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The authors consider a phase based Maximum Likelihood (ML) approach for identifying the modulation format of a linearly modulated signal. Since, the optimal ML scheme is computationally intensive, the authors propose two approximate ML alternatives derived from Gauss quadrature rules. The proposed approximate ML schemes can offer virtually optimal performance with reduced complexity. They, then present a general performance analysis for classification of multiple modulation constellations. Automatic modulation recognition, is a desirable feature for emerging wireless communication systems such as software-defined radio, and cognitive radio. Modulation classification methods generally fall into two categories: statistical properties of the signal are used to determine its modulation format; the Maximum Likelihood (ML) principle is applied to choose the most possible modulation format in use.
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