# Research Progress on Modulation Format Recognition Technology for Visible Light Communication
## 3 Feature-Based Modulation Recognition Methods
### Frequency-Domain Histogram  
In underwater optical wireless communication (UOWC) systems, dynamic channel conditions pose challenges for the demodulation of orthogonal frequency division multiplexing index modulation (OFDM-IM). The difficulty lies in the need for the receiver to identify the number of activated subcarriers \(l\) within a sub-block in real-time to complete the joint demodulation of index bits and constellation symbols. [PERSON] et al. [24] proposed an intelligent index recognition scheme based on the histogram of the frequency-domain signal. By analyzing the amplitude distribution characteristics of OFDM-IM signals in the frequency domain under different \(l\) values, they found that the difference in the number of activated subcarriers significantly changes the morphological features of the signal histogram: when \(l=1\), the amplitude is concentrated in the low-order range, and when \(l=4\) (i.e., the traditional OFDM case), it shows a uniform distribution. The researchers normalized the amplitude of the received signal after fast Fourier transform (FFT) and frequency-domain equalization (FDE) as follows:  
\[\hat{X}_{i}^{z}=\frac{\left|X_{i}^{z}\right|-\left|X^{z}\right|_{min}}{\left| X^{z}\right|_{max}-\left|X^{z}\right|_{min}},\ i=1,2,\ldots,N, \tag{18}\]  
where \(X_{i}^{z}\) represents the \(i\)-th frequency-domain signal sample after FFT and FDE processing. \(z\) is the index of the OFDM symbol, and \(i\) is the sequence number of the subcarrier. They then generated an \(H\)-dimensional histogram feature vector by dividing the amplitude range into \(H\) intervals and used machine learning and deep learning algorithms to classify the \(l\) values.  
Experiments showed that the four schemes could effectively distinguish the activation patterns of \(l\in{1,2,3,4}\) in \(n=4\) sub-blocks in a 2 m underwater channel environment. The recognition performance was jointly affected by the number of histogram intervals \(H\) and the cumulative number of symbols \(K\). As shown in Figure 6, the k-nearest neighbors(k-NN) algorithm demonstrates significant strengths. When applied to BPSK, 4 QAM, and 8 QAM modulations, it achieves recognition accuracy close to 100% at SNRs of 8.6 dB, 9.1 dB, and 13 dB, respectively. Its majority voting mechanism exhibits strong robustness against noise distribution variations. In contrast, the decision tree (DT) algorithm achieves the lowest accuracy due to its insufficient sensitivity to features with continuously varying amplitudes. The accuracy curves of support vector machine (SVM) and convolutional neural network (CNN) closely overlap, suggesting that deep feature extraction does not confer additional performance gains given the limited dimensionality of histogram features. This observation implies that traditional machine learning algorithms may be more practically applicable for such low-dimensional feature classification tasks. This method is sensitive to the number of histogram intervals and symbols. Insufficient partitioning of amplitude ranges may result in the loss of classification feature details, while excessive partitioning increases sensitivity to noise and computational complexity. Furthermore, the normalization process in this method assumes stable channel gain; however, fluctuations in light intensity in practical UOWC can lead to distortion in the normalized amplitude distribution.