The formula is as ${{\mathop{\rm Re}\nolimits} \left( {{\bf{q}}_{k(l)}^H{\bf{H}}_k^H{z_{k,l}}} \right)}$. The variable is ${{\bf{q}}_{k,l}} \in {C^{N \times 1}}$. ${\bf{H}}_k \in {C^{M \times N}}$ and ${{z_{k,l}}} \in {C^{M \times 1}}$ are constant matrix and vector, respectively.
This formula seems to be concave in the paper that I read, but I cannot prove it. Hoping for help.
I have figured it out. The formula can be written as ${{\bf{q}}_{k(l)}^H{\bf{H}}_k^H}+{{\bf{q}}_{k(l)}}{{\bf{H}}_k}$, which is affine over ${{\bf{q}}_{k(l)}}$, therefore it is convex or concave.