  Entanglement is vulnerable to degradation in a noisy sensing scenario, but
surprisingly, the quantum illumination protocol has demonstrated that its
advantage can survive. However, designing a measurement system that realizes
this advantage is challenging since the information is hidden in the weak
correlation embedded in the noise at the receiver side. Recent progress in a
correlation-to-displacement conversion module provides a route towards an
optimal protocol for practical microwave quantum illumination. In this work, we
extend the conversion module to accommodate experimental imperfections that are
ubiquitous in microwave systems. To mitigate loss, we propose amplification of
the return signals. In the case of ideal amplification, the entire six-decibel
error-exponent advantage in target detection error can be maintained. However,
in the case of noisy amplification, this advantage is reduced to three-decibel.
We analyze the quantum advantage under different scenarios with a Kennedy
receiver in the final measurement. In the ideal case, the performance still
achieves the optimal one over a fairly large range with only on-off detection.
Empowered by photon number resolving detectors, the performance is further
improved and also analyzed in terms of receiver operating characteristic
curves. Our findings pave the way for the development of practical microwave
quantum illumination systems.
