Statistical Beamforming Techniques for Power Domain NOMA System
Round 1
Reviewer 1 Report
Comment 1: The paper studies multi-antenna NOMA, which has been shown to be an inefficient strategy in multi-antenna networks [Ref 1]. However, [Ref 1] is not discussed in the work.
[Ref 1] B. Clerckx, Y. Mao, R. Schober, E. Jorswieck, D. J. Love, J. Yuan, L. Hanzo, G. Y. Li, E. G. Larsson, and G. Caire., "Is NOMA efficient in multi-antenna networks? A critical look at next generation multiple access techniques," in IEEE Open Journal of the Communications Society, vol. 2, pp. 1310-1343, 2021.
Comment 2: There is no novelty in the system model, only the simplest two-user power-domain NOMA is considered, which has been widely studied.
Comment 3: The system model is unclear, the paper cited [13] and omitted the explanation of many notations, making the mathematical notations unclear. i.e., in Equation (7) why matrix A is a subscript of a l2-norm?
Comment 4: It is unclear how the formulated optimization problems are solved in detail. There is no technical contributions in the current paper.
Author Response
Reviewer #1:
Comment 1: The paper studies multi-antenna NOMA, which has been shown to be an inefficient strategy in multi-antenna networks [Ref 1]. However, [Ref 1] is not discussed in the work.
[Ref 1] B. Clerckx, Y. Mao, R. Schober, E. Jorswieck, D. J. Love, J. Yuan, L. Hanzo, G. Y. Li, E. G. Larsson, and G. Caire., "Is NOMA efficient in multi-antenna networks? A critical look at next generation multiple access techniques," in IEEE Open Journal of the Communications Society, vol. 2, pp. 1310-1343, 2021.
Our Response: We thank the reviewer for mentioning this point. We have now included this reference (as reference [10]) in the revised manuscript.
Comment 2: There is no novelty in the system model, only the simplest two-user power-domain NOMA is considered, which has been widely studied.
Our Response: We thank the reviewer for mentioning this issue. We have now revised the whole derivation to include general scenario of any number of users which can be observed in Equations (1)-(14). Now, we have not only modified the system for multiuser scenario but also derived the outage probabilities for this general scenario. Moreover, we have also developed the two beamforming optimization algorithms for this general scenario as can be found in Equs. (15) and (17). Although our proposed solution is valid for any number of users in the NOMA system, we present the results for two users only to show the proof of concept. However, the results can be obtained for any number of users with the provided expressions.
Comment 3: The system model is unclear, the paper cited [13] and omitted the explanation of many notations, making the mathematical notations unclear. i.e., in Equation (7) why matrix A is a subscript of a l2-norm?
Our Response: We thank the reviewer for highlighting this point. We have now included more details (see Equs. (6)-(9)) and the definitions of notations such as weighted l2-norm (see the paragraph after Equ. (9))
Comment 4: It is unclear how the formulated optimization problems are solved in detail. There is no technical contributions in the current paper.
Our Response:
We have mentioned in the Sections 2.3.1 and 2.3.2 that we have used Active Set (AS) optimization and Sequential Quadratic Programming (SQP) methods to solve the proposed constraint optimization tasks. These are well known optimization techniques which are standard techniques in the field of optimization. For readers we have now added more references for these methods (see [16-18] in the revised draft). Regarding technical contribution, we did not claim to develop optimization method. Our major contribution is the development of statistical CSI based algorithm using closed form expressions of various outage probabilities. Our contributions are detailed in the last paragraph of Section 1.
Reviewer 2 Report
The paper Statistical beamforming techniques for Power Domain NOMA system is focused on Power-domain Non-orthogonal multiple access technique in combination with beamforming possibilities. The solution proposed in this article is based on channel statistical information in order to reduce the transmission overhead. The paper contains theoretical formulation and derivation as well as results of simulations.
First, the paper is well organized and written in right format. Its length and organization is appropriate and the paper is technically sound. However, I recommend to perform various language corrections and proofreading in order to increase the language level. I was able to notice various typos and mistakes in the text.
Next, the authors used just one power scheme (user location) based on Pw = 0.2 and Pv = 0.8. I recommend to include some deep analysis of power distribution as well as some example using more than just 2 users.
Author Response
Reviewer #2:
Comment 1: First, the paper is well organized and written in right format. Its length and organization is appropriate and the paper is technically sound. However, I recommend to perform various language corrections and proofreading in order to increase the language level. I was able to notice various typos and mistakes in the text.
Our Response: We thank the reviewer for these comments. We have now revised the draft to improve its writing.
Comment 2: Next, the authors used just one power scheme (user location) based on Pw = 0.2 and Pv = 0.8. I recommend to include some deep analysis of power distribution as well as some example using more than just 2 users.
Our Response: We thank the reviewer for this comment. We have now revised the whole derivation to include general scenario of any number of users which can be observed in Equations (1)-(14). Now, we have not only modified the system for multiuser scenario but also derived the outage probabilities for this general scenario. Moreover, we have also developed the two beamforming optimization algorithms for this general scenario as can be found in Equs. (15) and (17). Although our proposed solution is valid for any number of users in the NOMA system, we present the results for two users only to show the proof of concept. However, the results can be obtained for any number of users with the provided expressions.
Reviewer 3 Report
The authors propose a reduced complexity beamforming technique to support a power-domain NOMA (PD-NOMA) scheme employing SIC receivers. The main idea is to relax on the CSI requirements at the BS, and consider only a statistical knowledge of the channel (avoiding the overhead required for an operation based on full-CSI).
In my opinion, the idea is interesting and the results show the benefits of the proposed TX precoding, especially in terms of the outage probability for near and far users.
As a suggestion, I think that it will be interesting to analyze scenarios with more than 2 users in the NOMA environment and see the corresponding complexity increase of the SIC chain. Moreover, a complexity comparison with other state-of-the-art precoding designs will be a plus.
In general, the presentation is good, although the figures' size is too small.
If the paper is accepted, the authors should not neglect previous works on the same field. Note that the idea of SIC PD-NOMA is not new and some references regarding prior works should be considered, for instance:
[A] F. Ribeiro, J. Guerreiro, R. Dinis, F. Cercas, D. Jayakody, Multi-user detection for the downlink of NOMA systems with multi-antenna schemes and power-efficient amplifiers, Physical Communication, Vol. 33, No. April 2019, pp. 199 - 205, April, 2019
[B] A. Kassir, R. A. Dziyauddin, H. M. Kaidi and M. A. Mohd Izhar, "Power Domain Non Orthogonal Multiple Access: A Review," 2018 2nd International Conference on Telematics and Future Generation Networks (TAFGEN), 2018.
[C] J. Guerreiro, R. Dinis, P. Carvalho, M. Silva, Nonlinear Effects in NOMA Signals: Performance Evaluation and Receiver Design, IEEE Vehicular Technology Conf. - VTC-Fall, Waikoloa, HI, United States, September, 2019
Author Response
Reviewer #3:
Comment 1: In my opinion, the idea is interesting and the results show the benefits of the proposed TX precoding, especially in terms of the outage probability for near and far users.
Our Response: We thank the reviewer for these comments and the efforts to review the manuscript.
Comment 2: As a suggestion, I think that it will be interesting to analyze scenarios with more than 2 users in the NOMA environment and see the corresponding complexity increase of the SIC chain. Moreover, a complexity comparison with other state-of-the-art precoding designs will be a plus.
Our Response: We thank the reviewer for this comment. We have now revised the whole derivation to include general scenario of any number of users which can be observed in Equations (1)-(14). Now, we have not only modified the system for multiuser scenario but also derived the outage probabilities for this general scenario. Moreover, we have also developed the two beamforming optimization algorithms for this general scenario as can be found in Equs. (15) and (17). Although our proposed solution is valid for any number of users in the NOMA system, we present the results for two users only to show the proof of concept. However, the results can be obtained for any number of users with the provided expressions. In regards to computational complexity, it has been mentioned in the last paragraph of the Section 1 that the proposed method has lesser computational complexity as it does not require the channel estimation. Hence, both the computational complexity and the spectral efficiency of the proposed methods are better than that of the existing methods.
Comment 3:
If the paper is accepted, the authors should not neglect previous works on the same field. Note that the idea of SIC PD-NOMA is not new and some references regarding prior works should be considered, for instance:
[A] F. Ribeiro, J. Guerreiro, R. Dinis, F. Cercas, D. Jayakody, Multi-user detection for the downlink of NOMA systems with multi-antenna schemes and power-efficient amplifiers, Physical Communication, Vol. 33, No. April 2019, pp. 199 - 205, April, 2019
[B] A. Kassir, R. A. Dziyauddin, H. M. Kaidi and M. A. Mohd Izhar, "Power Domain Non Orthogonal Multiple Access: A Review," 2018 2nd International Conference on Telematics and Future Generation Networks (TAFGEN), 2018.
[C] J. Guerreiro, R. Dinis, P. Carvalho, M. Silva, Nonlinear Effects in NOMA Signals: Performance Evaluation and Receiver Design, IEEE Vehicular Technology Conf. - VTC-Fall, Waikoloa, HI, United States, September, 2019.
Our Response: We thank the reviewer for this comment. We have now included these references as [11]-[13] in the revised manuscript.
Round 2
Reviewer 1 Report
The comments of the reviewer are not well addressed.
1. Even though there are many standard optimization algorithms, but they are for convex problems. How to approximate the non-convex problem to a convex one should be carefully designed. This has been investigated in a wide range of beamforming works. For different optimization problem, the approximation algorithm should be uniquely designed, same for (15).
2. The novelty is still limited. The system model is still outdated, the outage probability has been derived in existing works while the beamforming design is still unclear.
3. The reason the reviewer mentioned [10] is to highlight the system model used in the paper is not efficient, and rate-splitting, multi-user linear precoding should be considered as baseline schemes. [10] is discussed inappropriately in the paper.
Author Response
Please see the attached file
Author Response File: 
Author Response.pdf
Reviewer 2 Report
All my queries and questions were successfully addressed, I recommend to accept the paper.
Author Response
We thanks the reviewer for his time and efforts. We have tried to improve the English Language in the revised submission.
