  Quantum illumination utilizes an entanglement-enhanced sensing system to
outperform classical illumination in detecting a suspected target, despite the
entanglement-breaking loss and noise. However, practical and optimal receiver
design to fulfil the quantum advantage has been a long open problem. Recently,
[arXiv:2207.06609] proposed the correlation-to-displacement (`C$\rightarrow$D')
conversion module to enable an optimal receiver design that greatly reduces the
complexity of the previous known optimal receiver [Phys. Rev. Lett. {\bf 118},
040801 (2017)]. There, the analyses of the conversion module assume an ideal
target with a known reflectivity and a fixed return phase. In practical
applications, however, targets often induce a random return phase; moreover,
their reflectivities can have fluctuations obeying a Rayleigh-distribution. In
this work, we extend the analyses of the C$\rightarrow$D module to realistic
targets and show that the entanglement advantage is maintained albeit reduced.
In particular, the conversion module allows exact and efficient performance
evaluation despite the non-Gaussian nature of the quantum channel involved.
