$A$ is an $N \times N$ complex matrix
$W$ is an $N \times N$ complex matrix
$C$ is an $N \times N$ complex diagonal matrix
$u$ is a scalar
$V$ is an $N \times N$ complex matrix, whose diagonal elects are null
$P$ is a scalar
The problem is a data-rate maximization using a precoder $W$ to mitigate the crosstalk introduced by the real channel matrix $A$

Implementation:
cvx_begin
variable W(N,N)
variable u
C = diag(diag(A*W))
V = A*W - C
maximize( log_det(C) )
subject to
norm(W,'fro') <= u*sqrt(P)
u^2 + (norm(V,'fro')^2)/N <= 1
cvx_end
I'm getting the following errors:
CVX Warning: Models involving "log_det" or other functions in the log, exp, and entropy family are solved using an experimental successive approximation method. The method requires multiple calls to the solver, so it can be slow; and in certain cases it fails to converge. See Appendix D of the the user's guide for more information about this method, and for instructions on how to suppress this warning in the future. Error using cvx/geo_mean (line 111) Disciplined convex programming error: Invalid computation: geo_mean( {complex affine} )
Error in cvx/det_rootn (line 17) cvx_optval = geo_mean( diag( X ) );
Error in log_det (line 28) cvx_optval = size(X,1)*log(det_rootn(X));
Error in optimization_problem (line 58) maximize( log_det(C) )