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In MIMO systems we have: $y=Hx+n$ with $H$ is a matrix $N_r \times N_t$.

But the previous equation is only true for non-frequency selective channels.

What is the formula for frequency-selective channels?


Normally, $y=h \star x +n$. But if H is a matrix, we can not the convolution. How to solve this problem

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    $\begingroup$ $H$ becomes three dimensional matrix of which the third dimension is frequency. $\endgroup$ – AlexTP Apr 14 '18 at 13:00
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The input-otput relation for frequency selective channel:

$y_i=\sqrt{\frac{P}{M_T}}H_is_i+n_i$

More information can be found here.

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