Theoretical Results about MIMO Minimal Distance Precoder and Performances Comparison

This study deals with two linear precoders: the maximization of the minimum Euclidean distance between received symbol-vectors, called here max-dmin, and the maximization of the post-processing signal-to-noise ratio termed max-SNR or beamforming. Both have been designed for reliable MIMO transmissions operating over uncorrelated Rayleigh fading channels. Here, we will explain why performances in terms of bit error rates show a significant enhancement of the max-dmin over the max-SNR whenever the number of antennas is increased. Then, from theoretical developments, we will demonstrate that, like the max-SNR precoder, the max-dmin precoder achieves the maximum diversity order, which is warrant of reliable transmissions. The current theoretical knowledge will be applied to the case-study of a system with two transmit- or two receive-antennas to calculate the probability density functions of two channel parameters directly linked to precoder performances for uncorrelated Rayleigh fading channels. At last, this calculation will allow us to quickly get the BER of the max-dmin precoder further to the derivation of a tight semi-theoretical approximation.