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This paper describes a likelihood test based modulation classification method for identifying the modulation scheme of a software-defined radio (SDR) in real-time without pilot symbols between transmitters and receivers. Unlike the prior art, the paper converts an unknown signal symbol to an address of the look-up table (LUT), loads the pre-calculated values of the test functions for the likelihood ratio test, and produces the estimated modulation scheme in real-time. The statistical performance of the LUT based classifier is studied. Simulation results are presented to confirm the theoretical analysis.