Modulation classification of linearly modulated signals in slow flat fading channels

In this study, the authors study the modulation classification of linearly modulated signals including amplitude shift keying (ASK), phase shift keying (PSK) and quadrature amplitude modulation (QAM) signals. The authors consider an unknown frequency non-selective slowly fading channel with an unknown variance additive white Gaussian noise. The authors treat this classification problem as a multi-hypotheses test which is invariant under the complex scale. In such a case, the authors objective is to find uniformly most powerful (UMP) test in the class of invariant decisions. However, the authors find out that the UMPI test does not exist; instead, they provide a most powerful invariant (MPI) PSK signal classifier for known signal to noise ratio and use it as the upper performance bound for any invariant classifier. The authros also propose a hybrid likelihood ratio test (HLRT) solution which can be employed for the classification of linearly modulated signals, inter-family and intra-family. The authors also explain the efficient implementation of these algorithms in some steps. In order to reduce the computational cost, the authors propose quasi-HLRT classifiers for PSK signals. Some simulation examples are provided that show the power of the proposed algorithms in the classification of linearly modulated signals.