Statistical comparison between max-dmin, max-SNR and MMSE precoders

In this study, we considered a MIMO system with available channel state information at the transmitter side and compared three known precoders based on different and pertinent criteria: the post processing signal-to-noise ratio (max-SNR), the mean square error between transmitted and received symbols (MMSE) and the minimum distance of the received constellation (max-d_min). We demonstrate that, alike the max-SNR and contrarily to the MMSE, the max-d_min gives the maximum diversity order for a Rayleigh channel. An upper- bound of the MMSE diversity order is given. On the other hand, d_min of the three precoders will be statistically studied as a function of the number of antennas. In addition, BER simulations showed that the best precoder is the max-d_min.