# Research Progress on Modulation Format Recognition Technology for Visible Light Communication
## 3 Feature-Based Modulation Recognition Methods
### Constellation Diagram Features  
The constellation diagram is a vital tool in digital communication systems for representing the characteristics of modulated signals. It illustrates the geometric features of modulation symbols in the complex plane, with each symbol corresponding to a point defined by its in-phase (I) and quadrature (Q) components. Different modulation formats exhibit significant variations: low-order modulations such as 4-QAM feature sparse constellation points, while high-order modulations like 64-QAM display densely packed points. Channel noise causes the constellation points to spread out, with the degree of spread being negatively correlated with the SNR. Consequently, the constellation diagram is useful not only for modulation recognition but also for assessing channel quality.  
In 2020, [PERSON] et al. [20] proposed a method for the efficient recognition of M-QAM signals (M = 4, 16, 32, 64) in OFDM-VLC systems based on the geometric and statistical properties of constellation diagrams. After normalizing the received signal, they performed clustering analysis on the symbols using ideal M-QAM constellation templates. They calculated the Euclidean distance between each symbol point and the cluster centers of the templates and classified the symbols into the nearest cluster, thereby matching the ideal constellation distribution. This process can be expressed as:  
\[d\left(x_{i},c_{j}\right)=\sqrt{\left(x_{1}-c_{1}^{\left(j\right)}\right)^{2}+ \left(x_{2}-c_{2}^{\left(j\right)}\right)^{2}}, \tag{14}\]  
where \(\left(x_{i}=\left(x_{1},x_{2}\right)\right)\) represents the coordinates of the received symbol, and \(\left(c_{j}=\left(c_{1}^{\left(j\right)},c_{2}^{\left(j\right)}\right)\right)\) is the center of the \(j\)-th cluster. After clustering, they established a two-dimensional Gaussian model to extract feature parameters: for low-order modulation (4-QAM), they used the mean of the high-probability region \(T_{2}\); for high-order modulations, they selected the means of the top 75% high-probability clusters \(T_{4}\), \(T_{5}\), and \(T_{6}\). They constructed a multi-level decision tree: if \(T_{2}\) is significantly high, it is determined to be 4-QAM; comparing \(T_{4}\) and \(T_{6}\) distinguishes between 16-QAM and 64-QAM. This method achieved 100% recognition of 4-QAM at OSNR = 4 dB and the same precision for 64-QAM at 18 dB, reducing the requirement by 1-2 dB compared to traditional unsupervised clustering method in reference [15], thus verifying its advantage at low SNR. However, constellation diagrams have limited representation of the signal's complex features, particularly in nonlinear channels and environments with significant background noise, where distortion in constellation point distribution can hinder  
Figure 4: The Pc (accuracy) on classification among 4/16-PAM and 4/16-QAM ACO-OFDM in reference [19].  
recognition accuracy. Additionally, constellation diagrams cannot differentiate between all VLC modulation formats; for example, they are unable to distinguish time-domain modulation methods such as pulse width modulation or pulse position modulation (PWM/PPM).