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Blind identification of single-input multiple-output (SIMO) systems is not normally possible if common zeros exist in the channels. Studies of measured acoustic SIMO systems show that near-common zeros occur in such systems as encountered in the speech dereverberation task. We therefore introduce a method to add additional diversity to the SIMO system to be identified which we term forced spectral diversity (FSD) and we show that its use leads to an identification-equalization approach that gives improved dereverberation. As part of this work, we show the link between channel diversity and the effect of common zeros. We also define and discuss in more detail the concept and impact of near-common zeros. The proposed algorithm is presented specifically for a two-channel system where such near-common zeros exist.