Particle Hole symmetry in Interacting superconductor

For noninteracting superconductors (fermion hopping plus fermion pairing), there is a particle hole (PH) symmetry which is a redundancy. The redundancy says that the BdG Hamiltonian satisfies the equation $$C H_{k}^T C^{-1} = -H_{-k}$$ where $$H_k$$ and $$C$$ are $$2n\times 2n$$ matrices where $$n$$ is the number of orbitals in each unit cell. Depending on $$C C^*= \eta=\pm 1$$ we have different topological classifications.

However, for interacting superconductors, the Hamiltonian is not quadratic, and there is no BdG single-particle Hamiltonian. So I can't write down an similar equation like $$C H^T C^{-1} = -H$$. So I don't know how to define $$C$$ and, correspondingly, $$\eta$$. Could any one help to clarify how to define these?