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In this paper, the inherent drawbacks of the naive lattice decoding for MIMO fading systems is investigated. The authors show that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the rate-diversity trade-off. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal rate-diversity trade-off. Indeed, they show that in the case of naive lattice decoding, when they fix the underlying lattice, all the codes based on full-rate lattices have the same rate-diversity trade-off as V-BLAST.
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