  In this paper, we study the basic locus in the fiber at $p$ of a certain
unitary Shimura variety with a certain parahoric level structure. The basic
locus $\widehat{\mathcal{M}^{ss}}$ is uniformized by a formal scheme
$\mathcal{N}$ which is called Rapoport-Zink space. We show that the irreducible
components of the induced reduced subscheme $\mathcal{N}_{red}$ of
$\mathcal{N}$ are Deligne-Lusztig varieties and their intersection behavior is
controlled by a certain Bruhat-Tits building. Also, we define special cycles in
$\mathcal{N}$ and study their intersection multiplicities.
