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I am trying to create a non-i.i.d channel: correlated Rayleigh fading channel. $$ H= R_H \cdot H_o,$$ where $H_o$ is i.i.d. channel ( uncorrelated) and $ R_H$ is a channel correlation matrix, is defined as $$ R_H= R_T^T \otimes R_R,$$ with $R_R$ receive antenna and $ R_T$ transmit antenna correlation matrices.

My question is how to find $R_T$ and $R_R$, if numbers transmit and receive antennas are given only? Can I assume them as identity matrices?

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$R_H$ could be anything other than identity and you would get correlated fading with the definitions you have in place in the question. Defining a kronecker matrix product is one way.

$R_H$ should be $N_R \times N_R$ matrix, you can make the kronecker product to result in a non identity matrix of this size.

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