Consider we have to design a signal $ \mathbf{x} \in \mathbb{C}^{1_{} \times N_{\mathrm{}}} $ that needs to have the lowest correlation with an unknown signal $\mathbf{y} \in \mathbb{C}^{1_{} \times N_{\mathrm{}}}: $ \begin{equation} \begin{array}{cc} \text { minimize } & E\left[\mathbf{x}_{} \mathbf{y}^{H}_{}\right] \\ \text { subject to } & \mathbf{x}_{} \mathbf{x}^{H}_{}=1 \end{array} \end{equation}
Is it optimum to make $\mathbf{x}$ to be Gaussian? I am trying to prove that based on Entropy of $\mathbf{x}$.