Can you enter the equation here, complete with all assumptions, explanation of notation, specification of which variables are decision (optimization) variables vs. input data?

In the problem, Matrix P with dimension NxQ is unknown.
r is a column vector with size N. r is actually an intermediate variable.
Es and Wopt are known matrices with dimension MxK and KxK. \Phi is also known as Mxk. \Beta is a known positive priori.
Our goal is to solve matrix P.

Thanks again for your help. If you have any questions, please feel free to post it.

sqrtm is NOT a CVX function. It is a MATLAB function which can be applied to MATLAB variables, not to CXV variables or expressions. You wrote that Wopt is a known matrix, i.e., input data., so therefore, MATLAB functions can be applied to it. I wrote
presuming sqtm(Wopt) is W_{opt}^{1/2}
because I was leaving it to you to create whatever input matrix is needed there.That has nothing to do with CVX.