$$ \mathbf \Phi =\begin{bmatrix} \mathbf p_1^T \mathbf \otimes Q^* \\ \mathbf p_2^T \mathbf \otimes Q^*\\ .\\ .\\ .\\ \mathbf p_{Mt}^T \mathbf \otimes Q^* \\ \end{bmatrix} $$
and $\mathbf Q=[\mathbf q_1 \mathbf q_2 ...\mathbf q_{Mr}],\mathbf P=[\mathbf p_1 \mathbf p_2 ...\mathbf p_{Mt}],\mathbf q_i^* \mathbf q_i=||\mathbf q_i||^2_2=\gamma,||\mathbf P||^2_F= P,\mathbf q_i$ is a $N_r \times 1$ matrix ,and $\mathbf p_i$ is a $N_t \times 1$ matrix
And the paper said $\mathbf \Phi \mathbf \Phi ^* =\frac{\gamma P}{N_t N_r} \mathbf I$,and i think it just
$$ \mathbf \Phi \mathbf \Phi^*=\begin{bmatrix} \mathbf p_1^T \mathbf \otimes Q^* \\ \mathbf p_2^T \mathbf \otimes Q^*\\ .\\ .\\ .\\ \mathbf p_{Mt}^T \mathbf \otimes Q^* \\ \end{bmatrix}\begin{bmatrix} \mathbf p_1^T \mathbf \otimes Q^* \\ \mathbf p_2^T \mathbf \otimes Q^*\\ .\\ .\\ .\\ \mathbf p_{Mt}^T \mathbf \otimes Q^* \\ \end{bmatrix}^* $$ and may be some reason to let the formula become $\mathbf q_i ^* \mathbf q_i=\gamma$ ,and $\mathbf p_i ^* \mathbf p_i=P$,but i don't know how do thy really calculate it,so i want to ask,does anyone know about that?
And why should $\gamma P \mathbf I $ divided by $N_t N_r$,that is ,divided by the dimension of $\mathbf p_i$ and $\mathbf q_i$
By the way,i think "*" means transpose conjugate,$||\mathbf P||_F=\sqrt{trace(\mathbf P^* \mathbf P)}$