Laser Inter-Satellite Link Visibility and Topology Optimization for Mega Constellation

Round 1

Reviewer 1 Report

The authors analyze the Azimuthal, Elevation, Range (AER) of the optical laser links of Starlink constellation. This constellation of satellites is equipped with optical links to increase the capacity of the satellite network. However, the optical links not always are permanent. For that reason the authors consider two types of optical links: permanent and time-varying. The first ones are the optical links of the satellites contained in the same orbital plane. The others are mainly given between the satellites of consecutive inter-orbital planes. For that reason in this second case compute the service continuity of the links. It is shown that the inter-orbital links have discontinuities of the service that have to be considered in order to design the satellite network successfully.

Regarding the comments,

1) the authors comment the constellation as if they knew the exact properties of the starlink constellation when they are not from the company. So, some kind of caution should be given.

2) Generallize the expressions for a whatever constellation and then introduced a section of results particularizing for the constellation that you want.

3) Comparisions among the results of several constellations when (2) is done results in a much interesting paper.

This is basically a performance evaluation talking as if the authors were designed perfectly the starlink constellation when it is not the case. I would recommend to generalize the expressions and then particularize for several constellations. More conclusions can be achieved.

Author Response

Reviewer #1:

[general] In terms of overall structure, this article supplements Background, adds a comparison of LEO constellations in Table 1, and indicates the relevant sources when companies and data are involved in the article. Streamlined the Conclusions section and moved the Recommendation to Section 4.7. Added the comparison of constellation coverage performance in Section 4.3, mainly for OneWeb and Starlink constellations. Finally, the content of Abstract is adjusted and summarized. All parts with text changes are marked in red font, and green font indicates the part that only moved the position without changing the content.

1. Response to comment: the authors comment the constellation as if they knew the exact properties of the Starlink constellation when they are not from the company. So, some kind of caution should be given.

Response: We are very sorry for our negligence of explanations about the properties of the Starlink constellation. In the introduction part, the relevant information of SpaceX, the production company of Starlink, is supplemented. In addition, a citation about the source of the FCC report was added in Line 44, and a footer was added after Table 1 to illustrate the detailed orbital parameters of various constellations. Besides, in Section 2.1, a footer was added to Table 2, which illustrates the source of orbital data about Starlink Constellation Phase I, and the data is available in the link" https://www.ucsusa.org/nuclear-weapons //space-weapons/ satellite - database, 2022-1-1."

2. Response to comment: Generallize the expressions for a whatever constellation and then introduced a section of results particularizing for the constellation that you want.

Response: Considering the Reviewer’s suggestion, we have made changes in Section 3.4. Replace the pseudo-code of the algorithm for finding the optimal factor in Table 2 with the general LEO constellation. And in Line 292~296, the derivation process of related expressions is given. And the corresponding mathematical formulas in Section3 are also modified. In addition, for the conclusion part of Section4, simulation tests and result analysis are also carried out for a specific constellation. Among the LEO constellations proposed in Table 1, the Starlink and OneWeb constellations with a large number of satellites are mainly selected. In Section 4.1, the shortest distance under different phase factors is calculated respectively, and the optimal factor of OneWeb is 9 by the binomial criterion, while the optimal phase factor of Starlink is 11.

3. Response to comment: Comparison among the results of several constellations when (2) is done results in a much interesting paper.

Response: First of all, it is really true as Reviewer suggested that comparison among the results of several constellations results in a much interesting paper. For the content of adding constellation comparison, we have considered it carefully. As mentioned in (2), we have added the simulation modeling of OneWeb constellation, and added the following two angles of comparison. On the one hand, set F=1 and F=9 respectively in OneWeb, and set F=1 and F=11 respectively in Starlink. The effects of changing the phasing factor on the coverage performance are compared, and the results show that when the optimal factor is set, the global coverage multiplicity is significantly increased. On the other hand, comparing the coverage performance of OneWeb and Starlink constellations when the optimal factor is also set, the results show that for most user locations between 60° north and south latitude, the coverage of Starlink constellation is better than that of OneWeb. The above comparison is mainly described in Section 4.3. It is also for this consideration that the following visibility and AER analysis and connection strategies are based on the Starlink constellation simulation of F=11.

Special thanks to you for your helpful comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper addresses the laser Inter-satellite link visibility for LEO satellites in the Starlink constellation. The considered issue is interesting and practical. Detailed comments/suggestions are as follows.  

1) The introduction part should be revised carefully to make the motivation and contribution clear. 

2) A lot of statements in the Introduction part are without citations. For example, "assumption that the total number of satellites does not exceed 100, as is the case with the Iridium constellation's topology design, which has only 66 satellites." Please include citations to support those statements. 

3) Line 43: therefore = as a result. Please remove one of them   

4) Citation is required for Table I. 

5) Please include comparative results between the proposed solution with others available in the literature. 

6) Section 5 is too long. I would suggest the authors move the recommendation part to section 4 to make the conclusion concise. 

Author Response

Reviewer #2:

[general] In terms of overall structure, this article supplements Background, adds a comparison of LEO constellations in Table 1, and indicates the relevant sources when companies and data are involved in the article. Streamlined the Conclusions section and moved the Recommendation to Section 4.7. Added the comparison of constellation coverage performance in Section 4.3, mainly for OneWeb and Starlink constellations. Finally, the content of Abstract is adjusted and summarized. All parts with text changes are marked in red font, and green font indicates the part that only moved the position without changing the content.

1. Response to comment: The introduction part should be revised carefully to make the motivation and contribution clear.

Response: As Reviewer suggested that we have carefully and thoroughly revised the introduction part. Firstly, the introduction part is adjusted to supplement the relevant background of the new low-orbit constellation; secondly, the related work is explained from the perspective of topology, and the optimal phasing factor and LISLs connection strategy in different situations are explored on the basis of predecessors. Finally, it summarizes the context of the article, points out the focus of the research, and proposes a universal geometrical approach for an optimal inter-satellite visibility. Taking Starlink constellation as an example, it verifies the effectiveness of the simulation and draws relevant conclusions. After revision, the motivation and contribution of this article are clearer, and readers can capture the research focus more quickly at the beginning of reading, which is convenient for reading and open research.

2. Response to comment: A lot of statements in the Introduction part are without citations. For example, "assumption that the total number of satellites does not exceed 100, as is the case with the Iridium constellation's topology design, which has only 66 satellites." Please include citations to support those statements.

Response: The revised introduction part adds some background and citations. Line71-73, the statements of "assumption that the total number of satellites does not exceed 100, as is the case with the Iridium constellation's topology design, which has only 66 satellites." were corrected as" assumption that the total number of satellites does not exceed 100, as is the case with the optimal Walker constellation's topology design", and a citation was added for the statements. Here is the citation: Guan, M.; Xu, T.; Gao, F.; Nie, W.; Yang, H. Optimal Walker Constellation Design of LEO-Based Global Navigation and Augmentation System. Remote Sensing 2020, 12, 1845, doi:10.3390/rs12111845.

3. Response to comment: Line 43: therefore = as a result. Please remove one of them

Response: After modifying the article, the original Line 43 content was moved to Line73, and in Line 73, “therefore” was deleted.

4. Response to comment: Citation is required for Table I.

Response: We added a table to the text, so the Table2 replaced the original Table1. A footer of Table 2 was given in Line 131-133, which explains the origin of the orbital data and illustrates the citations to avoid disagreement. 

5. Response to comment: Please include comparative results between the proposed solution with others available in the literature.

Response: In the article, we have added the contrasting part in Section 4. We changed the algorithm pseudocode in Section 3.4 to a form that is common to general LEO constellations, and modified the mathematical formula derivation in Section 3 accordingly. Then, in Section 4.1~4.3, the simulation modeling of OneWeb constellation is added as a comparison group. Not only the effects of different phasing factors on the multiples of constellation coverage within a specified period are compared, but also the advantages and disadvantages of the coverage performance of OneWeb and Starlink constellations when the optimal phasing factors are also set. The comparison results are given in Section 4.3 in detail, and corresponding revisions have been made in the Abstract and Conclusions.

6. Response to comment: Section 5 is too long. I would suggest the authors move the recommendation part to section 4 to make the conclusion concise.

Response: We have re-written the conclusions part according to the Reviewer’s suggestion and moved some of the recommendation part to section 2 while others to section 4. After rewriting, the conclusion part is more focused, concise and clear. The revised recommendation part can be seen in the green font in the text. The content has not changed, only the position has been moved.

Thank you for the detailed review, I found the reviewer’s comments are quite helpful, and I revised my paper point-by-point.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is important and straightforward and is ready for researchers and others who are interested in this subject and would like to know more. 

However, it may be complemented by recent publications. Recommend looking at recently published papers.  For instance, the following paper added a few more parameters to the optimizations. I recommend relating to this paper. Here is the citation: Zeng, L., Lu, X., Bai, Y. et al. Topology design algorithm for optical inter-satellite links in future navigation satellite networks. GPS Solut 26, 57 (2022). https://doi.org/10.1007/s10291-022-01241-3

Comments for author File: Comments.pdf

Author Response

Reviewer #3:

[general] In terms of overall structure, this article supplements Background, adds a comparison of LEO constellations in Table 1, and indicates the relevant sources when companies and data are involved in the article. Streamlined the Conclusions section and moved the Recommendation to Section 4.7. Added the comparison of constellation coverage performance in Section 4.3, mainly for OneWeb and Starlink constellations. Finally, the content of Abstract is adjusted and summarized. All parts with text changes are marked in red font, and green font indicates the part that only moved the position without changing the content.

1. Response to comment: It may be complemented by recent publications.

Response: As the reviewer suggested, I read the recommended article content carefully and it was really helpful for my article, so I'm adding citations to this article where appropriate, see Line 61~64 in Introduction.

Thank you very much for your comments and suggestions.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have introduced the suggested comments in the new version of the paper and so for me it is acceptable. This version uis much better and interesting for the readers.