A Low-Complexity Channel Estimation Based on a Least-Squares Algorithm in OFDM Systems
Round 1
Reviewer 1 Report
- Results are limited. Only BER simulations are considered in different speeds/scenarios. Can more parameters be considered?
- What tool/software was used for simulations?
- Concept of virtual odd pilot subcarriers can be explained in more details.
- Avoid 'If' and 'let' in same sentence; example: "If the time-varying channel is approximately invariant in an OFDM symbol, let the digital CIR corresponding to some OFDM symbol be h[n] " and couple of more places. If and then can be used.
- Comb type pilot arrangement should be clearly explained.
- What happens when maximum delay points of a channel is larger than half the number of pilots ?
- Block arrangement, comb arrangement, and scattered arrangement can be explained in a sentence or so. They appear random in introduction.
- In introduction why authors write "pi-lots'?
- Novelty and contributions are limited.
Author Response
Response to Reviewer 1 Comments
We would like to thank the Reviewer #1 for providing useful insights to our work. We have addressed all the concerns in a systematic manner. A detailed description has been added in the manuscript upon the requirements.
Point 1: Results are limited. Only BER simulations are considered in different speeds/scenarios. Can more parameters be considered?
Response 1: Thanks for your valuable comment and recommendation. We have added another channel model for simulation. This channel model is shown in table 5 and simulation results are shown in figure 5 in the manuscript.
Point 2: What tool/software was used for simulations?
Response 2: Thanks for your valuable comment and recommendation. All simulations were performed using MATLAB software.
Point 3: Concept of virtual odd pilot subcarriers can be explained in more details.
Response 3: Agreed and amended accordingly. More detailed descriptions for estimating CFRs at virtual odd pilot subcarriers have been added to the manuscript. Please see lines 149-158 in the manuscript.
Point 4: Avoid 'If' and 'let' in same sentence; example: "If the time-varying channel is approximately invariant in an OFDM symbol, let the digital CIR corresponding to some OFDM symbol be h[n] " and couple of more places. If and then can be used.
Response 4: Agreed and amended accordingly. We have rewritten this sentence as follows: “When the time-varying channel is approximately invariant in an OFDM symbol, the digital CIR corresponding to some OFDM symbols will be set to h[n].”
Point 5: Comb type pilot arrangement should be clearly explained.
Response 5: Agreed and amended accordingly. We have included a description of the comb-type arrangement in the manuscript. Please lines 32-33 in the manuscript.
Point 6: What happens when maximum delay points of a channel is larger than half the number of pilots ?
Response 6: Thanks for your valuable comment and recommendation. We have added another channel model for simulation. The number of maximum channel delay points is larger than half the number of pilots in this channel model. Simulation results are shown in figure 5. The channel estimation efficiency of our proposed method is still close to those of LS methods [10,11], even if the number of maximum channel delay points is greater than half the number of pilots.
Point 7: Block arrangement, comb arrangement, and scattered arrangement can be explained in a sentence or so. They appear random in introduction.
Response 7: Agreed and amended accordingly. We have included descriptions of comb-type , block-type and scattered-pilot arrangements in the manuscript. Please see lines 32-37 in the manuscript.
Point 8: In introduction why authors write "pi-lots'?
Response 8: Thanks for your valuable comment and recommendation. We found only one "pi-lots" in introduction. “Word” automatically breaks the “pilots” at a space or a hyphen at the end of a line. I don't know if the "pi-lots" you are seeing is different in the manuscript.
Point 9: Novelty and contributions are limited.
Response 9: Thanks for your valuable comment and recommendation.
- The CFRs at odd pilot subcarriers and the CFRs at even pilot subcarriers are related if the number of maximum channel delay points is smaller than or equal to half the number of pilots (including virtual pilot). According to this correlation, we propose a low-complexity LS method to estimate the CFRs at virtual even and odd pilot subcarriers respectively. The adverse effect of unknown CFRs at virtual pilot subcarriers for the con-ventional DFT channel estimation can be solved to enhance the channel estimation effectiveness of DFT channel estimation.
- While the channel estimation effectiveness of the proposed method is very similar to that of the LS method, it is noteworthy that the former’s computational complexity is much lower than that of the LS method [11]. The proposed method does not need to know the statistical properties of the channel or insert extra pilots as with some estimation methods.
- The channel estimation efficiency of our proposed method is still close to that of LS method [10,11], even if the number of maximum channel delay points is greater than half the number of pilots.
- Therefore, the low-complexity method proposed in this paper is very suitable for equalizer hardware implementation.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors proposed a low-complexity least square method to estimate the channel frequency responses at virtual pilot subcarriers when the number of maximum channel delay points is smaller than or equal to half the number of pilots (including virtual pilot). It is a well-structured paper with interesting results. However, it requires further improvements before publication.
- The abstract should be rewritten to reflect the significance of the proposed work. The current abstract shows a lot of background information.
- In the abstract section, I would suggest that the author should provide to the point and quantitative advantages of the proposed method.
- The main contributions of this paper should be further summarized and clearly demonstrated.
- The method/approach in the context of the proposed work should be written in detail.
- To explore Comparative results with existing approaches/methods relating to the proposed work.
- Some new references should be added to improve the reviews the literatures. For example, 10.1109/TCYB.2020.3033005; 10.1007/s12559-021-09871-4; 10.1016/j.ins.2021.11.052 and so on.
- In page 3, ‘the mathematical expression is as follows’->‘the mathematical expression is given as follows’, …..
- The authors need to interpret the meanings of the variables.
- Please add the contents of Author Contributions, Institutional Review Board Statement, Informed Consent Statement, Data Availability Statement and Conflicts of Interest.
Author Response
Response to Reviewer 2 Comments
We would like to thank the Reviewer #2 for providing useful insights to our work. We have addressed all the concerns in a systematic manner. A detailed description has been added in the manuscript upon the requirements.
Point 1: The abstract should be rewritten to reflect the significance of the proposed work. The current abstract shows a lot of background information.
Response 1: Agreed and amended accordingly. The abstract has been modified accordingly in the manuscript.
Point 2: In the abstract section, I would suggest that the author should provide to the point and quantitative advantages of the proposed method.
Response 2: Agreed and amended accordingly. The abstract has been modified accordingly in the manuscript.
Point 3: The main contributions of this paper should be further summarized and clearly demonstrated.
Response 3: Agreed and amended accordingly. The abstract and conclusion has been modified accordlingly in the manuscript.
Point 4: The method/approach in the context of the proposed work should be written in detail.
Response 4: Agreed and amended accordingly. The whole procedure of the proposed method in every OFDM symbol was organized as lines 179-188 in the manuscript.
Point 5: To explore Comparative results with existing approaches/methods relating to the proposed work.
Response 5: Agreed and amended accordingly. The method proposed in [10] is added to the BER simulations and the simulation results of [10] are shown in figures 2 to 5 in the manuscript.
Point 6: Some new references should be added to improve the reviews the literatures. For example, 10.1109/TCYB.2020.3033005; 10.1007/s12559-021-09871-4; 10.1016/j.ins.2021.11.052 and so on.
Response 6: Agreed and amended accordingly. We have cited related papers, as [17], [21] and [22] in the manuscript.
Point 7: In page 3, ‘the mathematical expression is as follows’->‘the mathematical expression is given as follows’, …..
Response 7: Agreed and amended accordingly. It has been modified accordingly in the manuscript.
Point 8: The authors need to interpret the meanings of the variables.
Response 8: Thanks for your valuable comment and recommendation. Related parameters of pilot arrangement wear described in table 1 and simulation parameters were described in table 2 in the manuscript.
Point 9: Please add the contents of Author Contributions, Institutional Review Board Statement, Informed Consent Statement, Data Availability Statement and Conflicts of Interest.
Response 9: Agreed and amended accordingly. All of these have been added to the manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper proposed a low complexity solution however this is a well studied area of research and considering a special case to proposed a solution may not be sufficient for publication. I would suggest to submit this work in a letter format and this will be more valuable for readers. Most of research is moving forward towards 6G so it is important to highlight that if proposed solution is really have a impact/application in future wireless networks.
Author Response
Response to Reviewer 3 Comments
We would like to thank the Reviewer #3 for providing useful insights to our work. We have addressed all the concerns in a systematic manner. A detailed description has been added in the manuscript upon the requirements.
Point 1: The paper proposed a low complexity solution however this is a well studied area of research and considering a special case to proposed a solution may not be sufficient for publication. I would suggest to submit this work in a letter format and this will be more valuable for readers. Most of research is moving forward towards 6G so it is important to highlight that if proposed solution is really have a impact/application in future wireless networks.
Response 1: Thanks for your valuable comment and recommendation. We agree to change the format of this paper from communication to letter.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
According to the revised paper, I have appreciated the deep revision of the contents and the present form of this manuscript. There is little content, which need be revised according to the comment of reviewer in order to meet the requirements of publish. A number of concerns listed as follows:
(1) The authors need to interpret the meanings of the variables.
(2) Please highlight your contributions in introduction.
(3) The abstract should be rewritten to reflect the significance of the proposed work. The current abstract shows a lot of background information.
(4) Conclusion: What are the advantages and disadvantages of this study compared to the existing studies in this area?
(5) The inspiration of your work must further be highlighted. Some suggested recent literatures should add.
(6) Correct typological mistakes and mathematical errors.
Author Response
We would like to thank the Reviewer #2 for providing useful insights to our work. We have addressed all the concerns in a systematic manner. A detailed description has been added in the manuscript upon the requirements.
Point 1: The authors need to interpret the meanings of the variables.
Response 1: Agreed and amended accordingly. We have added table 2 to interpret the meanings of the variables in the manuscript. The variables n and k are described in lines 84 and 86 respectively.
Point 2: Please highlight your contributions in introduction.
Response 2: Agreed and amended accordingly. New content has been added to the introduction as follows: “The channel estimation efficiency of our proposed method is still similar to that of LS method, even if the number of maximum channel delay points is greater than half the number of pilots”. Please see lines 71-73 in the manuscript.
Point 3: The abstract should be rewritten to reflect the significance of the proposed work. The current abstract shows a lot of background information.
Response 3: Agreed and amended accordingly. The first three sentences in the abstract have been rewritten as follows: “As the channel frequency responses (CFRs) at virtual pilot subcarriers are assumed to be zero, the estimated CFRs will have a leakage effect for discrete Fourier transform (DFT)-based channel estimation in OFDM systems. The CFRs at odd pilot subcarriers and even pilot subcarriers are related if the number of maximum channel delay points is smaller than or equal to half the number of pilots (including virtual pilot).” Please see lines 9-13 in the manuscript.
Point 4: Conclusion: What are the advantages and disadvantages of this study compared to the existing studies in this area?
Response 4: Thanks for your valuable comment and recommendation. The conclusion section has been modified accordlingly. Lines 317-328 and 329-332 show the advantages and disadvantages of this study compared to the existing studies in this area respectively.
Point 5: The inspiration of your work must further be highlighted. Some suggested recent literatures should add.
Response 5: Agreed and amended accordingly. We have added the three suggested recent literatures [23-25] in the manuscript.
1.10.1109/TCYB.2020.3033005:
23. E. Q. Wu, M. Zhou, D. Hu, L. Zhu, Z. Tang, X.-Y. Qiu, P.-Y. Deng, L.-M. Zhu and H. Ren. Self-Paced Dynamic Infinite Mixture Model for Fatigue Evaluation of Pilots' Brains, IEEE Trans. Cybern., 2020, accepted for future publication.
2. 10.1016/j.ins.2021.11.052:
24. W. Deng, X. Zhang, Y. Zhou, Y. Liu, X. Zhou, H. Chen and H. Zhao. An enhanced fast non-dominated solution sorting genetic algorithm for multi-objective problems, Inf. Sci., Mar. 2022. vol. 585, pp. 441–453.
3. 10.1007/s12559-021-09871-4:
25. Z.-H. Zhang, F. Min, G.-S. Chen, S.-P. Shen, Z.-C. Wen and X.-B. Zhou. Tri-Partition State Alphabet-Based Sequential Pattern for Multivariate Time Series, Cognit. Comput., May 2021, vol. 18, no. 12, pp. 1–19.
Point 6: Correct typological mistakes and mathematical errors.
Response 6: Agreed and amended accordingly. We have corrected some typological mistakes and mathematical errors in the manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
Thanks for improving the paper, I would suggest to consider this letter for publication in current state.
Author Response
We would like to thank the Reviewer #3 for providing useful insights to our work. We have addressed all the concerns in a systematic manner. A detailed description has been added in the manuscript upon the requirements.
Point 1: Thanks for improving the paper, I would suggest to consider this letter for publication in current state.
Response 1: Thanks for your valuable comment and recommendation. We have changed the format of this paper from communication to letter.
Author Response File: 
Author Response.docx
Round 3
Reviewer 2 Report
This paper can be accepted now.
