Deep-Unfolded Tikhonov-Regularized Conjugate Gradient Algorithm for MIMO Detection
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsUsing Tikhonov regularization with the complex conjugate gradient method in a deep learning-based approach for MIMO detection is an interesting work. Congratulations to the authors for their hard work Here are a few comments for helping their work to reach more audience.
1. Though a lot of work has been done, the organization of the paper needs improvement. A lot of redundant sentences were written in multiple sections conveying the same purpose. For example, when writing about linear MIMO, the advantages of the method were written in many sentences. Similarly, for each concept, there are more statements conveying the advantages. It may deviate the reader from the main focus of the paper. Concise writing will help focus on the proposed work.
2. The justification for using Tikhonov regularization with the complex conjugate gradient method for MIMO detection is missing in the introduction though written in section 3.1. Stating how the proposed work deviates from the existing work in achieving the goal and how the chosen technique helps to improve the performance will be interesting to read. Why use Tikhonov regularization, how does it help in detecting MIMO with reduced BER?
3. There is a typo in saying s in equation (2), is it x?
Comments on the Quality of English Language
The language looks okay. But there is more content. Concise writing will be interesting to read. Also, the organization of the contents needs improvement.
Author Response
We thank to the reviewer for the constructive comments.
The reviewer considers the work as an interesting study and has a few comments for helping the manuscript to reach more audience.
Our Response: We thank to the reviewer for the constructive comments. In the lights of the appreciated comments and feedbacks from the reviewer, we have revised the manuscript thoroughly.
Though a lot of work has been done, the organization of the paper needs improvement. A lot of redundant sentences were written in multiple sections conveying the same purpose. For example, when writing about linear MIMO, the advantages of the method were written in many sentences. Similarly, for each concept, there are more statements conveying the advantages. It may deviate the reader from the main focus of the paper. Concise writing will help focus on the proposed work.
Our Response: We have checked the manuscript and removed the redundant sentences. Also stated by another Reviewer, unnecessary sections and figures have been extracted from the manuscript. Section 2.3 is rewritten in a concise manner to help the reader catch the main focus of the manuscript. Redundant sentences in Section 1 and Section 3 are also removed to improve the quality of the manuscript.
The justification for using Tikhonov regularization with the complex conjugate gradient method for MIMO detection is missing in the introduction though written in section 3.1. Stating how the proposed work deviates from the existing work in achieving the goal and how the chosen technique
helps to improve the performance will be interesting to read. Why use Tikhonov regularization, how does it help in detecting MIMO with reduced BER?.
Our Response: At the end of the introduction section, we provide a relevant reference to explain how the proposed Tikhonov regularization improves the detection performance in general. We also add new sentences to explain how the proposed work differs from the existing CG and LCG methods in Section 3.1 before Fig. 3.
There is a typo in saying s in equation (2), is it x?
Our Response: It was mistakenly written and corrected in the revised version.
The language looks okay. But there is more content. Concise writing will be interesting to read. Also, the organization of the contents needs improvement.
Our Response: Section 2.3 is written in a concise manner. Redundant sentences and Figures are discarded from the entire manuscript. Therefore, organization of the manuscript is improved by fixing the unnecessary sections, redundant sentences, and figures.
Reviewer 2 Report
Comments and Suggestions for Authors1. The description of proposed DU-TCG algorithm (see Fig. 6) is not clear for readers. It should be done an accurate description of proposed DU-TCG algorithm in mathematical form with complete parameters caclculation. It is not clear, how to calculate L, alfa and beta. This description must provide to repeat simulation results.
2. Algorithm 2. Step 6 is not clear. Please explain in the text. Step 7 is absent. Step 9 is not clear. Please explain it carefully in the text.
3. Complexity analysis of proposed DU-TCG algorithm is absent. It should be done to compare it with complexity of known algorithms.
Author Response
We thank to the reviewer for the constructive comments.
- The description of proposed DU-TCG algorithm (see Fig. 6) is not clear for readers. It should be done an accurate description of proposed DU-TCG algorithm in mathematical form with complete parameters caclculation. It is not clear, how to calculate L, alfa and beta. This description must provide to repeat simulation results.
Our Response: Based on the Reviewer’s constructive comment, we inserted a new paragraph explaining in Section 3.1 before Fig. 3 explaining how the algorithm works and clarified the steps in Algorithm 2. The process of updating the values of L, alpha, and beta by training is explained in this new paragraph.
- Algorithm 2. Step 6 is not clear. Please explain in the text. Step 7 is absent. Step 9 is not clear. Please explain it carefully in the text.
Our Response: Missing Step 7 is fixed in the algorithm 2. Besides, according to the Reviewer’s constructive comment, a new paragraph is inserted to explain Step 6 and Step 9 in the manuscript after Figure 3.
Complexity analysis of proposed DU-TCG algorithm is absent. It should be done to compare it with complexity of known algorithms.
Our Response: In Section 4, which is added to the manuscript, we discuss the complexity analysis of the proposed DU-TCG algorithm and compare it with well-known algorithms.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe claimed contribution of this article is highlighted in p.3 as:
“This study presents a significant advance in the field of MIMO signal detection by introducing a unique detection strategy that combines Tikhonov regularization and CG method with deep unfolding”
Indeed this manuscript presents a well written and well explained mathematical formulation in section 2. However, the validation of the methodology in section 4 is carried out for non practical bit error rates (BER).
B. Specific Comments.
1. Some definitions although nicely given they are unnecessary repeated over and over again, e.g. the Tikhonov regularization given in p.10 is repeated in p.11. Every definition should be given only once in the most clarified way.
2. In p.3 it is claimed that “The matrix H and the vectors y, s, n have complex values, due to the necessity of using real numbers in the deep learning structure”. Following that expression (2) is given, but it is not explained how this is utilized then. This seems as a technique to handle vectors-matrices of complex numbers (signals with magnitude and phase) by doubling their dimensions. Explain how this approach is exploited and what complication is causing.
3. The most serious drawback of this article refers to the assumed BER for the numerical examples elaborated herein. Practical communication systems need a BER of the order of 10^(-9) with an SNR between 12 to 14 dB. Herein, in Fig. 7 to 11 a BER higher than 10^(-4) is considered, which renders the corresponding signal just useless.
4. Training according to section 3.2 is carried out for “The training process uses 5𝑥104 samples with an SNR of 25 dB”. This is also impractical, since it appears as trainining with perfect data, which may not be practically available.
5. The simulation results of section 4 are carried out for BPSK modulation. However, BPSK is far too simple especially for sub-6 GHz and terrestrial communications where MIMO is mostly exploited. Thus, the presented cases are misleading too simple.
Author Response
.
Author Response File: 
Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsPlease find the attached file for detailed comments.
Comments for author File: 
Comments.pdf
Author Response
We thank to the reviewer for the constructive comments.
The Reviewer has some comments and feedbacks on the manuscript before recommending for publication.
- It would be better to describe only the method used in this paper and briefly mention the existing methods for comparison. In particular, the content in sections 2.3 and 2.4.1 seems unnecessary.
Our Response: According to the comments of the Reviewer, Section 2.3 is rewritten in a concise manner. Discussion of the existing methods is limited with the CG and LCG methods as they are in the focus of the manuscript and the reader is referred to relevant literature for the well-known methods. Unnecessary figures and sentences are extracted from the manuscript in various sections in the entire manuscript.
- The advantages mentioned are difficult to intuitively grasp from the structure in Figure 4. If there isn’t a strong reason for including it, I recommend removing it. Also, it seems there are too many unnecessary images.
Our Response: We agree with the Reviewer #3’s comment. Figure 4 is redundant and doesn’t act as an illustrative and explanatory. Therefore, we removed Figure 4. Besides, Figure 2 and Figure 3, which are also considered as redundant, are discarded while revising Section 2.3.
- It is necessary to explain the reason for the poor performance at low SNR in Fig. 7. Additionally, to demonstrate performance improvement, you should highlight specific areas in the figure where this improvement is visible. Furthermore, to effectively show the measure of performance enhancement in Figs. 7, 10, 11, and 13, please indicate how many times the performance has improved by fixing either the y-axis or x-axis.
Our Response: A new explanation is inserted to the manuscript in order to explain the performance at low SNR in Figure 7 (now Fig. 4). Besides, we also modified Figure 11 (now Fig. 8) and Figure 13 (now Fig. 10) in order to show the performance enhancement by fixing BER and SNR values, respectively.
- It would be better to label what the x-axis represents in Fig. 12.
Our Response: We labelled the x-axis in Fig. 12.
- Parameters for simulation results needs to be clearly clarified like the number of layers.
Our Response: We provide the number of layers for different simulation scenarios in Section 3.2.
- There are too many repeating paragraphs in the manuscript. In addition, there are many basic presentation issues that must be corrected, such as inconsistent formatting, spacing errors.
Our Response: Narration was made more fluent with in-depth review of the grammar, spelling, and formatting in order to improve the clarity of the manuscript. We also removed the repeating paragraphs, redundant sections, and unnecessary Figures in the manuscript to improve the readability.
Presentation error instances:
- When using abbreviations, you should write out the full term the first time, and then use
the abbreviation afterward, but this is not being done consistently.
Our Response: The Reviewer is right. The manuscript was in-depth reviewed and the mentioned presentation errors were fixed.
- On Page 13, the content below Equation (13) seems more suitable for the conclusion section as it summarizes key points. It should be relocated accordingly.
Our Response: According to the Reviewer’s constructive comment, we relocated that paragraph to enhance the content of the Discussion section while summarizing the key points of the manuscript.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe description of proposed DU-TCG algorithm (see Algorithm 2) is still not clear for readers. It should be done an accurate description of proposed DU-TCG algorithm in mathematical form with complete parameters caclculation. It is not clear, how to calculate L, alfa and beta. This description doesn't let to repeat and verify presented simulation results.
Author Response
We thank to the reviewer for the constructive comments.
- The description of proposed DU-TCG algorithm (see Algorithm 2) is still not clear for readers. It should be done an accurate description of proposed DU-TCG algorithm in mathematical form with complete parameters caclculation. It is not clear, how to calculate L, alfa and beta. This description doesn't let to repeat and verify presented simulation results.
Our Response: We apologize for not being able to provide sufficient explanation for the Algorithm 2 to repeat the simulation results for readers. Now, we revised the paragraph in page 7 after equation (6) to make clear how the regularization matrix and regularization parameter is calculated. Besides, calculation of and is given in Algorithm 1. Since the proposed method is based on deep unfolding, updating these parameters do not consist of mathematical forms. Thus, updating these parameters is based on a training process which is performed by a learning process, as given by "train: AdamOptimizer(minimize(loss),parameters{α,β,L})". Besides, we inserted a new sentence to the paragraph after Algorithm 2 to make clear how the initilalization is done for these three parameters. After making the essential revisions to clarify the Algorithm 2 in the manuscript, we can assure that the issue of how to update the parameters and determine the initial values of the parameters with the deep learning approach instead of mathematical equations in Algorithm 2 has been clarified.
Reviewer 3 Report
Comments and Suggestions for AuthorsOnly the 1st out of my 5 previous comments and suggestions is adequately addressed.
Explicitly, the Authors use:
1) Impractical bit error vallues, unacceptably high BER of the order of 10^(-4), while it should be 10^(-9).
2) Use perfect but non-existent data to train the neural (AI) network with SNR around 25dB, while it should be around 12dB.
3) They study the BPSK case which is not utilized in the considered 5G sub-6 GHZ.
In their reply they refuse to correct the above. If their algorithm is correct, then it should be able to handle the realistic values I have suggested in my precious comments.
Author Response
Please find our response in the attached file.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors have addressed all my concerns, and I do not have further comments.
Author Response
We thank the Reviewer for valuable comments to improve the quality of the manuscript.
Round 3
Reviewer 2 Report
Comments and Suggestions for AuthorsI propose to give a reference to the description of AdamOptimizer in Algorith 2.
Author Response
We thank to the reviewer for the constructive comments.
- I propose to give a reference to the description of AdamOptimizer in Algorith 2.
Our Response: We added two references after Algorithm 2 for a detailed explanation of AdamOptimizer.
Reviewer 3 Report
Comments and Suggestions for AuthorsAlthough I’m not convinced by the Authors reply, I could find their reply sufficient provided that the corresponding changes would be done in the manuscript. Obviously, these comments are not for my information, thus they should be included in the paper. Replying only to the Reviewer without making any changes in the manuscript is completely unacceptable. Thus:
- The numerical experiment resulting to Fig.1 for the first comment (Impractical bit error values) should be included in the manuscript along with the appropriate discussion.
- The reasoning in answering of comments 2 (use of perfect data) and 3 (analyzing BPSK for sub-6 GHz) should also be included in the manuscript as a related discussion.
Author Response
Although I’m not convinced by the Authors reply, I could find their reply sufficient provided that the corresponding changes would be done in the manuscript. Obviously, these comments are not for my information, thus they should be included in the paper. Replying only to the Reviewer without making any changes in the manuscript is completely unacceptable. Thus:
The numerical experiment resulting to Fig.1 for the first comment (Impractical bit error values) should be included in the manuscript along with the appropriate discussion.
The reasoning in answering of comments 2 (use of perfect data) and 3 (analyzing BPSK for sub-6 GHz) should also be included in the manuscript as a related discussion.
Our Response: We agree with the Reviewer's concerns and we try to respond appropriately to all of the Reviewer's comments and suggestions.
We added a new paragraph after the discussion of Figure 7 in page 12 to explain not having lower bit error rates in the manuscript. We explained obtaining lower BER values is impractical with our current simulation setup as well as added references to state that our BER values are in line with the existing literature. We also inserted the Figure 1, given in the previous response, to improve the quality of the manuscript with a brief discussion of the importance of employing higher order modulation schemes.
A description of the validity of using high SNR values for training is also added to the manuscript in Section 3.2 by giving references.
Additionally, during the first revision in line with the comments of the other reviewers, we did not receive your evaluation. Consequently, when we submitted the first revision to the journal, we were unable to incorporate our responses to your comment. However, in the subsequent revision, we have addressed the necessary modifications in accordance with your feedback.
We would like to convey our sincere apologies for the inconvenience encountered by the reviewer.
Round 4
Reviewer 3 Report
Comments and Suggestions for AuthorsMy comments and concerns are adequately addressed.
Author Response
We thank to the reviewer for the constructive comment.
