Transmit Beampattern Design for Distributed Satellite Constellation Based on Space–Time–Frequency DoFs

Round 1

Reviewer 1 Report

Concern#1：

The decomposition of coherent integration efficiency seems somewhat tedious. Actually, by employing the Cauchy- Schwarz (CS) inequality, the range of coherent integration efficiency can be well described. Please redefine the range of coherent integration efficiency from this view.

Concern#2:

I recommend changing the paper title to “Transmit Beampattern Design for Distributed Satellite Constellation Based on Space-Time-Frequency Information”. Obviously the “Space- Time- Frequency Information” is necessary.

Concern#3:

Section 3, Step2:

Receiving and transmit signal ----> receive and transmit signal

Other definitions should also be consistent throughout the whole article. Please check the paper carefully.

Author Response

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Author Response File: Author Response.doc

Reviewer 2 Report

This manuscript proposes a transmit beampattern optimization method for dynamic coherent radar based on distributed satellite constellation. This study provided a coherent detection scheme solution for the swarm satellite systems, including evaluation results on synchronization error, beam pointing error, and high-speed motion characteristics based on numerical simulations. Before proceeding to publication stage, I encourage the authors to address my following comments:

1. [Line 149 and line 153] “the scattering point (k,l) can be expressed as ”

- Please define what k and l stand for respectively.

2. [Equation 26, line 235] “system synchronization error is represented by …”

- Do you take the relative orbit error into consideration for synchronization error?

3. [Line 324- 325] “Assume the constellation configuration is a 6*6 square array with an anti-collision distance of 50m, as shown in Figure 4.”

- In order to achieve your proposed distributed satellite constellation system, what formation orbit configuration do you implement? To maintain the fixed relative geometry, natural formation motion with elliptic relative orbit can be considered [1].

[1] Peng, Y.; Scales, W.; Esswein, M.; Hartinger, M. Small satellite formation flying simulation with multi-constellation GNSS and applications to future multi-scale space weather observations. In Proceedings of the ION GNSS+; Institute of Navigation: Miami, FL, USA, 2019; pp. 2035–2047 https://doi.org/10.33012/2019.16883

[2] Vallado DA (2001), Fundamentals of astrodynamics and applications, space technology library, 2nd edn. Kluwer, Dordrecht

4. [Figure 8- 11]. The font and embedded texts in these figures are too small to view.

Author Response

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Author Response File: Author Response.doc

Reviewer 3 Report

Major comments:

1. While I understand that modeling the satellites on a plane makes modeling easier, it is inaccurate (Fig. 1). The satellite constellation is always part of a sphere (orbit around Earth), hence I would like to see the authors to respond to this comment very carefully. If they are modeling the satellites to be on a sphere, please change Fig. 1 accordingly.

2. How does this optimization compare to the beamwidth link optimization in satellite constellations presented in: https://ieeexplore.ieee.org/abstract/document/9684552

3. Can the authors comment on the use of cartesian coordiantes? They certainly are more complicated than polar/spherical coordiantes and make the derivation more compact?

4. What is the altitude of the constellation used to derive the results? I recommend the authors provide a table that summarizes the different simulation parameters and why they chose these values.

Minor comments:

1. A pseudo code would help readers better undertstand the optimization technique deployed in the paper.

Author Response

Please see the attachment.

Author Response File: Author Response.doc