Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper investigates the minimum transmit power required to sustain connectivity in optical inter-satellite links in a specific constellation. The paper is well-written, but the contribution is very limited to justify a journal publication. 

1.  The paper's contribution is limited under several aspects. Only one constellation is investigated. The only studied modulation format is OOK. Only the power budget is investigated, and other transmitter and receiver limitations are disregarded (e.g. eventual FEC or signal processing algorithms). The authors consider OOK even for 100 Gb/s, which requires a very high transmitter and receiver bandwidth.
2. The authors devote an entire section to the implemented software, which is made public. Although providing open software is meritorious, implementing the orbit dynamics is not extremely complex. Therefore, I recommend the authors move the software details to an appendix.
3.  I found it surprising in Fig. 7 that the calculated inter-satellite distance varies from 200 km to 1600 km for neighboring orbits. Actually, I would expect such behavior for polar orbits but not for regular orbits with 53 degrees of inclination. Could the authors please double-check the parameters used in the simulations?

Author Response

Reviewer #1

The authors would like to thank the reviewer for the consideration of our work. We have addressed your comments as discussed below.

Comment #1 (R1C1)

The paper's contribution is limited under several aspects. Only one constellation is investigated. The only studied modulation format is OOK. Only the power budget is investigated, and other transmitter and receiver limitations are disregarded (e.g. eventual FEC or signal processing algorithms). The authors consider OOK even for 100 Gb/s, which requires a very high transmitter and receiver bandwidth.

Response

In our work, we assume the Starlink Phase 1 V2 constellation at an altitude of 550 km as a practical and realistic scenario to demonstrate the applicability of our model. We also consider two alternative scenarios where we vary the number of orbits and satellites/orbit and thus, do apply our model on different constellations, albeit with the same inclination angle.

Regarding FEC, we agree that this is an important aspect and one way to include this in our calculations, is to assume the uncoded channel BER target is slightly higher than the BER threshold of the code in question. We now mention this in the revised manuscript. The same approach can be used for signal equalization schemes but we believe that in intersatellite links such schemes may not be relevant unless signal distortion is significant.

Regarding the 100Gbps data rate there are OOK systems that can achieve this using external modulation. We now provide relevant references in the manuscript. In any case, we believe that varying the model to account for multi-level modulation is straightforward.

Please refer to the changes made in the second paragraph of subsection 1.1 and the third paragraph of subsection 3.3.

Comment #2 (R1C2)

The authors devote an entire section to the implemented software, which is made public. Although providing open software is meritorious, implementing the orbit dynamics is not extremely complex. Therefore, I recommend the authors move the software details to an appendix.

Response

Following the reviewer's suggestion, the detailed explanation of the Pyminisat module implementation has been moved to Appendix A, located at the end of the manuscript.

Please refer to Appendix A for a detailed explanation of the Pyminisat module implementation, as well as the last paragraph of subsection 3.3.

Comment #3 (R1C3)

I found it surprising in Fig. 7 that the calculated inter-satellite distance varies from 200 km to 1600 km for neighboring orbits. Actually, I would expect such behavior for polar orbits but not for regular orbits with 53 degrees of inclination. Could the authors please double-check the parameters used in the simulations?

Response

We have added a new figure in subsection 4.1 to provide the values of F in the constellation distribution which are in agreement to the results in [6] thereby providing a validation of the overall orbital dynamics calculations.

Please refer to Subsection 4.1 and Figure 7 in the revised manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is well written for most parts and seems to be mostly correct. However, I have some important issues with this paper:

1. I understand that, different from stated in table 1,  Starlink’s Phase 1 V2 has about 3000 satellites,  
2. Line 156 states that F = 13, the same as in table 1 (for ~1500 satellites?). Why redo the calculations? Also, a graph showing how F influences maximum distance would be interesting
3. Reference [33] does not show eq. 17. For OOK, BER = Q(sqrt(SNR)). Eq. 18 seems to be correct and shows (something proportional to) SNR. Where is the mistake?
4. I do not understand how Be = Rb/2 in line 231. Shouldn't it be Be approximately equals to Rb? If pulse shaping is being used, Be should be even greater, but not (numerically) smaller than Rb for binary singalling.

This is sufficient to give me doubts on the reliability of results.

Although the new work has been done, there are no new ideas.

Author Response

Reviewer #2

The authors would like to thank the reviewer for the consideration of our work. We have addressed your comments as discussed below.

Comment #1 (R2C1)

I understand that, different from stated in table 1,  Starlink’s Phase 1 V2 has about 3000 satellites. 

Response

We used the data provided by reference [6] and assumed only the layer located at approximately 550 km with a 53° inclination to establish global broadband coverage.   

Comment #2 (R2C2)

Line 156 states that F = 13, the same as in table 1 (for ~1500 satellites?). Why redo the calculations? Also, a graph showing how F influences maximum distance would be interesting.

Response  

The value of F changes depending on the constellation parameter and therefore it needs to be re-calculated for all scenarios. We have added a paragraph explaining this and included a graph illustrating how F influences the maximum distance.  

Please refer to the last paragraph of subsection 2.2, Figure 7, and the second paragraph of Subsection 4.1.

Comment #3 (R2C3)

Reference [33] does not show eq. 17. For OOK, BER = Q(sqrt(SNR)). Eq. 18 seems to be correct and shows (something proportional to) SNR. Where is the mistake?

Response  

The term Pavg denotes the optical signal power and due to IM/DD, the photocurrent is proportional to Pavg,  making the electrical SNR proportional to Pavg, so γ scales proportionally to Pavg. We clarify this in the text.

Please refer to Subsection 3.2.

Comment #4 (R2C4)

I do not understand how Be = Rb/2 in line 231. Shouldn't it be Be approximately equals to Rb? If pulse shaping is being used, Be should be even greater, but not (numerically) smaller than Rb for binary singalling.

 

Response

Thank you for pointing this out.  In our work, we assume the absolute minimum roll-off factor for simplification. We now state in the document.

Please refer to Subsection 3.2.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors study a model enabling the dynamical evaluation of optical power requirements for realistic low Earth orbit satellite constellations by the orbital period. They incorporate the constellation architecture, link budget analysis and optical transceiver design, to accurately estimate the power required for sustaining connectivity for both intra- and inter-orbit links. Applying the Walker delta-type constellations of varying densities, in dense constellations even at high data rates, the required transmission power can be low enough to mitigate the need of optical amplification. Dynamically estimating the power requirements is vital when evaluating energy savings in adaptive scenarios where terminals adaptively change the emitted power depending on link status.

These results make sense and sound interesting, and I believe can be of interest to Photonics readers as well. I can therefore recommend this manuscript for publication in Photonics once the authors address the following questions:

1.All formulas are missing punctuation; therefore, it is recommended to add it.

2.For aesthetic purposes, it is recommended to center the figures in the article.

3.The repetition of “offer several” in the sixth line of the introduction should be deleted; the use of “need of” in the tenth line of the Abstract is inappropriate and should be changed to “need for”.

4.How to derive Eq. (22) in detail, please give more derivation processes.

5. The paper primarily examines closed I suggest that the authors briefly address ‌the implications of dissipationeffects on their results [Physical Review A 101, 013826 (2020); Reviews of Modern Physics 88, 021002 (2016)]; Physical Review A 98, 023856 (2018); Phys. Rev. A 81, 042103 (2010); Physical Review A 91, 063808 (2015); Physical Review Letters 103, 210401 (2009)].

6. The authors should briefly discuss how this scheme can be implemented in current experiments and cite relevant references.

 

 

Author Response

Reviewer #3

The authors would like to thank the reviewer for the consideration of our work. We have addressed your comments as discussed below.

Comment #1 (R3C1)

All formulas are missing punctuation; therefore, it is recommended to add it.

Response

We have added punctuation in all formulas. 

Comment #2 (R3C2)

For aesthetic purposes, it is recommended to center the figures in the article.

Response

Thank you for pointing this out.  We have ensured that all figures are centered.  

Please refer to the updated figures.

Comment #3 (R3C3)

The repetition of “offer several” in the sixth line of the introduction should be deleted; the use of “need of” in the tenth line of the Abstract is inappropriate and should be changed to “need for”.

Response

We made the corresponding changes.

Comment #4 (R3C4)

How to derive Eq. (22) in detail, please give more derivation processes.

Response

We have included a brief explanatory paragraph for better clarity.

Please refer to Subsection 3.2.

Comment #5 (R3C5)

The paper primarily examines closed I suggest that the authors briefly address ‌the implications of dissipation effects on their results [Physical Review A 101, 013826 (2020); Reviews of Modern Physics 88, 021002 (2016)]; Physical Review A 98, 023856 (2018); Phys. Rev. A 81, 042103 (2010); Physical Review A 91, 063808 (2015); Physical Review Letters 103, 210401 (2009)].

Response

Thank you for pointing this out. We have included a brief paragraph in the Introduction.

Please refer to the first paragraph in subsection 1.1.

Comment #6 (R3C6)

The authors should briefly discuss how this scheme can be implemented in current experiments and cite relevant references.

Response

Our model is designed to analyze circular orbit constellations with uniform distribution, such as Starlink and Kuiper. By adjusting parameter values, it can also be applied to constellations with different distributions. Additionally, it is adaptable to various modulation scenarios. To further demonstrate its versatility, our study examines three distinct scenarios (A,B,C).  

The primary objective of our analysis is to provide a realistic link budget assessment for inter-satellite links, considering the dynamic relative motion of satellites within the same constellation. We believe our approach can be applied to real-world scenarios, offering accurate link budget predictions that are valuable for adaptive optics schemes. 

We have modified the second paragraph in Subsection 1.1.

Please refer to  the second paragraph in subsection 1.1.

Reviewer 4 Report

Comments and Suggestions for Authors

1.The Figure 3, 6 caption must be clear and readable, please follow minimum resolution of 600 dpi.
2.The authors stated equation (8) and in page 5 line 150, "the optimal value for F ..." , how to decision the F value, I suggest including the reference 10.1109/5GWF52925.2021.00093 into paragraphy.
3.The Figure 6 receiver sensitivity with respect to the data rate obtained for the parameters of Table 2, there are data rate range 1-100 Gbps. Suggest the authors futher clarify on more data curve into figure.
4.The authors stated in Table 3. Scenarios considered, overall scenarios described in the result section with the Table 3 conditions are not easy for readers to quickly understand the relationship between Pyminisat algorithm and Optical Inter-Satellite Communication Model. Suggest the authors include some paragraphy state this part.

Author Response

Reviewer #4

The authors would like to thank the reviewer for the consideration of our work. We have addressed your comments as discussed below.

Comment #1 (R4C1)

The Figure 3, 6 caption must be clear and readable, please follow minimum resolution of 600 dpi.

Response

We made sure figures conform to this.

Comment #2 (R4C2)

The authors stated equation (8) and in page 5 line 150, "the optimal value for F ..." , how to decision the F value, I suggest including the reference 10.1109/5GWF52925.2021.00093 into paragraphy.

Response

Thank you for pointing this out. We have included a brief paragraph in Subsection 2.2. 

Please refer to the third paragraph of subsection 2.2.

Comment #3 (R4C3)

The Figure 6 receiver sensitivity with respect to the data rate obtained for the parameters of Table 2, there are data rate range 1-100 Gbps. Suggest the authors futher clarify on more data curve into figure.

Response

We have updated Figure 6 to reflect the range of 0–100 Gbps. 

Please refer to Figure 6.

Comment #4 (R4C4)

The authors stated in Table 3. Scenarios considered, overall scenarios described in the result section with the Table 3 conditions are not easy for readers to quickly understand the relationship between Pyminisat algorithm and Optical Inter-Satellite Communication Model. Suggest the authors include some paragraphy state this part.

Response

We revised the third paragraph in the Results Section for further clarification. 

Please refer to the revised third paragraph in the Results section.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors addressed most of my concerns. One remaining comment is that the authors mention signal processing algorithms as something optional that "can enhance BER performance." However, DSP algorithms can be mandatory for certain ISLs, e.g., for timing recovery. I recommend that the authors emphasize an eventual need for DSP algorithms in these systems.

Author Response

Reviewer #1 
The authors would like to thank the reviewer for the consideration of our work. We have 
addressed your comments as discussed below. 
Comment #1 (R1C1) 
The authors addressed most of my concerns. One remaining comment is that the authors mention 
signal processing algorithms as something optional that "can enhance BER performance." However, 
DSP algorithms can be mandatory for certain ISLs, e.g., for timing recovery. I recommend that the 
authors emphasize an eventual need for DSP algorithms in these systems. 
Response 
Following the reviewer's suggestion, we have extended our discussion of DSP's role throughout the 
manuscript. We now explicitly state that DSP algorithms (including timing recovery and adaptive 
equalization) are mandatory for reliable operation in dynamic LEO environments, particularly for 
high-rate (>10 Gbps) links. 
Please refer to the changes made in the second paragraph of subsection 3.3.

Reviewer 2 Report

Comments and Suggestions for Authors

I am satisfied with the changes.

Author Response

Reviewer #2

We thank the reviewer for their valuable report.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper has been revised and I recommend publication.

Author Response

Reviewer #4

We thank the reviewer for their valuable report.