i am new to mathematics. I want to know if the following function is jointly convex in term of X and h? where X $\in $ discrete complex set and h and n has a gaussian distribution with zero mean and unit variance.
$\begin{bmatrix} {\bf y}^p\\ {\bf y}^d_1 \\ \vdots \\ {\bf y}^d_N \end{bmatrix} = \begin{bmatrix} \bf \Phi \\ \bf \Phi X_1 \\ \vdots \\ \bf \Phi X_N\end{bmatrix} \bf \alpha\bf{h} + \bf{n} $
No. Only linear equalities represent a convex set, and this equality is bilinear in $h$ and $X$