Automatic modulation classification in the manner of pattern recognition has caught massive attention due to its simplicity in workflow design. Recently, enormous interest has been aroused because of the boosting development of deep learning and numerous network structures, leading to various substantial contributions. However, to the best of our knowledge, current approaches fail to handle two essential concerns simultaneously: the statistical distribution of the noise and the computational complexity due to the network structure. Since these factors play critical roles when facing practical applications, a modified constellation concept based on the Score function of Cauchy distribution is proposed as a robust feature to impulsive noise. Besides, a lightweight structure based on Shuffle Unit and Gated Recurrent Unit is proposed as the recognizer to lower the potential risk of overfitting and cope with the time-consuming problem. Monte-Carlo experiments involving multiple comparison algorithms are executed under different conditions, and results verify the superior performance of the proposed AMC scheme.