Automatic Modulation Classification: Principles, Algorithms and Applications

3Likelihood-based Classifiers

3.1 Introduction

Likelihood-based (LB) modulation classifiers are by far the most popular modulation classification approaches. The interest in LB classifiers is motivated by the optimality of its classification accuracy when perfect channel model and channel parameters are known to the classifiers (Huang and Polydoros, 1995; Sills, 1999; Wei and Mendel, 2000; Hameed, Dobre and Popescu, 2009; Ramezani-Kebrya et al., 2013).

The common approach of an LB modulation classifier consists of two steps. In the first step, the likelihood is evaluated for each modulation hypothesis with observed signal samples. The likelihood functions are derived from the selected signal model and can be modified to fulfil the need of reduced computational complexity or to be applicable in non-cooperative environments. In the second step, the likelihood of different modulation hypothesizes are compared to conclude the classification decision. Earlier methods of decision making are enabled with a ratio test between two hypothesizes. The requirement of a threshold provides another level of optimization which may provide improved classification performance but also requires more tentative effort to select thresholds. The more intuitive approach of decision making would be to find the maximum likelihood among all candidates. It is much easier to implement and does not require carefully designed thresholds.

In reality, much effort has been made to modify the likelihood approach ...