The inequality is as follows:
$$\left\| {\bf{h}} {\bf W}^\top \right\|_2 + \text{Tr}\left(\frac{({\bf W}^\top)^H{\bf{h}}^H{\bf{h}}}{\|{\bf{h}}\bf{W}^t\|_2}\left({\bf W} - {\bf W}^\top \right)\right)\leq\|{\bf h} {\bf W}\|_2,$$
where ${\bf W}^t \in \mathbb{C}^{L \times L}$ and ${\bf h} \in \mathbb{C}^{1 \times L}$ are known. So I wonder why this inequality holds?