When is Mimo Massive in Radar?

This work considers a co-located MIMO radar with M T transmitting and M R receiving antennas in a so-called massive MIMO regime, that is, where the number of virtual spatial antennas N = M T M R is large. Recently, it has been demonstrated that as N grows to infinity, one can fully characterize the false alarm and detection probabilities with very minimal assumptions on the disturbance vector. In this work, these results are partially refined and a lower bound on the probability of detection is provided for any fixed, finite N under certain randomness models for the noise. This result can serve as a rule of thumb for the design of massive MIMO radar systems by indicating the number of antennas required to attain a desired target detection probability.