Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels
, Pietro Monsurrò *, Giuseppe Scotti, Pasquale Tommasino and Alessandro Trifiletti
Round 1
Reviewer 1 Report
This paper prunes the complexity of Volterra model for nonlinear calibration for an IF amplifer, by comparing (LASSO, DOMP, OBS) and their variants (WLASSO, OBD). A methdology to correct the linear and nonlinear errors seperately is presented. 6dB improvement in EVM is obtained. It shows that the OBS and DOMP outperform other 3 techniques, and these two combined together can yield better efficiency and higher accuracy. Overall, the paper is well presented and the experimental part is carefully designed to get the accurate EVM results. Two comments:
1. In Lines 43-44, it claims that OBS has never been used for pruing Volterra models, but some previous studies have investigated it:
Tian, Xiange, et al. "A method for measuring the robustness of diagnostic models for predicting the break size during LOCA." Annual Conference of the PHM Society. Vol. 9. No. 1. 2017.
Rubiolo, Mariano, Georgina Stegmayer, and D. Milone. "Compressing arrays of classifiers using Volterra-neural network: application to face recognition." Neural Computing and Applications 23.6 (2013): 1687-1701.
2. For figure 6 and 7, the y axis error: how many time/symbols do you use to calculate the average error?
Author Response
This paper prunes the complexity of Volterra model for nonlinear calibration for an IF amplifer, by comparing (LASSO, DOMP, OBS) and their variants (WLASSO, OBD). A methdology to correct the linear and nonlinear errors seperately is presented. 6dB improvement in EVM is obtained. It shows that the OBS and DOMP outperform other 3 techniques, and these two combined together can yield better efficiency and higher accuracy. Overall, the paper is well presented and the experimental part is carefully designed to get the accurate EVM results. Two comments:
We thank the reviewer for his kind comment.
- In Lines 43-44, it claims that OBS has never been used for pruing Volterra models, but some previous studies have investigated it:
Tian, Xiange, et al. "A method for measuring the robustness of diagnostic models for predicting the break size during LOCA." Annual Conference of the PHM Society. Vol. 9. No. 1. 2017.
Rubiolo, Mariano, Georgina Stegmayer, and D. Milone. "Compressing arrays of classifiers using Volterra-neural network: application to face recognition." Neural Computing and Applications 23.6 (2013): 1687-1701.
We have added these two works to the reference list, together with additional papers on OBS, on OBD, and other topics. There is of course a larger number of papers related to these topics, especially nonlinear calibration, but our focus is on pruning of Volterra networks, and most of the references we have added are related to pruning techniques.
We agree with the reviewer that Volterra kernels can be seen as a kind of neural network, as in Rubiolo’s paper. Hence, if OBS is a technique used for neural networks, it is applicable also to Volterra kernels, or even to linear regression models. Hence, we have modified the text of the paper accordingly. We notice however that Rubiolo’s paper doesn’t use OBS and OBD on Volterra models, but compares the proposed Volterra neural network with OBS and OBD pruning techniques in terms of accuracy and computational cost. We have updated the text.
- For figure 6 and 7, the y axis error: how many time/symbols do you use to calculate the average error?
The figures have been obtained with 3174 symbols, or equivalently 15870 samples. In Fig. 10, the x-axis shows the number of symbols used for training, and error is computed on the entirety of the 3174 symbols, also those not used for training. The text has been updated.
Reviewer 2 Report
The paper entitled "Methods for model complexity reduction for the nonlinear calibration of amplifiers using Volterra kernels" is well written. Presented research results are up to the academic standards. The paper has a lot of merit and should be recommended for publication, but after correcting some important issues from the point of view of the quality of "Electronics" journal.
1. I would like to suggest authors to extension of the introduction so that this section can fully present the current state of art.
2. I also propose to add nomenclature (description of used symbols and abbreviations) to improve the readability of the article.
3. Figures presented in the paper are not readable and make it difficult for the reader to precisely analyze the presented research results.
4. Although the topic and research results presented in the paper is current and interesting, the references section in the peer-revied paper is poor. The references section does not contain the current state of knowledge in the scope presented in the peer-revied paper, and a large part of the items in the references section is related to the authors of the peer-reviewed paper (a large proportion of self-citations).
Author Response
The paper entitled "Methods for model complexity reduction for the nonlinear calibration of amplifiers using Volterra kernels" is well written. Presented research results are up to the academic standards. The paper has a lot of merit and should be recommended for publication, but after correcting some important issues from the point of view of the quality of "Electronics" journal.
We thank the reviewer for his kind comments.
- I would like to suggest authors to extension of the introduction so that this section can fully present the current state of art.
We have extended the introduction to better describe the state of the art: references have been added, especially on pruning techniques, but also on nonlinear calibration of ADCs and transceivers, and nonlinear models. Though there are many more papers about ADC, mixer or power amplifier calibration, the focus of our paper is on pruning methods, so that we have avoided a complete summary of all the literature regarding nonlinear digital calibration of analog systems, while extending the references regarding model pruning.
- I also propose to add nomenclature (description of used symbols and abbreviations) to improve the readability of the article.
A Table has been added with the acronyms. The symbols have been more carefully explained in the text near the equations in which they are used.
- Figures presented in the paper are not readable and make it difficult for the reader to precisely analyze the presented research results.
We have enlarged the figures to improve their readability. Now the texts should be fairly readable.
- Although the topic and research results presented in the paper is current and interesting, the references section in the peer-revied paper is poor. The references section does not contain the current state of knowledge in the scope presented in the peer-revied paper, and a large part of the items in the references section is related to the authors of the peer-reviewed paper (a large proportion of self-citations).
We have extended the reference section by adding several papers. We have removed two self-citations [ex 8-9] which were not specifically related to nonlinear digital calibration, and added new ones, which are related to nonlinear ADC calibration, tranceiver calibration, and another example of nonlinear feedforward LIP model to which our methodology may be applied. We have preferred to avoid a detailed summary of the literature on nonlinear calibration of ADCs, power amplifiers, mixers, because the focus of our work is on pruning techniques. We have added several references about OBS and OBD pruning, which were directly related to our work.
Reviewer 3 Report
1- The abstract needs more interest and rewriting some paragraphs.
2- There are still some aspects that can be improved (for grammar and punctuations). Improve the technical writing of your paper, where there are several grammatical errors and spelling I think they need to be checked out.
3- The conclusion needs more efforts to elaborate the achieved results with respect to the future work,
4- The practical part is very important,
5- Future work is an important part of the conclusion.
Author Response
1- The abstract needs more interest and rewriting some paragraphs.
We have improved and extended the abstract.
2- There are still some aspects that can be improved (for grammar and punctuations). Improve the technical writing of your paper, where there are several grammatical errors and spelling I think they need to be checked out.
We have revised the paper and corrected several typos.
3- The conclusion needs more efforts to elaborate the achieved results with respect to the future work
We have added a paragraph about the topics related to this paper we wish to investigate in the future, and summarized the results of our work more clearly in the conclusion.
4- The practical part is very important,
We thank the reviewer for his kind comment.
5- Future work is an important part of the conclusion.
We have added a paragraph about the topics related to this paper we wish to investigate in the future.
Round 2
Reviewer 2 Report
I think that the paper in its current form can be published in Electronics journal.
