Enhancing Performance of Air–Ground OAM Communication System Utilizing Vector Vortex Beams in the Atmosphere

Round 1

Reviewer 1 Report

Authors propose an air-ground orbital angular momentum communication system using vector vortex beams (VVB) for enhancing the performance under atmospheric turbulence. They simulated the optical communication system and demonstrated numerical results to prove the enhancement of communication capabilities. However, there are some concerns need to be addressed and require at least one major revision before recommending it for publication in the journal.

 

1.       The results are demonstrated in low order VVB and SVB for enhancing the performance of air-ground communication, and I wonder whether this enhancement exist for a higher topological charge.  

2.       In page 14, authors state that “The average BER of air-ground ….to noise”. However, as the increase of turbulence intensity, the BER value increase but not decrease. Besides, as mentioned above, the LG beam performs better than BG beam under long-distance turbulence propagation, what is the boundaries for the definition of long and short distance?

3.       The BER values in this manuscript can only reach 10^-2, which is higher than the FEC value (3.8*10^-3). Therefore, I wonder how to ensure the communication quality for the actual application.

4.       C-point and V-point are mentioned in the manuscript but not marked in the Figures. Besides, in page 10, “The comparisons of BG … in Fig.5 (c)”, this description should belong to Fig. 4.

5.       For optical communication, the signal multiplexing and demultiplexing are essential in practical applications. Therefore, I wonder the performance of multiplexed VVB in the air-ground communication under turbulence.

 

Author Response

Response Letter

Dear Editor and Reviewers,

We gratefully thank you for your treasure time, great efforts and useful comments towards making this paper better in quality and readability. Now, after a careful revision, we present a point-by-point response to the comments and the suggestions of the reviewers along with the new paper and hope it meets the requirement of publication. Below are the replies to the comments.

Reviewer 1,

1. Comment: The results are demonstrated in low order VVB and SVB for enhancing the performance of air-ground communication, and I wonder whether this enhancement exist for a higher topological charge.

Reply: We sincerely appreciate the valuable comment and thank you for pointing this out. As shown in Fig. 4, the enhancement only exists in the lower topological charge and the difference between vector and scalar vortex with higher topological charge can be ignored. It is reasonable, since the vector vortex beam can be regarded as the superimposed OAM modes of opposite signs ±s0 in the same proportion, and the atmospheric turbulence effects on transmission of signal OAM mode can be effectively reduced due to the reciprocal features of the OAM mode crosstalk. The interval between the two OAM modes of vector vortex beams with smaller topological charge is smaller, and the effect of OAM mode crosstalk reciprocal features is significant.

 

2. Comment: In page 14, authors state that “The average BER of air-ground ….to noise”. However, as the increase of turbulence intensity, the BER value increase but not decrease. Besides, as mentioned above, the LG beam performs better than BG beam under long-distance turbulence propagation, what is the boundaries for the definition of long and short distance?

Reply: Thank you for your careful reading of our manuscript. It is a clerical error. As you said, as the increase of turbulence intensity, the BER value increase. The average BER of the air-ground OAM communication system increases with the increase of signal OAM mode and the decrease in the ratio of power to noise. There is no fixed boundary for the definition of long and short distance, it depends on the source parameters and turbulence parameters. As shown in Figs. 10-11, the location of the intersection of the average BER with LG and BG beams changes all the time.

 

3. Comment: The BER values in this manuscript can only reach 10-2, which is higher than the FEC value (3.8*10-3). Therefore, I wonder how to ensure the communication quality for the actual application.

Reply: We are very grateful for your specific comments for the improvement of this paper. Turbulence has a stronger influence on the transmission of OAM modes in the long-distance atmosphere. In order to reach the FEC value (3.8*10-3), several turbulence correction methods (such as deep learning and adaptive optics technologies) and OAM identification methods have been studied. In this manuscript, we focus on the basic physical layer of air-ground OAM communication system without any correction methods, thus the BER values in this manuscript can only reach 10-2, it can be improved with correction methods.

 

4. Comment: C-point and V-point are mentioned in the manuscript but not marked in the Figures. Besides, in page 10, “The comparisons of BG … in Fig.5 (c)”, this description should belong to Fig. 4.

Reply: Thank you for your careful reading of our manuscript. That's a hypothetical here, as a vector vortex beam can be regarded as the superimposed OAM modes of opposite signs ±s₀ in the same proportion, and the atmospheric turbulence effects on transmission of signal OAM mode can be effectively reduced due to the reciprocal features of the OAM mode crosstalk. The interval between the two OAM modes of C-point vector vortex beams (superposition of the s₀ = 0 and s₀ OAM modes) is smaller than the V-point vector vortex beams (superposition of the ±s₀ OAM modes), and the effect of OAM mode crosstalk reciprocal features of C-point vector vortex beams is clearer.

 

5. Comment: For optical communication, the signal multiplexing and demultiplexing are essential in practical applications. Therefore, I wonder the performance of multiplexed VVB in the air-ground communication under turbulence.

Reply: Thank you very much for your valuable advice. As you mentioned, OAM division multiplexing communication is essential in practical applications, and turbulence will induce the channel crosstalk of the OAM multiplexing communication system, and the use of the VVB will increase the average capacity and decrease the average BER of OAM multiplexing communication system in the atmosphere.

 

Again, we are grateful to the reviewers for their efforts towards making this paper better in quality and readability. We have revised the paper in accordance with the comments and suggestions by the reviewers. And we have checked the whole manuscript and corrected the grammar and format errors, also the other questions to comply with the style guidelines. It is our hope that the revised version of the paper meets the requirement and is acceptable for publication.

 

Sincerely,

Mingjian Cheng

School of Physics, Xidian University, Xi’an 710071, Shanxi, China

mjcheng@xidian.edu.cn

Author Response File: Author Response.docx

Reviewer 2 Report

In their manuscript “Enhancing performance of air-ground OAM communication system utilizing vector vortex beams in the atmosphere” the authors propose a theoretical model to describe the detection probability of OAM modes as well as a measure of information loss for the communication between a ground station and UAVs. They test this model using both Bessel and Laguerre-Gauss modes, and conclude the former behave better for short elevations of the UAVs and the latter for longer ones.

Although I find the work interesting and the results compelling, the manuscript needs a bit of work before I can recommend it for publication. I have several comments that I hope will help the authors to improve the manuscript:

1. The authors state the value for the balance parameter c_0 (line 123), but do not explain how or why they choose this particular value. At the very least they should mention the physical conditions for which this is reasonable, or in other words, a range of applicability.

2. To obtain equation 22 the authors mention they use a “second order approximation”. A brief description of what they mean by that is missing. A citation to the type of procedure would be also acceptable.

3. What is the physical meaning of BER?

4. Why are the behavior of the down and up-links so different?

5. In general, when comparing information in two graphs is advisable to use the same scale. This is not the case in most of the plots the authors show, effectively making it harder for the reader to see the trends the authors highlight.

6. In figure 4, on one hand, the insets shown interfere with the main graphs. On the other, I miss the ones corresponding to the LG beams so I can compare the behaviors. One option is to add the latter (but this will make the graph crowded). Another option is to use log scale for the x-axis.

7. The paragraph on page 9 reads Fig. 5, where it should be Fig. 4.

8. At first glance is not clear there are 4 independent density plots in each subfigure in Fig. 5. I recommend the authors add some black space between cases.

9. Just as in Fig. 4, Fig. 6 is missing an inset (Two options again). Considering there is space, I would move the legend outside the plot to the right.

10.  What are the values s_0 and s for Figs. 7-11?

11.  In the paragraph referring to Fig. 7, the authors state “Noted that, for the vector LG beam transmitted in the downlink atmosphere channel, the dynamic curves of signal OAM mode detection probability against the UAV height show a trend of increasing first and then decreasing.” It’s my understanding that “detection probability against the UAV height” refers to a vertical line on the graphs shown. If this is the case, Fig. 7c shows the cited behavior only up to about C_n^2(0)=15e-15, thus reducing the claim’s validity. Could you please clarify this?

12.  Regarding Table 1, I believe vertical lines between pairs parameter/value would be advisable. Also, it doesn’t help the table extends two pages.

13.  I found several minor English mistakes (For instance, the first sentence of the introduction says “unmanned aerial vehicles (UAVs) has become…” where should say “have”).

 

Author Response

Response Letter

Dear Editor and Reviewers,

We gratefully thank you for your treasure time, great efforts and useful comments towards making this paper better in quality and readability. Now, after a careful revision, we present a point-by-point response to the comments and the suggestions of the reviewers along with the new paper and hope it meets the requirement of publication. Below are the replies to the comments.

Reviewer 2,

1. Comment: The authors state the value for the balance parameter c_0 (line 123), but do not explain how or why they choose this particular value. At the very least they should mention the physical conditions for which this is reasonable, or in other words, a range of applicability.

Reply: We sincerely appreciate the valuable comment and thank you for pointing this out. As we know, during the uplink or downlink atmospheric turbulence channels, the anisotropic parameter is varying with the height, and turbulence eddies have the larger anisotropic parameter in upper atmosphere. In this paper, we firstly propose the anisotropic turbulence spectrum with the varying anisotropic parameter. In the early literature, there is no report about the balance parameter c_0, and balance parameter c_0 has not particular value, any value can be selected. From the early calculation, there was a small difference in the results when anisotropic parameter is larger than 2. Here, we set c_0 = 2000 to keep the anisotropic parameter is smaller than 2, when height is lower than 2500 m.

 

2. Comment: To obtain equation 22 the authors mention they use a “second order approximation”. A brief description of what they mean by that is missing. A citation to the type of procedure would be also acceptable.

Reply: We are very grateful for your specific comments for the improvement of this paper. Here, the second order approximation is an approximation of 0 order Bessel function, J₀ (x)≈1− x²/4, which refer to Shirai T, Dogariu A, Wolf E. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence[J]. JOSA A, 2003, 20(6): 1094-1102. We have added it in the new draft.

 

3. Comment: What is the physical meaning of BER?

Reply: Thank you very much to point out the details in our manuscript. Similar with average capacity, average bit error rate (BER) is another important parameter to measure the performance of communication system performance. BER = Transmitted bit error / Total number of transmitted codes *100%. If there is a bit error, there is BER. BER is a measure of the accuracy of data transmission within a specified time. In addition, bit error rate is also defined to measure the frequency of error codes.

 

4. Comment: Why are the behavior of the down and up-links so different?

Reply: Thank you for your careful reading of our manuscript. Down and uplinks atmospheric channels are different because of the turbulence. First of all, be clear about three things: Beam size of laser beam increase with the propagation distance, due to the free space diffraction effect; According to Hufnagel-Valley (H-V) model of the turbulence structure parameter, the strength of atmospheric turbulence decreases with the altitude; The atmospheric turbulence with the same level strength results in stronger turbulence effects of laser beams with smaller beam size. For same link distance, laser beam of downlinks experiences the weak turbulence firstly, and laser beam of uplinks leaded in passing the strong turbulence with small beam size. Consequently, atmospheric turbulence in uplinks is stronger than that in downlinks.

 

5. Comment: In general, when comparing information in two graphs is advisable to use the same scale. This is not the case in most of the plots the authors show, effectively making it harder for the reader to see the trends the authors highlight.

Reply: We are very grateful for your specific comments for the improvement of this paper. As you mentioned, two graphs are preferred to use the same scale, and we have corrected them in the new draft.

 

6. Comment: In figure 4, on one hand, the insets shown interfere with the main graphs. On the other, I miss the ones corresponding to the LG beams so I can compare the behaviors. One option is to add the latter (but this will make the graph crowded). Another option is to use log scale for the x-axis.

Reply: We sincerely appreciate the valuable comment and thank you for pointing this out. The insets shown may interfere with the main graphs. Actually, the insets graph does not play a major role in the description of changing trend. Using log scale for the x-axis does not bring any real change of the figures. Thus, we have deleted them in the new draft.

 

7. Comment: The paragraph on page 9 reads Fig. 5, where it should be Fig. 4.

Reply: Thank you for pointing out it. There exists some clerical errors page 9. Because we deleted one figure in the early manuscript, so that the Fig.5 should be rewritten as Fig. 4. We have corrected them.

 

8. Comment: At first glance is not clear there are 4 independent density plots in each subfigure in Fig. 5. I recommend the authors add some black space between cases.

Reply: Thank you for your suggestion. We have added the black space between four cases in Figs. 5.

 

9. Comment: Just as in Fig. 4, Fig. 6 is missing an inset (Two options again). Considering there is space, I would move the legend outside the plot to the right.

Reply: Thank you for pointing out it. As you said, the insets shown would interfere with the main graphs. We have deleted the inset to make to main graph clearer.

 

10. Comment: What are the values s_0 and s for Figs. 7-11?

Reply: Thank you for your careful reading of our manuscript. The simulation parameters are summarized in Table 1 unless otherwise specified. The values of the signal OAM mode s_0 is equal to 3. In Figs 7-8, to calculate the signal mode detection probability, the value of s is equal to 3. And for calculating the average BER, the values of s is meaningless, we need to iterate over all the values.

 

11. Comment: In the paragraph referring to Fig. 7, the authors state “Noted that, for the vector LG beam transmitted in the downlink atmosphere channel, the dynamic curves of signal OAM mode detection probability against the UAV height show a trend of increasing first and then decreasing.” It’s my understanding that “detection probability against the UAV height” refers to a vertical line on the graphs shown. If this is the case, Fig. 7c shows the cited behavior only up to about C_n^2(0)=15e-15, thus reducing the claim’s validity. Could you please clarify this?

Reply: Thank you for your careful reading of our manuscript. As you said, the detection probability against the UAV height should refer to a vertical line on the graphs shown. In Fig. 7c, we cannot find the peak value phenomenon. Only for the vector LG beam transmitted in the downlink atmosphere channel (shown in Fig. 7d), the dynamic curves of signal OAM mode detection probability against the UAV height show a trend of increasing first and then decreasing. The reason is similar with the comment 4. We gave the physical interpretation as follow, as the turbulence in the upper atmosphere is weak, the atmospheric turbulence strengths during the transmission process of the laser beam in downlink atmospheric channel. However, beam size will increase due to the due to the free space diffraction effect, and the laser beam with the larger beam size has stronger resistance to turbulence disturbance, these two factors result in the optimal link height (height of UAV), when other parameters are determined.

 

12. Comment: Regarding Table 1, I believe vertical lines between pairs parameter/value would be advisable. Also, it doesn’t help the table extends two pages.

Reply: Thank you for pointing out it. According to your suggestion, we add the vertical lines between pairs parameter/value.

 

13. Comment: I found several minor English mistakes (For instance, the first sentence of the introduction says “unmanned aerial vehicles (UAVs) has become…” where should say “have”).

Reply: Thank you for pointing out it. We have checked the English grammar carefully.

 

Again, we are grateful to the reviewers for their efforts towards making this paper better in quality and readability. We have revised the paper in accordance with the comments and suggestions by the reviewers. And we have checked the whole manuscript and corrected the grammar and format errors, also the other questions to comply with the style guidelines. It is our hope that the revised version of the paper meets the requirement and is acceptable for publication.

 

Sincerely,

Mingjian Cheng

School of Physics, Xidian University, Xi’an 710071, Shanxi, China

mjcheng@xidian.edu.cn

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Authors have addressed most of my concerns in the revised manuscript, and this version can be accepted for publication in the journal.