Given a $N\times K$ matrix $A$ of full rank with $ K < N $, a diagonal matrix $D$ and knowing that $E[D]=bI_N$, where $E[\cdot]$ is the expected value and $I_N$ is the $N\times N$ identity matrix and $b>0$ is a known scalar,

how can I compute (or bound): $E[\operatorname{trace}((A^H D A)^{-1} A^HA)]$