  Using the decorated domain wall procedure, we construct Finite Depth Local
Unitaries (FDLUs) that realize Fermionic Symmetry-Protected Topological (SPT)
phases. This results in explicit 'full' commuting projector Hamiltonians, where
'full' implies the fact that the ground state, as well as all excited states of
these Hamiltonians, realizes the nontrivial SPT phase. We begin by constructing
explicit examples of 1+1D phases protected by symmetry groups $G=\mathbb Z_2^T
\times \mathbb Z_2^F$ , which also has a free fermion realization in class BDI,
and $G=\mathbb Z_4 \times \mathbb Z_4^F$, which does not. We then turn to 2+1D,
and construct the square roots of the Levin-Gu bosonic SPT phase, protected by
$\mathbb Z_2 \times \mathbb Z_2^F$ symmetry, in a concrete model of fermions
and spins on the triangular lattice. Edge states and the anomalous symmetry
action on them are explicitly derived. Although this phase has a free fermion
representation as two copies of $p+ip$ superconductors combined with their
$p-ip$ counterparts with a different symmetry charge, the full set of commuting
projectors is only realized in the strongly interacting version, which also
implies that it admits a many-body localized realization.
