Gramian Matrix Eigenvalues--Stronger Statement than Non-Negative

Question

I'm struggling to find conditions under which this holds:

$AA^T - B \succeq 0\,.$

If it helps, A is not necessarily square and $A_{ij} \in \{-1, 0,1\}$. B is diagonal and I would like to find conditions on $B_{ii}$ such that the above statement is true.

I have googled Gram Matrices but didn't find anything particularly helpful. Any ideas?