# Research Progress on Modulation Format Recognition Technology for Visible Light Communication
## 4 Deep Learning-Based Modulation Recognition Methods
### Convolutional Neural Networks (CNN)  
In the field of MFR, phase and frequency offsets pose significant challenges that can degrade classification performance. To address this, [PERSON] et al. [25] proposed a CNN-based blind MFR method. Their approach achieved the high-precision recognition of five modulation formats (BPSK, QPSK, SPSK, 16 QAM, and 64 QAM) through two key innovations. First, they constructed multi-dimensional signal feature inputs. Second, they implemented an offset-resistant training strategy. This combination enables the method to maintain strong performance even under severe phase- and frequency-offset conditions. To overcome the limitations of traditional manual feature extraction, the researchers decomposed the received signal into four channels: real part, imaginary part, amplitude, and phase. This decomposition generates a feature tensor of dimension \(N\times 4\). The input can be represented as:  
\[\mathrm{X}=[\mathrm{R}(\mathrm{r}(\mathrm{n})),\mathrm{I}(\mathrm{r}(\mathrm{ n})),|\mathrm{r}(\mathrm{n})|,\angle\mathrm{r}(\mathrm{n})], \tag{19}\]  
where the signal length \(N\) is 128. The explicitly introduced phase component \(\angle r(n)\) enables the network to directly perceive the continuous phase-shift features caused by frequency offsets, while the amplitude component \(|r(n)|\) retains the signal envelope characteristics. For network architecture, a seven-layer convolutional network was designed with \(3\times\mathrm{F}_{1}\times\mathrm{F}_{\mathrm{O}}\) convolutional kernels and configurable channel dimensions. Skip connections were incorporated to reuse features, forming a residual learning structure. This structure mitigates the vanishing gradient problem through cross-layer identity mapping, enabling the network to fuse shallow details with deep semantic features during training. Simulation experiments show that the proposed method outperforms traditional techniques (e.g., order statistics and HOC) and existing shallow CNN models [26], especially under phase/frequency offsets. This advantage stems from three factors: the deeper network architecture, the inclusion of amplitude/phase input features, and the use of a dataset with diverse channel perturbations. The multidimensional fusion strategy employed by this method serves as a significant reference for optical-domain signal processing. In discrete multitone modulation visible light communication (DMT-VLC) systems, the dynamic allocation of subcarrier modulation formats is essential due to time-varying channels and bandwidth limitations. To tackle the challenges of real-time operation and data scarcity in modulation recognition under short-time channel conditions, reference [27] proposed a lightweight deep learning classification method based on pseudo-constellation diagram generation. By generating pseudo-constellation images, this method achieves high-precision classification using only tens of received symbols. This approach effectively solves the challenges of real-time processing and data scarcity in modulation recognition. Assuming the received symbol sequence is \(\{s_{1},s_{2},\ldots,s_{N}\}\), pseudo-symbols are generated by calculating the differential vectors of all symbol pairs:  
\[s_{i,j}^{\mathrm{pseudo}}=s_{i}-s_{j}\;(i\
eq j;\,i,j=1,2,\ldots,N). \tag{20}\]  
This operation expands the number of original symbols to \(N(N-1)\), forming dense pseudo-constellation points to enhance the features of sparse data. After normalization, these pseudo-constellation points are mapped to grayscale images, which are subsequently transformed into RGB three-channel images using multi-scale Gaussian filtering. These images serve as inputs to the GoogLeNet V3 network, allowing for the extraction of spatial features at different scales. Experiments demonstrate that the proposed scheme achieves a classification accuracy of 98% for six modulation formats, ranging from 2-QAM (BPSK) to 64-QAM.