# MIMO channel covariance matrix

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#### acaris

##### Newbie level 6
Hello,

In MIMO communications with interference, the noise matrix and the interference covariance matrix due to the signals from other sources are written as a single covariance matrix. How does this matrix change when the received power is different from different interferers?

To elaborate, we have Y = HS + sqrt(Pinterference/L) Σi=1Lhisi+W

where Y is the received vector, H is the channel matrix and the signal of interest, there are L interferers, hi are their corresponding channel matrices, and W is the noise.

and we can write R=(Pinterference2i=1Lhihi*+ IN

And here, I am assuming that the power term can be taken out because the interference power from each interferer is the same, but what happens if that is not the case, and the powers are different?

#### Pulkit Varshney

##### Member level 5
idea is that, you are weighing each si with sqrt(P_interference) in case of same interference power for other sources, so if each interferer has different power , it will be
sum from 1 to L (hi*sqrt(Pi)*si).

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