We present techniques for solving the problem of detecting element failures in phased array antennas by using a combination of a single fixed probe and an optimization of element excitations using principles derived from compressive sensing. This departs significantly from conventional techniques where the excitations are held constant and probes are instead moved spatially to collect measurements. Doing so helps us to accomplish two objectives with regards to successful fault diagnosis. First, we achieve a reduction in the number of measurements required compared to the state of the art; this reduction is particularly significant in the case of high-noise measurements where existing methods fail. Second, our techniques solve the problem of fault diagnosis in the case of real valued measurements (i.e. intensity measurement along with phase detection instead of phase measurement), which leads to simpler measurement hardware. We use nonconvex optimization algorithms to generate numerical results in support of our conclusions.