# Research Progress on Modulation Format Recognition Technology for Visible Light Communication
## 4 Deep Learning-Based Modulation Recognition Methods
### Other Innovative Deep Learning Models
The algorithm retained local salient features through 3-4 foldings, reducing redundant information and highlighting local features, effectively enhancing the feature distinguishability of complex modulated signals such as 16 APSK. In terms of the model, they employed a RC structure with fixed random weights, featuring a leaky integration mechanism in the state update:  
\[u(t)=(1-\alpha)u(t-1)+\mathrm{atanh}(W_{in}x(t)+W_{res}u(t-1)), \tag{28}\]  
here, \(u(t)\in R^{N}\) represents the reservoir state vector at time step \(t\), with \(N\) being the number of reservoir nodes; \(\alpha\in(0,1]\) is the leakage rate parameter, balancing the fusion ratio of historical states and current inputs; \(W_{in}\) and \(W_{res}\) are the input weights and the internal sparse connection weight matrix, respectively. The output weights \(W_{out}\) were optimized through ridge regression:  
\[\widehat{W_{out}}=\Big{(}UU^{T}+\epsilon I\Big{)}^{-1}\Big{(}YU^{T}\Big{)}, \tag{29}\]  
where \(U=[u(1),u(2),\ldots,u(T)]\in R^{N\times T}\) is the state matrix composed of all reservoir states concatenated column-wise, with \(T\) being the input sequence length; \(Y\in R^{L\times T}\) is the target output matrix, with each column corresponding to the label of the input sequence at time step \(t\), and L being the total number of classes; \(\epsilon>0\) is the ridge regression regularization coefficient. This structure reduced the number of trainable parameters to 0.3% of that of traditional CNNs, with training time shortened to the second level. Experiments demonstrated that within the LED bias range of 0.2-1.3 V, the system achieved over 90% recognition accuracy for six modulation types (OOK, 4 QAM, 8 QAM-DIA, SQAM-CIR, 16 APSK, 16 QAM), with the highest accuracy reaching 100%. Compared to the benchmark dropout-CNN [38] model, the proposed method shows a maximum improvement of up to 30% in recognition accuracy, along with a significant enhancement in inference speed. In UVLC systems, the nonlinearity of LEDs poses a significant challenge for modulation recognition. Reference [39] proposed a super lightweight recognition framework based on communication-inspired knowledge distillation (CIKD), achieving breakthroughs in performance through the deep integration of physical priors and knowledge transfer. Central to this solution is the collaborative design of a dynamic feature purification mechanism and a hierarchical knowledge transfer architecture. Recognizing the strong correlation between LED nonlinearity and driving voltage, the authors constructed a learnable dynamic masking module. This module adaptively adjusts the truncation of high-amplitude distortion regions in the constellation diagram, transforming the original dense constellation into a sparse representation while preserving essential discriminative features. This physics-driven preprocessing significantly enhances the system's resilience to nonlinear distortion. The study further developed a teacher-student collaborative distillation architecture. In this setup, the teacher model is a multi-layer CNN that extracts geometric features from the constellation diagram, while the student model consists of only a single-layer classifier to process the purified sparse features. To bridge the capacity gap between the two models, a hierarchical distillation mechanism was proposed. On one hand, intermediate-layer feature similarity preservation (ILFSP) was employed \[L_{SP}=\frac{1}{bs^{2}}|G_{T}-G_{S}|_{F}^{2}, \tag{30}\]  
to constrain the similarity between the student model's purified features \(G_{S}\) and the teacher's intermediate features \(G_{T}\), enabling the student model to replicate the teacher's high-order feature distribution in a lower-dimensional space.