Magnitude-only detectors for complex-valued Gaussian processes

This paper considers a detection problem wherein the underlying process is complex-valued, but only the magnitude samples of the process are available to the detector. Such a situation occurs, for example, in radar-based automatic target recognition where the phase data of the pulse-compressed returns are considered unreliable. This paper takes a first principles approach and develops matched-subspace detection statistics. Like their complex-valued counterparts, these statistics are invariant to both power of the signal and the noise variance.