## 1 Introduction
The LB approach is based on building a probabilistic model for the received signal, and decision is made to classify the modulation type by comparing the likelihood functions (LFs) or the li  
Figure 1: Communication system model that utilizes automatic modulation recognition (AMR). threshold [7]. The average likelihood ratio test (ALRT) treats unknown quantities as random variables and computes the LF by averaging them. LB classification presents the classification of a combination of hypothesis and testing problems. Hypothesis estimates that each incoming signal has a modulation type. Generalized likelihood ratio test (GLRT) computes the probability density function (PDF) of incoming signals by applying maximum likelihood estimations (MLEs) based on unknown quantities. Then, the LF defines the most possible modulation type of the signal [8]. In addition to the two techniques, hybrid likelihood ratio test (HLRT), quasi ALRT, and quasi HLRT have been proposed in the literature. Several researchers have utilized the LB approach for MR [9; 10]. The likelihood method shows optimal performance by increasing the accuracy of classification probabilities, but it has high computational complexity due to other computation likelihoods; nevertheless, it formulates the correct hypotheses, carefully selects the appropriate threshold values, and exhibits high sensitivity to modelling mismatches, such as timing, phase and frequency offset, and noise divergence [11]. When a closed-form solution exists, the computational complexity can make a classifier impractical. For the low signal-to-noise ratio (SNR) approximation of the LF, the quasi-ALRT algorithm provides near-optimal performance for recognizing FSK and PSK-modulated signals, but it fails in the case of quadrature amplitude modulation (QAM)-modulated signals. Although GLRT has benefits, it fails in finding nested constellations. HLRT with many unknown parameters has high time complexities. Complexity is decreased in quasi-HLRT classifiers, which rely on low complexity but accurate estimators. The FB approach can be considered a mapping relationship that conducts mapping of time-series signals to the feature field, and these featured parameters are used for signal recognition [8]. Feature extraction is based on various aspects of signals, such as instantaneous amplitude, phase, frequency, wavelet transform (WT), zero-crossing intervals, statistical features (e.g., higher-order moments and cumulants), cyclic cumulants [8; 12], and signal spectra [6]. In feature selection, the most relevant features must be utilized to improve the classification accuracy. After the signal features are extracted, they pass through classificatory decision to identify the modulation type [13]. The FB approach not only produces suboptimal performance but also has low computational costs. Therefore, this approach achieves near-optimal performance when it is systematically designed [12]. In addition to the LB and FB approaches which are usually used in AMR, there is another approach which is used in MR known as the 'distribution test' approach. In this approach, the empirical distribution of the modulated signal is used. The signal distribution is reconstructed using the empirical distribution, then the observed signals are analyzed using their signal distributions. If the theoretical distribution for the different modulation candidates is available, one will exist which is the best match for the underlying distribution of the signal we want to classify. The amount of equality between difference distributions is usually known as Goodness of Fit (GoF), which is an indication of how well the sampled data fit the reference distribution. Finally, the classification is completed by finding the assumed or hypothesized signal distribution that has the highest goodness of fit.