Let $B\subseteq \mathbb{N}$ be an additive basis of order $k$ with $0\in B$. Is it true that for every $A\subseteq \mathbb{N}$ we have$$d_s(A+B)\ge \alpha +\frac{\alpha (1-\alpha )}{k},$$where $\alpha =d_s(A)$ and$$d_s(A)=\inf \frac{|A\cap \{1,\dots ,N\}|}{N}$$is the Schnirelmann density?