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. Letâ€™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_{R}=4 and N_{T}=4):