On the diversity of the Naive Lattice Decoder

"Naive Lattice Decoding" (NLD) and its low-complexity approximations such as lattice reduction-aided linear decoders represent an alternative to Maximum Likelihood lattice decoders for MIMO systems. Their diversity order has been investigated in recent works. These showed that the NLD achieves only the receive diversity and that MMSE-GDFE left preprocessing followed by NLD or its approximations achieves the maximum diversity. All the theoretical results have so far focused on the diversity order but this is not the only relevant parameter to achieve good performance and the coding gain also needs to be considered. In addition, up to now there has not been any numerical analysis of the actual performance of these techniques for the coded systems for moderate SNR. In this paper, we consider MIMO systems using high-dimensional perfect space-time codes. We show that by adding MMSE-GDFE preprocessing, the NLD has a loss of only 1.5 dB with respect to optimal decoding in the case of the Perfect Code 4×4. However, even with MMSE-GDFE preprocessing, the performance of lattice-reduction aided linear receivers is still very poor for high-dimensional lattices.