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In this letter, we consider a decentralized detection problem in which a number of sensor nodes collaborate to detect the presence of an unknown deterministic signal. Due to stringent power/bandwidth constraints, each sensor quantizes its local observation into one bit of information. The binary data are then sent to the fusion center (FC), where a generalized likelihood ratio test (GLRT) detector is employed to make a global decision. In this context, we study one-bit quantizer design and analyze the asymptotic performance of the one-bit GLRT detector for cases where the quantized data are sent to the FC via perfect or imperfect channels. Simulation results are carried out to corroborate our theoretical analysis and to illustrate the performance of the proposed scheme.