$$f(\bf{x}) = \Vert \mid{Ax}\mid^2 -b \Vert_2^2 =(\mid{Ax}\mid^2 -b)^T(\mid{Ax}\mid^2 -b ) $$ Then, gradient is, $$\frac{\partial f(\bf{x})}{\partial \bf{x}}= 2(\mid{\bf{Ax}}\mid^2 -\bf{b})^T\frac{\partial (\mid{Ax}\mid^2 -b ) }{\partial \bf{x}} $$
where $\mid{\bf{Ax}}\mid^2$ is element by element absolute value squared.
How do I proceed after this?
P.S $A$ ,$x$ and $b$ are complex-valued matrix and vectors respectively