  Quantum illumination (QI) theoretically promises up to a 6dB error-exponent
advantage in target detection over the best classical protocol. The advantage
is maximised by a regime which includes a very high background, which occurs
naturally when one considers microwave operation. Such a regime has well-known
practical limitations, though it is clear that, theoretically, knowledge of the
associated classical benchmark in the microwave is lacking. The requirement of
amplifiers for signal detection necessarily renders the optimal classical
protocol here different to that which is traditionally used, and only
applicable in the optical domain. In this work we outline what is the true
classical benchmark for microwave QI using coherent states, providing new
bounds on the error probability and closed formulae for the receiver operating
characteristic (ROC), for both optimal (based on quantum relative entropy) and
homodyne detection schemes. We also propose an alternative source generation
procedure based on coherent states which demonstrates potential to reach
classically optimal performances achievable in optical applications. We provide
the same bounds and measures for the performance of such a source and discuss
its potential utility in the future of room temperature quantum detection
schemes in the microwave.
