# Research Progress on Modulation Format Recognition Technology for Visible Light Communication
## 3 Feature-Based Modulation Recognition Methods
### Chaotic Mapping and Autocorrelation Estimation  
[PERSON] et al. [23] proposed a lightweight MFR scheme for optical wireless communication (OWC) systems based on the concept of cancellable biometrics, which integrates chaotic Baker mapping (CBM), wavelet image fusion, and autocorrelation estimation to efficiently classify eight modulation formats (including 2/4/8/16-PSK and 8/16/32/64-QAM). The method first uses CBM to nonlinearly shuffle the constellation diagram, generating an encrypted template by randomizing the spatial distribution of constellation points, which effectively reduces the impact of background noise. Algorithm 1 outlines the implementation process of the CBM:  
Figure 5: The accuracy performance of DT, KNN, SVM, and LM model for all distances between receiver and transmitter in reference [22]. ```
1:Input:
2:\(CD\): Constellation diagram (\(N\times N\) matrix) \(N\): Image size (integer) \(n_{i}\): Partition sequence (array of integers where \(N=\sum n_{i}\)) Output:
3:\(CD_{permuted}\): Permuted constellation diagram (\(N\times N\) matrix) Procedure: //Initialize \(CD_{permuted}\):
4: Create an empty \(N\times N\) matrix \(CD_{permuted}\) to store the permuted pixel values. // Partition and permutation:
5:\(I=\text{length}(n_{i})\) // Total number of partitions
6:\(N_{i}=0\) // Cumulative partition start index
7:for each partition \(i\) in \(1\) to \(I\)do:
8:\(n_{i}=n_{i}[i-1]\) // Current partition width // Iterate over partition columns
9:for\(r\) from \(N_{i}\) to \(N_{i}+n_{i}-1\)do:
10:for\(s\) from \(0\) to \(N-1\)do: // Compute CBM permuted pixel coordinates
11:\(\text{r}^{{}^{\prime}}=\frac{N}{n_{i}}\left(r-N_{i}\right)+s\;mod\left(\frac{N} {n_{i}}\right)\)
12:\(\text{s}^{{}^{\prime}}=\frac{n_{i}}{N}\left(s-s\;mod\left(\frac{N}{n_{i}} \right)\right)+N_{i}\)
13:\(CD_{permuted}\left[r^{{}^{\prime}}\right]\left[s^{{}^{\prime}}\right]=CD[r][s ]\) // Assign permuted pixel
14:endfor
15:endfor
16:\(\text{N}_{i}=N_{i}+n_{i}\) // Update cumulative partition index
17:endfor
18:
19:Return \(CD_{permuted}\) as the output. // Return permuted constellation diagram
```  
**Algorithm 1**Chaotic Baker Map Permutation for Constellation Diagram Pixels  
The CBM is a nonlinear pixel permutation algorithm based on chaotic dynamics. Its core principle involves dynamically rearranging the pixel positions of an original constellation diagram through iterative chaotic sequences, thereby constructing an encrypted constellation space with high complexity. During this process, the sensitivity of the chaotic system to initial keys ensures that even slight parameter variations can generate entirely distinct permutation patterns, thus increasing the projection distances between adjacent constellation points in the encrypted space. This nonlinear property introduces noise-like pixel distributions, causing encrypted constellation diagrams of different modulation formats to exhibit significantly differentiated texture patterns in the image domain. This effectively addresses the challenge of overlapping modulation format features under low-SNR conditions. Subsequently, wavelet-domain image fusion technology is employed to merge the shuffled constellation diagrams of five adjacent SNR levels into a single reference template to reduce storage overhead. After this processing step, the constellation diagrams demonstrate sufficient feature separability. The pixel values in these diagrams are not completely random; rather, they exhibit certain statistical characteristics. Consequently, during the classification stage, the normalized correlation coefficient between the shuffled diagram of the test signal and the reference template is calculated as follows:  
\[C_{pq}=E\left[\frac{\left(p_{i}-\mu_{p}\right)\left(q_{i}-\mu_{q}\right)}{\sigma_ {p}\sigma_{q}}\right], \tag{17}\]  
where \(p_{i}\) and \(q_{i}\) are the values of the \(i\)-th pixel in images \(p\) and \(q\), respectively. \(\mu_{p}\) and \(\mu_{q}\) are the mean values of the pixels in images \(p\) and \(q\).