# Research Progress on Modulation Format Recognition Technology for Visible Light Communication
## 4 Deep Learning-Based Modulation Recognition Methods
### Recurrent Neural Networks (RNN)  
Recurrent neural networks (RNNs) are specifically designed for processing sequential data, allowing them to remember information from sequences through recurrent units (hidden units) and pass it to subsequent time steps, effectively capturing temporal dependencies. However, RNNs encounter challenges related to vanishing and exploding gradients during training, which limit their capacity to learn long-range dependencies. To overcome these limitations, researchers have introduced improved architectures such as long short-term memory (LSTM) and gated recurrent unit (GRU), which incorporate gating mechanisms to better control the flow of information and enhance the modeling of long sequences.  
In 2024, [PERSON] et al. [33] addressed the inherent difficulty of distinguishing between QAM and APSK modulated signals in the Cartesian coordinate system within UVLC systems. They proposed a joint recognition algorithm based on bidirectional gated recurrent units (BiGRU) and polar coordinate transformation. The study focused on ten modulation formats, including MQAM (M = 2, 4, 8, 16, 32, 64) and MAPSK (M = 8, 16, 32, 64). The original I and Q components of the received signal were combined with the polar coordinate-transformed \(\rho\), \(\theta\) to create a four-dimensional feature vector, following similar processing methods outlined in references [25; 30]. The core of the algorithm lies in the BiGRU network's in-depth mining of temporal features. BiGRU captures the forward and backward dependencies in the signal sequence through its bidirectional gating mechanism, with the gating unit calculations as follows:  
The reset gate controls the influence of historical information:  
\[R_{t}=\sigma(W_{r}[x_{t},h_{t-1}]+b_{r}). \tag{24}\]  
The update gate determines the proportion of information to be retained:  
\[Z_{t}=\sigma(W_{z}[x_{t},h_{t-1}]+b_{z}). \tag{25}\]  
The candidate state integrates the current input with the historical information filtered by the reset gate:  
\[\widetilde{h_{t}}=\tanh(W[x_{t},R_{t}\odot h_{t-1}]+b_{h}). \tag{26}\]  
The final hidden state is dynamically updated by the update gate:\[h_{t}=Z_{t}\odot h_{t-1}+(1-Z_{t})\odot\widetilde{h_{t}}. \tag{27}\]  
Here, \(W_{r}\), \(W_{z}\), \(W\) are the weight coefficients within the GRU module; \(b_{r}\), \(b_{z}\), \(b_{h}\) are the corresponding bias coefficients; \(h_{t}\) is the output of the GRU module at the current time step; the symbol \(\odot\) denotes the element-wise multiplication, also known as the Hadamard product. The temporal features \(h_{t1},h_{t2}\) output by the bidirectional GRU layer are then passed through a fully connected layer and Softmax classification to recognize the ten modulation formats. Experiments showed that in the 0.2-0.4 V linear working area (BER < 3.8 \(\times\) 10\({}^{-3}\)), the algorithm achieved an average recognition accuracy of over 96%. Additionally, the training speed was improved by 100% compared to scenarios that did not incorporate polar coordinate features.