How would I represent the following constraint in the linear form?

Question

Given the optimization variables $\mathbf{a}, \mathbf{b} \in \mathbb{C}^{n}$ and $\mathbf{y} \in \mathbb{R}^{n}$, I would like to represent the following constraint to the linear form

$\mathrm{diag}(\mathbf{|b|})(|\mathbf{a}|-|\mathbf{b}|) = \mathbf{y}$.

Notation: $\mathrm{diag}$ represents diagonal and $|.|$ is an absolute value