The Soft Gamma-ray Detector (SGD), to be deployed onboard the {it ASTRO-H} satellite, has been developed to provide the highest sensitivity observations of celestial sources in the energy band of 60-600~keV by employing a detector concept which uses a Compton camera whose field-of-view is restricted by a BGO shield to a few degree (narrow-FOV Compton camera). In this concept, the background from outside the FOV can be heavily suppressed by constraining the incident direction of the gamma ray reconstructed by the Compton camera to be consistent with the narrow FOV. We, for the first time, demonstrate the validity of the concept using background data taken during the thermal vacuum test and the low-temperature environment test of the flight model of SGD on ground. We show that the measured background level is suppressed to less than 10% by combining the event rejection using the anti-coincidence trigger of the active BGO shield and by using Compton event reconstruction techniques. More than 75% of the signals from the field-of-view are retained against the background rejection, which clearly demonstrates the improvement of signal-to-noise ratio. The estimated effective area of 22.8~cm$^2$ meets the mission requirement even though not all of the operational parameters of the instrument have been fully optimized yet.
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