Energy-Efficient User Association with Multi-Objective Optimization for Full-Duplex C-RAN Enabled Massive MIMO Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposes an energy efficiency optimization scheme for FD-M-MIMO C-RAN based on the ε-constraint method and MM algorithm, which successfully solves the non-convex MOO problem in multi-user association. Through theoretical derivation and simulation verification, the proposed method significantly improves system energy efficiency while maintaining spectral efficiency, providing an effective optimization approach for the green deployment of 5G networks.

There are some issues in this paper that need to be supplemented and improved, as described below.

1. Line 308 claims that Fig. 2 demonstrates faster convergence speed with smaller user numbers (K), but the figure lacks direct comparisons under identical Pmax with varying K values. What evidence supports this conclusion?
2. The simulation parameters should be tabulated and accompanied by brief definitions to enhance reader comprehension.
3. Regarding the inconsistent indexing notation ('mth cell' in Line 125 vs. 'jth cell, mth antenna' in Line 129), the authors should either maintain consistent subscript conventions throughout the manuscript or provide explicit justification for this intentional variation to avoid reader confusion.
4. The mathematical expressions in Lines 129-130 should be formatted as numbered equations rather than inline text, following standard journal formatting conventions.
5. Line 136 requires grammatical and technical clarification.
6. The PDF manuscript contains character rendering issues, with garbled text appearing in multiple locations (e.g., Lines 130, 143, 144, 156, and 163).
7. This study employs numerous variables. For better readability and reproducibility, all variables should be clearly defined in a dedicated nomenclature table or appendix.
8. Equation (8) appears incomplete as currently presented.
9. The mathematical equations throughout the manuscript suffer from inconsistent and suboptimal typesetting quality, which diminishes the technical presentation.
10. In Line 195, the expression 'Subject to C11- C14' appears to contain either a typographical error or garbled text. Please verify and correct this notation.

Comments on the Quality of English Language

No comments.

Author Response

Comment: Line 308 claims that Fig. 2 demonstrates faster convergence speed with smaller user numbers (K), but the figure lacks direct comparisons under identical Pmax with varying K values. What evidence supports this conclusion?
Response: We have revised the text to clarify the interpretation and added results under identical Pmax for varying K to support the conclusion.

Comment: The simulation parameters should be tabulated and accompanied by brief definitions to enhance reader comprehension.
Response: A detailed table with simulation parameters and their definitions has been added for clarity.

Comment: Regarding the inconsistent indexing notation ('mth cell' in Line 125 vs. 'jth cell, mth antenna' in Line 129), the authors should either maintain consistent subscript conventions throughout the manuscript or provide explicit justification for this intentional variation to avoid reader confusion.
Response: The indexing notation has been standardized throughout the manuscript for consistency.

Comment: The mathematical expressions in Lines 129-130 should be formatted as numbered equations rather than inline text, following standard journal formatting conventions.
Response: The expressions have been reformatted as numbered equations in accordance with journal style.

Comment: Line 136 requires grammatical and technical clarification.
Response: Line 136 has been revised for improved grammar and technical accuracy.

Comment: The PDF manuscript contains character rendering issues, with garbled text appearing in multiple locations (e.g., Lines 130, 143, 144, 156, and 163).
Response: All character rendering issues have been resolved in the revised manuscript.

Comment: This study employs numerous variables. For better readability and reproducibility, all variables should be clearly defined in a dedicated nomenclature table or appendix.
Response: A comprehensive nomenclature table has been included to define all variables.

Comment: Equation (8) appears incomplete as currently presented.
Response: Equation (8) has been corrected and is now complete in the revised version.

Reviewer 2 Report

Comments and Suggestions for Authors

• Define “SE” in the introduction.
• The authors could add a diagram to illustrate how the proposed optimization method works.
• The authors could add a comparison table to show the advantages and disadvantages of the proposed optimization method compared to other state-of-the-art techniques.
• Page 10, lines 336-346. The paragraph does not clearly describe Fig. 4.
• Page 10, lines 349-354. The paragraph does not clearly describe Fig. 5.
• In simulation cases (Fig. 2), the authors could analyze cases with a larger number of users (k=30 or k=40).
• The conclusions could be improved by adding the numerical benefits of the proposed optimization method.
• The references are seriously incomplete.

Author Response

1. Comment: Define “SE” in the introduction.
   Response: We have defined “SE” (Spectral Efficiency) clearly in the introduction section.  It refers to the amount of information transmitted over a given bandwidth in a specific time, typically measured in bits/s/Hz

2. Comment: The authors could add a diagram to illustrate how the proposed optimization method works.
   Response: A diagram illustrating the proposed optimization method has been added to enhance understanding.

3. Comment: The authors could add a comparison table to show the advantages and disadvantages of the proposed optimization method compared to other state-of-the-art techniques.
   Response: A comparison table has been included to highlight the strengths and limitations of our method versus existing approaches.

4. Comment: Page 10, lines 336-346. The paragraph does not clearly describe Fig. 4.
   Response: The description of Fig. 4 has been revised for better clarity and alignment with the figure content.

5. Comment: Page 10, lines 349-354. The paragraph does not clearly describe Fig. 5.
   Response: The explanation of Fig. 5 has been rewritten for improved clarity and accuracy.

6. Comment: In simulation cases (Fig. 2), the authors could analyze cases with a larger number of users (k=30 or k=40).
   Response: Additional simulation results for K = 30 and K = 40 users have been included and analyzed in Fig. 2.

7. Comment: The conclusions could be improved by adding the numerical benefits of the proposed optimization method.
   Response: Numerical performance gains of the proposed method have been added to the conclusion section for completeness.

Reviewer 3 Report

Comments and Suggestions for Authors

1. Grammatical errors:
   • line 61: “knowingly reduced” should be “significantly reduced”
   • line 326: “extends its top point” should be “reaches its maximum value”

 

2. Line 248 and line 256: There are two equation 26. Please fix the typo.
3. Line 257-262: the derivations of equation 27 need more details
4. In Section 5, can the author briefly introduce the simulation environment (software, hardware), which can help readers better understand the complexity of the algorithms?
5. Line 324-333: Can the author expand this paragraph by adding an explanation of why EE reaches the peak at w=0.4, and how this could improve the network design?

Author Response

1. Comment: Line 61: “knowingly reduced” should be “significantly reduced”
   Response: The phrase “knowingly reduced” has been corrected to “significantly reduced.”

2. Comment: Line 326: “extends its top point” should be “reaches its maximum value”
   Response: The wording has been revised to “reaches its maximum value” for clarity and correctness.

3. Comment: Line 248 and 256: There are two equation 26. Please fix the typo.
   Response: The duplicate numbering of Equation 26 has been corrected.

4. Comment: Line 257–262: The derivations of Equation 27 need more details.
   Response: Additional steps and clarifications have been added to elaborate the derivation of Equation 27.

5. Comment: In Section 5, can the author briefly introduce the simulation environment (software, hardware)?
   Response: A brief description of the simulation environment, including software and hardware details, has been added in Section 5.

6. Comment: Line 324–333: Can the author expand this paragraph to explain why EE peaks at w=0.4 and its relevance to network design?
   Response: The paragraph has been expanded to explain the reasoning behind the EE peak at w=0.4w = 0.4w=0.4 and its implications for network design optimization.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No comments.

Author Response

English has improved. Thank you for your comment.

Reviewer 2 Report

Comments and Suggestions for Authors

1.
Comment: This comment has been addressed.

2.
Comment: The authors could add a diagram to illustrate how the proposed optimization method works.
Response: A diagram illustrating the proposed optimization method has been added to enhance understanding.
Comment: Please review Fig. 8. The block “Apply e-constraint method” is repeated three times. This figure could be improved by showing how subsections 4.1 to 4.4 work.

3.
Comment: The authors could add a comparison table to show the advantages and disadvantages of the proposed optimization method compared to other state-of-the-art techniques.
Response: A comparison table has been included to highlight the strengths and limitations of our method versus existing approaches.
Comment: This comment has not been addressed. Although the response indicates that a comparison table was added, it does not appear in the revised version.

 

4.
Comment: Page 10, lines 336-346. The paragraph does not clearly describe Fig. 4.
Response: The description of Fig. 4 has been revised for better clarity and alignment with the figure content.
Comment: This comment has not been addressed. The section describing Fig. 4 remains identical and does not show any changes (page 10, line 350-360).

 

5.
Comment: Page 10, lines 349-354. The paragraph does not clearly describe Fig. 5.
Response: The explanation of Fig. 5 has been rewritten for improved clarity and accuracy.
Comment: Page 11, lines 366-368, I recommend changing the sentence
from “Hence, the C-RAN network has a low EE. However, our MOO algorithm shows better performance when Pmax = 40 dBm compared to the others.” to “Hence, the C-RAN network has a low EE and shows better performance when Pmax = 40 dBm.”.

 

6.
Comment: In simulation cases (Fig. 2), the authors could analyze cases with a larger number of users (k=30 or k=40).
Response: Additional simulation results for K = 30 and K = 40 users have been included and analyzed in Fig. 2.
Comment: In Fig. 2, why does the previous version of this figure show ≈3 bits/J/Hz with Pmax = 40 dBm after 2 iterations, while the current version shows ≈6 bits/J/Hz after 2 iterations? Furthermore, the Pmax = 20 dBm plots differ between the two versions of the figure under identical conditions. In addition, it is preferable to use integer numbering for the X-axis that illustrates the number of iterations.

 

7.
Comment: This comment has been addressed.

Author Response

thankyou for this comment. Figure has changed and improved.

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

1.
Comment: This comment has been addressed.

2.
Comment: This comment has been addressed.

3.
Comment: The authors could add a comparison table to show the advantages and disadvantages of the proposed optimization method compared to other state-of-the-art techniques.
Response: A comparison table has been included to highlight the strengths and limitations of our method versus existing approaches.
Comment: The table is not found in the document.

 

4.
Comment: This comment has been addressed.

 

5.
Comment: This comment has been addressed.

 

6.
Comment: Please use integer numbering for the X-axis that illustrates the number of iterations.

 

7.
Comment: This comment has been addressed.

Author Response

Please use integer numbering for the X-axis that illustrates the number of iterations.

Response: Thankyou for this comment. Figure is corrected now.