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In the increasingly important problem of identifying suicide bombers wearing explosives concealed under clothing, it is essential to detect suspicious individuals at a distance. Current systems employ multiple sensors to determine the presence of explosives on people, including observing and following individuals, identifying explosive residues or heat signatures on the outer surface of their clothing, or by characterizing explosives using penetrating X-rays or terahertz wave radar. At present, radar is the only modality that can penetrate and sense beneath clothing at a distance of 10 to 50 meters without causing physical harm. Unfortunately, current radar systems require impractically large synthetic apertures to effectively distinguish people wearing concealed body-worn improvised explosive devices from innocent individuals. We explore these limitations and propose strategies to maximize detection with limited apertures.