In a previous post we have seen that MIMO fading capacity is much higher than AWGN capacity with multiple antennas. How is this possible? How can randomness added by a fading channel help us? In this post we try to find the reason for this. Let’s assume the following signal model for a Multi Input Multi Output antenna system.

x=Hs+w

Here s is the N_T by 1 signal vector, w is the N_R by 1 noise vector and H is the N_R by N_T channel matrix. The received signal vector is represented by x which has dimensions of N_R by 1. In expanded form this can be written as (assuming N_T =4 and N_R =4):