A modern communication system's efficiency relies on the proper functioning of the phased array antennas. Impaired elements in an array always lead to inadequate system performance. So, fault diagnosis plays a vital role in making an antenna array suitable for the required applications such as radar, military, and remote sensing. An "inverse problem" arises for locating faulty elements from the field measurements, and is a topic of research interest over the years. This work illustrates the faulty elements' detection using compressive sensing, which guarantees success within a small number of measurements. The proposed method is more convenient than the existing state-of-art, which works by choosing for a single fixed probe for the measurements, as opposed to multiple measurements in space. The work's novelty lies in optimizing the elements' excitations by exploiting the sensing matrix property, the so-called mutual coherence. The optimized excitations and a single measurement location lead to a further reduction in the number of measurements required to achieve successful fault diagnosis.