Correction: Zhou et al. Research Progress on Modulation Format Recognition Technology for Visible Light Communication. Photonics 2025, 12, 512

Text Corrections

The following text corrections have been made to the original publication [1]:

1. 

The expression of Equation (7) in Section 2.2 has been revised to enhance its generality. The original simplified formulation placed the summation symbol outside the Bessel function and exponential term, implying an uncommon assumption that the carrier phases of symbols are independently distributed. The updated equation, which refers to Equation (19) in [16], provides a more comprehensive model.

A correction has been made to Section 2.2, Equation (7):

$$\mathsf{\Gamma }\left(\mathbf{R}|H_i\right)=E_{s_n^{k,i}{|}_{n=0}^{N-1}\cdot }\left[I_0\left(\sum _{n=0}^{N-1}{\displaystyle \frac{2\left|r_n^{\mathrm{*}}{s}_n^{k,i}\right|}{{\sigma }^2}}\right)\right.\times \left.\exp \left(-\sum _{n=0}^{N-1}{\displaystyle \frac{{\left|s_n^{k,i}\right|}^2}{{\sigma }^2}}\right)\right],$$

(7)

2. 

The original expression of Equation (8) represented the GLRT function for a single received sample rather than the overall function. It would be more appropriate to use the overall GLRT likelihood function here.

A correction has been made to Section 2.3, Equation (8):

$${\mathsf{\Gamma }}_{\mathrm{GLRT}}={\prod }_{n=0}^{N-1}\underset{{\mathbf{u}}_{\mathit{i}}}{\max }\mathsf{\Gamma }\left(r_n|H_i,{\mathbf{u}}_{\mathit{i}}\right),$$

(8)

3. 

The expression of Equation (9) has been generalized to better accommodate the various estimation methods applicable in the HLRT method. We have removed $\underset{I_g}{\mathrm{m}\mathrm{a}\mathrm{x}}$ and used $\widehat{I_g}$ to represent the estimated value of $I_g$.

Corrections have been made to Section 2.4, Equation (9) and its explanatory text:

$${\mathsf{\Gamma }}_{\mathrm{HLRT}}=E_{S_g}\left[\mathsf{\Gamma }\left(\mathbf{R}|H_i,\widehat{I_g},S_g\right)\right],$$

(9)

where $\mathbf{R}$ represents the multi-dimensional matrix of received signals, and $\mathsf{\Gamma }\left(\mathbf{R}|H_i,\widehat{I_g},S_g\right)$ represents the joint likelihood function given the modulation hypothesis $H_i$, the estimated active subcarrier index $\widehat{I_g}$, and the symbols $S_g$.

4. 

A sentence was misplaced during the translation process. A sentence describing the HLRT method appeared incorrectly in Section 2.3. It has been moved to its proper location in Section 2.4 with the subject corrected to HLRT.

A correction has been made to Section 2.3 Paragraph 1:

The last sentence of the paragraph, which read “Additionally, the GLRT method has a high dependence on the initial parameter estimates; inaccuracies in these estimates can adversely affect the final recognition results.”, has been deleted.

A correction has been made to Section 2.4 Paragraph 1:

However, the complexity of the HLRT method remains high, especially when multiple parameters need to be addressed simultaneously. Additionally, the HLRT method has a high dependence on the initial parameter estimates; inaccuracies in these estimates can adversely affect the final recognition results.

5. 

Section 3.1, Paragraph 3 has been revised for greater clarity and technical precision. The original text’s explanation of the distinguishability of QAM/PAM signals was ambiguous; it now clearly states that the cumulant difference arises from the complex nature of the original signal. The symbol for normalized cumulants has been corrected from $\widetilde{C_{40}}$ to $\widetilde{C_{4i}}$. To better describe the experiment in [19], the word “establish” was changed to “testing”. The original term was inappropriate as the threshold was pre-determined and then used for comparison, not established during the simulation. The description of complexity has been refined by removing the mention of Monte Carlo simulations, as its role in the cited work is limited to performance testing and does not affect the algorithm’s operational complexity.

Corrections have been made to Section 3.1, Paragraph 3:

By leveraging the asymmetric clipping characteristic of the ACO-OFDM signal, there is an essential difference in the cumulants of QAM signals compared to PAM signals, which stems from the original signal’s real/imaginary parts. The normalized cumulants $\widetilde{C_{4i}}$ of different-order PAM signals exhibit separable statistical boundaries. By testing classification thresholds through Monte Carlo simulations, a correct recognition rate of 88.9% can be achieved with 2000 samples when the SNR exceeds 15 dB. However, performance drops sharply when the SNR falls below 5 dB due to noise dominance (as shown in Figure 4). This study confirms that HOS possess both noise robustness and modulation sensitivity. However, the high computational complexity of HOS limits its feasibility in dynamic real-time applications.

6. 

The sentence preceding Equation (14) has been refined to enhance clarity. The previous phrasing could be misinterpreted as implying a temporal action of “reconstructing... before noise interference.” The intended meaning was to convey a state of matching the ideal and noise-free signal constellation. To express this concept more precisely, the text has been streamlined to “matching the ideal constellation.”

A correction has been made to Section 3.2, Paragraph 2, in the sentence before Equation (14):

They calculated the Euclidean distance between each symbol point and the cluster centers of the templates and classified the symbols into the nearest cluster, thereby matching the ideal constellation distribution.

7. 

The wording concerning the threshold processing function and feature extraction in Section 3.3 has been revised for greater accuracy. The term “adaptive” has been revised to clarify that the threshold is designed for flexible operator selection, not automatic adaptation. And our original description of feature extraction for the method in [21] was inaccurate regarding the information of wavelet domain and statistical measures.

Corrections have been made to Section 3.3, Paragraph 1:

The received signal is analyzed for time-frequency localization, combined with a threshold processing function based on noise statistics … to achieve the nonlinear suppression of high-frequency noise components. Here, $\mathsf{\delta }$ is the selected threshold based on noise statistical characteristics,

Corrections have been made to Section 3.3, Paragraph 2:

In terms of feature extraction, information from the time domain and frequency domain is integrated. The maximum amplitude spectral density is extracted as the pivotal feature, while the normalized peak spacing is amalgamated to augment the separability of modulation modes.

8. 

In Section 3.4, the terminology for performance metrics has been standardized by correcting “sensitivity” to “accuracy”. The description of SVM performance was not clear. It has been made more specific to provide a clearer comparison.

Corrections have been made to Section 3.4, Paragraph 2:

The k-nearest neighbors (KNN) method, which employs dynamic neighborhood search, performs best at medium distances (2.32 m), maintaining an accuracy of 79.99% at 3 m. The support vector machine (SVM), which maximizes the classification margin through the hyperplane $y=w^{T}x+b$, achieves comparable performance to LM at medium distances (2.25–2.86 m),

9. 

The interpretation of the symbols in Equation (18) has been revised. Our original explanation was based on a slight misinterpretation of the variable definitions in the cited work. The text has been corrected to accurately describe the definitions in the original reference.

A correction has been made to Section 3.6, Paragraph 1:

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.

10. 

In our introduction to [25] in Section 4.1, the notation of the signal length has been corrected from $n$ to $N$. The description of the model has been refined. Although the convolution kernel used in the work can be abstractly considered as a 3 × 1 temporal convolution kernel, it is now specified as 3 × F_I × F_O to more accurately reflect the original expression, and the text now clarifies that the channel design is configurable.

Corrections have been made to Section 4.1, Paragraph 1, The text below Equation (19):

where the signal length $N$ is 128... For network architecture, a seven-layer convolutional network was designed with 3 × F_I × F_O convolutional kernels and configurable channel dimensions.

11. 

A repeated sentence following Equation (22) was deleted, and the word “reconstructs” has been clarified to “transforms” to better describe the process.

A correction has been made to Section 4.1, Paragraph 5:

where $D$ is the distance from the projection source to the image center… This process transforms the constellation image, significantly enhancing inter-class separability.

12. 

In Section 4.1, our description of the work by Gu et al. [29] has been refined for greater accuracy. The term “alternating” was replaced by “utilizing” to clarify the application of two pooling methods. The discussion of robustness was also refined to emphasize the network’s inherent improvement. As for the description of the dropout layer, while its placement in the final layer is a reasonable logical inference based on the model’s structure, this detail was not explicitly stated in the reference. Therefore, it has been omitted to adhere strictly to the reference.

Corrections have been made to Section 4.1, Paragraph 7:

The network architecture consisted of a six-layer convolutional block structure, which balanced feature abstraction and detail retention by utilizing max pooling and average pooling. In strong turbulence scenarios, robustness was enhanced by integrating average pooling and batch normalization techniques, with a dropout rate of 0.6.

13. 

Our description of the work by Wang et al. [31] has been revised for greater accuracy. The “mAP” performance metric is now clearly specified in both the text and Table 4. Furthermore, the parameter count of the improved model has been corrected to 24.17MB, as the previously cited value was for the base model. This required revising the model’s description and updating the parameter reduction calculation to 79.3%.

Corrections have been made to Section 4.1, Paragraph 9:

At 20 dB high SNR, it reached an mAP of 0.993, all while maintaining a model parameter size of 24.17 MB, which represents a 79.3% reduction compared to YOLOv3.

14. 

The wording following Equation (23) has been refined by clarifying the “signal constellation”. It has been made clear that the Hough transform was applied to the constellation diagram.

A correction has been made to Section 4.1, Paragraph 11:

This transformation projects the modulated signal constellation into the $\left(\rho , \theta \right)$ parameter space, enhancing the amplitude and phase features of modulation formats such as QPSK and QAM.

15. 

Our description of the training process and data augmentation of the work by Zhang et al. [34] was inaccurate. It has been revised to more accurately reflect the reference and improve clarity. And "noise injection" is no longer categorized as data augmentation, as it is applied in the communication simulation.

Corrections have been made to Section 4.3, Paragraph 1:

In the early stages of training, tasks from fewer batches are utilized to learn the common features associated with channel fading. Subsequently, more batches including more diverse task combinations are gradually introduced, creating a progressive knowledge path… Coupled with data compensation strategies such as rotation augmentation, the framework effectively captures essential features,

16. 

The use of the word “integrate” in our introduction of the work by Zhao et al. could cause ambiguity. We changed it to “introduce” for better clarity.

Corrections have been made to Section 4.3, Paragraph 2:

Zhao et al. [36] proposed an enhanced solution that introduces active learning (AL) and transfer learning (TL) to address the challenge of acquiring labeled data in VLC systems… The results indicated that in an extremely small sample scenario with only 60 labeled samples, the introduction of AL and TL achieved accuracy improvements of 6.82% and 14.6%, respectively.

17. 

Our description of the work by Li et al. [37] has been revised for greater precision. In the feature extraction method, the terminology has been corrected from “image” to “map”. Additionally, our originally described voltage condition was relatively conservative; it has been updated to 0.2–1.3 V to more accurately reflect the full performance capabilities demonstrated in [37]’s source figures.

A correction has been made to Section 4.3, Paragraph 3:

For the original complex signal $y\left(i\right)$, they extracted both the IQ constellation map in the Cartesian coordinate system and the joint feature map of amplitude and phase in the polar coordinate system.

A correction has been made to Section 4.3, Paragraph 4:

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.

18. 

There was a typing error in the symbols following Equation (31). They have been corrected from “$b^T$ and $b^S$” to “$\widehat{p^T}$ and $\widehat{p^S}$”

A correction has been made to Section 4.3, Paragraph 5:

here, $\widehat{p^T}$ and $\widehat{p^S}$ represent the non-target class distributions after removing the target class probability $p_t^T$,

19. 

In our introduction of the dataset of reference [34], our original description of the query set was inaccurate. Unlike the validation set mentioned earlier, the query set contains unknown samples of existing classes, not unknown classes.

A correction has been made to Section 4.4, last sentence of paragraph 8:

The query set contained samples of the same classes for aggregating and optimizing parameters to achieve knowledge transfer and generalization.

20. 

Our performance description of the work in [51] has been updated to include necessary conditions for the stated accuracy, making the description more precise.

A correction has been made to Section 4.5, Paragraph 2:

The ternary weight quantization technique in [51], which restricts neural network parameters to {−1, 0, +1} at inference, combined with the MobileNetV3 architecture, achieves an average recognition accuracy of 90.1% on an ASIC.

Revision to Table 4

The entry for Wang Y. et al. [31] in Table 4 has been revised to more clearly distinguish its unique performance metric. To improve clarity and align with standard representation, the entry now explicitly includes “(mAP)” and presents the value in decimal format (0.993). The corrected Table 4 appears below.

Table 4. Summary and comparison of deep learning-based modulation recognition methods.

Reference	Year	Input	Model	Modulation Types	Typical Accuracy (%)	Typical Conditions
Liu W. et al. [27]	2020	Pseudo constellation diagram	GoogLeNet V3	BPSK, 4/8/16/32/64QAM	98	SNR = 15 dB
Mortada B. et al. [28]	2022	Fan-beam constellation diagram	AlexNet	2/4/8/16PSK, 8/16/32/64QAM	100	OSNR = 15 dB
Gu Y. et al. [29]	2022	2 × 1024 IQ sequence	CNN	OOK, BPSK, QPSK, 16QAM	99.98	SNR = 10~30 dB
Gao W. et al. [30]	2022	2 × 2N matrix	DrCNN	4/8/16QAM,8PSK, OOK, 16APSK	98.3	SNR = 20 dB
Wang Y. et al. [31]	2024	Time-frequency diagram	YOLOv5s	BPSK, QPSK, 8PSK, 16QAM	0.993(mAP)	SNR = 20 dB
Arafa N. et al. [32]	2024	Hough transform constellation diagram	Pre-Trained AlexNet	QPSK, 8/16PSK, 4/8/16/32/64QAM	100	SNR = 12 dB
Gao W. et al. [33]	2024	4 × N sequence	BiGRU	2/4/8/16/32/64QAM, 8/16/32/64APSK	>96	Linear working area
Zhang L. et al. [34]	2020	Constellation diagram	PGML-CNN	4/8/16/32/64/128/256 QAM, 2/4/8ASK, 2/4/8/16/32 PSK	95.63	SNR = 6 dB
Zhao Z. et al. [36]	2022	Contour stellar image	AlexNet-AL	2/4/8/16/32/64QAM	88.78	SNR = 0~15 dB
Li F. et al. [37]	2023	IQ samples processed by coordinate transformation and folding algorithm.	Reservoir Computing	OOK, 4QAM, 8QAM-DIA, 8QAM-CIR, 16APSK, 16QAM	>90	Linear working area
Yao L. et al. [39]	2024	Constellation diagram	CIKD-CNN	PAM4, QPSK, 8QAM-CIR, 8QAM-DIA, 16/32QAM, 16/32APSK	100	Ideal working area
Zheng X. et al. [40]	2024	Constellation diagram	TCN-LSTM + MMAnet	4/8/16/32/64QAM	99.2	SNR = 4 dB

Table 4. Summary and comparison of deep learning-based modulation recognition methods.

Reference	Year	Input	Model	Modulation Types	Typical Accuracy (%)	Typical Conditions
Liu W. et al. [27]	2020	Pseudo constellation diagram	GoogLeNet V3	BPSK, 4/8/16/32/64QAM	98	SNR = 15 dB
Mortada B. et al. [28]	2022	Fan-beam constellation diagram	AlexNet	2/4/8/16PSK, 8/16/32/64QAM	100	OSNR = 15 dB
Gu Y. et al. [29]	2022	2 × 1024 IQ sequence	CNN	OOK, BPSK, QPSK, 16QAM	99.98	SNR = 10~30 dB
Gao W. et al. [30]	2022	2 × 2N matrix	DrCNN	4/8/16QAM,8PSK, OOK, 16APSK	98.3	SNR = 20 dB
Wang Y. et al. [31]	2024	Time-frequency diagram	YOLOv5s	BPSK, QPSK, 8PSK, 16QAM	0.993(mAP)	SNR = 20 dB
Arafa N. et al. [32]	2024	Hough transform constellation diagram	Pre-Trained AlexNet	QPSK, 8/16PSK, 4/8/16/32/64QAM	100	SNR = 12 dB
Gao W. et al. [33]	2024	4 × N sequence	BiGRU	2/4/8/16/32/64QAM, 8/16/32/64APSK	>96	Linear working area
Zhang L. et al. [34]	2020	Constellation diagram	PGML-CNN	4/8/16/32/64/128/256 QAM, 2/4/8ASK, 2/4/8/16/32 PSK	95.63	SNR = 6 dB
Zhao Z. et al. [36]	2022	Contour stellar image	AlexNet-AL	2/4/8/16/32/64QAM	88.78	SNR = 0~15 dB
Li F. et al. [37]	2023	IQ samples processed by coordinate transformation and folding algorithm.	Reservoir Computing	OOK, 4QAM, 8QAM-DIA, 8QAM-CIR, 16APSK, 16QAM	>90	Linear working area
Yao L. et al. [39]	2024	Constellation diagram	CIKD-CNN	PAM4, QPSK, 8QAM-CIR, 8QAM-DIA, 16/32QAM, 16/32APSK	100	Ideal working area
Zheng X. et al. [40]	2024	Constellation diagram	TCN-LSTM + MMAnet	4/8/16/32/64QAM	99.2	SNR = 4 dB

Updated Funding

The name and number of the first project in the Funding section has been updated:

Innovation Project of Guangxi Graduate Education (No. YCSW2025507)

The authors apologize for any inconvenience these corrections may cause. The authors state that the scientific conclusions are unaffected. The corrections were approved by the Academic Editor. The original publication has also been updated.