Scaling laws and phase transitions for target detection in MIMO radar

The performance of MIMO radar has been a subject of intense study in the past decades. For such a system, however, the important phenomenon of phase transition has received little attention in the literature. In this paper, we study the phase transition on the target detection probability of a SNR maximizing detector. Such a detector declares a target to be present when the largest eigenvalue of the observed data matrix exceeds a threshold. In particular, we identify a critical value below and above which the limiting detection performance is described by the Tracy-Widom law and the Gaussian law, respectively. Under both laws, the scaling limits and asymptotic expansions of misdetection probability at the vanishing regime are derived using tools from random matrix theory.