997-2012 IEEE.