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?
$$R_H$$ 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.