A New Low PAPR Modulation Scheme for 6G: Offset Rotation Interpolation Modulation

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

This paper introduces a new low-PAPR modulation scheme for 6G, termed Offset Rotation Interpolation Modulation (ORIM). Building on the authors’ earlier work with the (1+D) π/2(1+D)\, \pi/2(1+D)π/2 BPSK scheme, ORIM extends the concept to I-QPSK, I-BPSK, and I-π/2\pi/2π/2 BPSK. The manuscript provides thorough mathematical derivations for both modulation and demodulation, along with simulation results on PAPR and BLER performance under AWGN and TDL-A channels. Comparisons with π/2\pi/2π/2-BPSK and trellis-coded QPSK are also included.

The topic is highly relevant for 6G, especially for low-power IoT and enhanced coverage scenarios. The proposed method demonstrates noticeable gains in PAPR reduction while keeping BLER performance at a comparable level. Overall, the work shows promise, but several areas require clarification and further development before the paper can be considered for acceptance.

• The difference between ORIM and the previously published (1+D) π/2(1+D)\, \pi/2(1+D)π/2 BPSK scheme (Energies, 2023) should be more clearly explained. As it stands, ORIM may appear to be a straightforward extension rather than a fundamentally new contribution. The paper should highlight the true novelty beyond the earlier work.

• The manuscript relies heavily on simulations. Given the focus on low-cost 6G terminals and IoT devices, readers will expect at least a basic complexity analysis or hardware feasibility discussion (e.g., FPGA/DSP implementation, computational requirements, or potential power savings). Without this, the practical relevance of ORIM remains uncertain.

• The mathematical derivations in the demodulation section, while rigorous, make the paper dense and less accessible for non-specialist readers. Consider moving detailed derivations to an appendix and keeping the main text concise.

• The related work section has improved compared to earlier versions but is still centered on traditional methods such as π/2\pi/2π/2-BPSK, 8-BPSK, CPM, and trellis-coded QPSK. Including comparisons with more recent PAPR reduction techniques (e.g., autoencoder-based OFDM shaping, polar/LDPC-assisted approaches, or learned pulse shaping) would strengthen the contribution.

• Although the scheme is intended for 6G IoT and enhanced coverage, there is little discussion of integration with core 6G technologies such as MIMO, NOMA, or advanced channel coding. Outlining how ORIM could be extended to multi-antenna or multiuser systems would significantly improve its impact.

• The conclusion is positive but does not sufficiently acknowledge the limitations of the work, such as the narrowband assumption, ideal channel estimation, and absence of multiuser evaluation. Explicitly stating these limitations and suggesting future research directions would make the paper more forward-looking.

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

The authors claim that the example in Fig. 3 "illustrates that ORIM can effectively reduce the phase variations between adjacent symbols, thereby lowering the PAPR." However, the example in Fig. 3 does not consider all possible combinations of adjacent symbols. If for example, the symbol stream used were 1 + 1i, -1 -1i, 1 - 1i, -1 + 1i, and the second stream was obtained by shifting the imaginary components circularly to the left. The resulting ORIM symbol stream would include phase shifts of pi.

For this reason, it seems suspicious that the proposed scheme provides such substantial improvements in the PAPR. 

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

This work presents offset rotation interpolation modulation (ORIM) which is a novel scheme with low PAPR. As mentioned by the authors, it is suitable for low-power and wide-coverage applications in 6G wireless systems. ORIM consists of I-QPSK, I-BPSK, and I-π/2 BPSK, obtained from QPSK, BPSK, and π/2 BPSK via cyclic offsetting, phase rotation, and interpolation. Simulations in DFT-s-OFDM systems show that ORIM achieves lower PAPR than the 5G NR π/2-BPSK without degrading block error rate (BLER). With frequency domain spectrum shaping (FDSS), I-π/2 BPSK further improves both PAPR and BLER under TDL-A channels. Moreover, ORIM introduces negligible additional complexity at the transmitter and receiver, while providing overall performance gains.

1. The abstract says that “I-π/2 BPSK demonstrates superior performance over π/2-BPSK in both PAPR and BLER metrics”. The claim “superior performance” should be supported by numerals. This could be in terms of percentage or actual values.
2. Similarly, the abstract also says, “ORIM does not introduce significant additional complexity”. This statement is a bit vague. What the authors are trying to say is that their method does introduce additional complexity but it is not significant. The question is, what range values will be considered significant and what range of values will be considered non-significant? To remove this confusion, it might be better to support the claim with numbers.
3. What is the difference between Fig. 1(a) and Algorithm 1? Aren’t they conveying the same thing? If this is the case then Fig. 1(a) should be removed. It is redundant. Moreover, the way it has been presented is not very intuitive. Also, there is a minor language issue with the text in Fig. 1(a). The text “the modulation mode comprise” should be “… comprises”.
4. The way Algorithm 1 has been presented is quite confusing. It is the heart of the paper and should be presented very clearly. Also, the algorithm should be self explanatory in that one should not need to go back and forth to the main text to understand the algorithm. For example, in Step 7, a new variable “N” has been used. However, this variable has not been defined anywhere in the algorithm. Also, in this same step, first_seq is being appended “N” times and similarly, the second sequence is being appended “N” times. What about other sequences, such as, Third, Forth, etc.?
5. Figure 3 is misleading. The fifth line says, “Add to get second seq”. However, it does not say what to add? All the six lines should be numbered and then the fifth line could say, for example, add lines x and y to get second seq.
6. What is the significance of Trellis coded modulation in this work? The authors begin with Figure 4 in which they show traditional QPSK and Trellis-coded QPSK without giving any background or relevance to their work.
7. The comment that I gave for Figure 3 applies to Figure 6 also. That is, all the lines should have numbers and which lines are being added to get a new line should be mentioned.
8. Figure 8: Same comment as for Figures 3 and 6.
9. In Section 2.4, PAPR analysis, the authors compare their work with Trellis coded QPSK along some other schemes. The justification of comparing with Trellis coded QPSK should be provided.
10. The proposed scheme has only 12 subcarriers while the number of IFFT points are 1024 which is very large compared to the number of subcarriers. It is true that by using a higher number of IFFT points, the curve becomes very close to continuous time case. However, the number of IFFT points should be reasonable. Either the authors should provide a reference for using such a large number of IFFT points or using simulations, they should show how 1024 IFFT points are justified. They can start with a lower number of IFFT points, say 64 and then go to 128, 256, 512, and finally 1024 and show the difference in CCDF. If the CCDF of 64 IFFT points turns out to be sufficient then there is no need to use such a high number of IFFT points.

 

   

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Based on the author's responses and the revised manuscript, I accept this article. 

Author Response

We would like to thank the reviewer again for the constructive comments, which helped us to improve the quality of the manuscript.

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

The authors are correct in that the previously stated stream of symbols will not present a shift of pi when the imaginary part is shifted to the left, but it does when the imaginary part is shifted to the right. This means that a flipped and circularly shifted version of the same symbol stream would still result in adjacent symbols having a shift of pi when imaginary parts are shifted left.

For example: 

-1 -1i; 1 +1i; -1 +1i; 1 -1i; 

Real: -1; 1; -1; 1

Im: -1i; 1i; 1i; -1i; 

Shifted Im: 1i; 1i; -1i; -1i; 

New Symbols: -1 + 1i; 1 + 1i; -1 - 1i; 1 - 1i; 

I apologize for my mistake when writing my previous review, but my concerns still stand.

Given the authors' unwillingness and/or inability to respond to the crux of my question: the fact that there will still be symbols experiencing a shift of pi in their ORIM constellation. I cannot recommend this paper for publication. The fact that thes pi shifts exist in-and-of itself does not necessarily mean that their modulation scheme does not provide the claimed performance. However, the authors have failed to make a strong claim as to how that happens, and I personally do not see how it could possibly happen. They have had ample opportunity to address this question; however they have continued to dodge it and instead attempt to claim something that is very clearly untrue. This makes me seriously doubt the validity of the work.

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

My comments have been addressed. The paper could be accepted.

Author Response

We would like to thank the reviewer again for the constructive comments, which helped us to improve the quality of the manuscript.

Round 3

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

Thank you for clarifying the modulation method. I understand now how it achieves the lower PAPR. Given the interpolation step, it seems that the modulation scheme trades the data rate for a lower PAPR because if I understand correctly, ORIM takes twice as long to send the same amount of information (i.e., due to the interpolation, it takes 2 ORIM symbols to send the same amount of data that was in 1 regular symbol). If this is the case, it should be mentioned and the results should take this trade-off into account.

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Round 4

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

The authors have addressed my concerns.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a modified modulation based on the QPSK modulation scheme used for DFT-s-OFDM. The authors should revise the manuscript to improve readability, provide more technical details, and strengthen the evaluation through broader comparisons and realistic datasets. Addressing these concerns will make the paper suitable for publication in a high-quality venue. Here, the following comments must be responded to:

1. Provide a dedicated subsection detailing how FDSs are applied, including the RRC filter’s configuration and its effect on PAPR reduction. A figure illustrating the FDS's process would enhance clarity.

2. Include a figure or table summarizing BLER performance across schemes, with clear metrics (e.g., BLER vs. SNR) to demonstrate ORIM’s advantages visually.

3. Add specific values (e.g., dB reductions or percentages) to quantify PAPR improvements, ideally in a table or as part of the discussion in Section 4.

4. Justify the AWGN assumption with references or brief analysis, and include a discussion or simulation results for ORIM’s performance in fading channels to reflect real-world 6G scenarios.

5. Add a brief analysis of computational complexity (e.g., number of operations or processing time) for ORIM’s demodulation algorithms, comparing them to baseline schemes to highlight trade-offs.

6. Conduct a comprehensive review of the manuscript for grammatical errors, formatting issues, and consistency in terminology. Ensure that all mathematical symbols.
7. The waveform chosen is DFT-s-OFDM. What do you see about PAPR and BLER when we apply DFT-s-OTFS waveform or DFT-s-LACO-OFDM compared to classical DFT-s-OFDM, for both Terahertz communication and visible light communication, as cited in the following recent research: 
- [1]. Robust FD-DFE equalization for optical OTFS-based NOMA multi-user MIMO in visible light communication systems. DOI: 10.1016/j.optlastec.2025.113214.
- [2]. RT-SVM: Channel modeling and analysis for indoor terahertz communication scenarios. DOI: 10.1016/j.nancom.2024.100551.
8. The authors must update the references of the paper with the recent indexed papers to enhance the quality of this contribution and avoid self-citation..

9. All abstract and conclusion must be rewritten as a scientific paper.  So what is the novelty of this contribution??

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors present a novel modulation scheme coined ORIM (offset rotation interpolation modulation) to lower peak-to-average power ratios for 6G applications. They compare their scheme to traditional BPSK and QPSK as well as trellis-modulated QPSK to show its performance, and they also consider how it performs after filtering.

If the presented modulation scheme does perform as claimed this would be a great paper, but I have serious doubts about the results' technical soundness. It is unclear to me how the ORIM scheme improves the PAPR. The authors show results in Fig. 6 and Fig. 7, but intuitively, I don't understand how the PAPR changes for the ORIM schemes when all the constellation points in regular BPSK or QPSK have the same amplitude as the constellation points in ORIM. The authors should provide some explanation for why their proposed scheme shows such substantial improvements. 

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper introduces a novel modulation scheme that the authors call Offset Rotation Interpolation Modulation (ORIM) which is designed to reduce peak-to-average power ratio (PAPR) for 6G applications targeting low power and extended coverage. ORIM comprises three variants (I-QPSK, I-BPSK, and I-π/2 BPSK), derived from standard QPSK and BPSK schemes via cyclic offsetting, phase rotation, and interpolation. Simulation results within DFT-S-OFDM systems demonstrate that ORIM achieves lower PAPR than the π/2 BPSK used in 5G NR, without degrading block error rate (BLER). With frequency domain spectrum shaping (FDSS), I-π/2 BPSK further improves both PAPR and BLER performance.

This is an interesting paper. However, the proposed scheme as presented in the paper is unclear and it is difficult to understand the underlying technique. Following are the detailed comments about the work. If the authors could address these comments, the paper could be published.

1. A major concern with this paper is the language quality. It requires English editing to correct grammatical mistakes. One example of serious grammatical mistakes can be seen in lines 41 to 43. Additionally, several explanations throughout the paper need to be rewritten more clearly to ensure that readers can grasp the authors' intended message.
2. The Introduction section needs significant revision and enhancement. It should thoroughly present the existing background work, highlight the limitations of prior studies and current research gaps, justify the need for addressing these gaps, and clearly articulate the contribution of this study.
3. Reference [19] has been cited in Line 44 with reference to low PAPR of CPM. However, this paper by Wylie-green does not talk about the power of CPM signals. This paper addresses a completely different topic.
4. The contributions of the paper should be clearly outlined in bullet points, followed by a concise summary of the paper’s structure. For example, the authors could write, “... Section 2 outlines the work done in this area, Section 3 provides details of the proposed method, …” and so on (not necessarily with these headings – this is just an example).
5. 1(a) presents the proposed algorithm. It would be better if this algorithm is presented in the form of a pseudo code as is normally done in research papers. The authors could go over some of the papers published in reputed journals that present their algorithms via pseudo code. Moreover, the pseudo code should be written such that the algorithm is easily understood by the reader.
6. The block diagram in Fig. 1(b) is unclear and needs to be redrawn to illustrate one specific scenario: either QPSK, BPSK, or π/2-BPSK, since it represents the proposed ORIM scheme. The operations of cyclic offset and phase rotation should be depicted as separate steps. Currently, the placement of the term "ORIM" in the third step gives the impression that ORIM is just that particular operation, whereas the caption suggests that ORIM refers to the entire process. This inconsistency should be resolved in the revised diagram. Additionally, an example input sequence should be included, with annotations showing the sequence before and after each processing block. The role of switches S1 and S2 in handling even and odd bits of the data is also not clearly conveyed and should be made more explicit in the diagram.
7. What is being conveyed via Fig. 2 is not clear. Both constellations show four points at identical locations. The only difference between the two diagrams seems to be unfilled and filled dots. Either the text or the diagram should highlight the difference between the two constellation diagrams. Also, the unfilled dots in the QPSK constellation are labeled with binary data while the filled dots in the I-QPSK constellation don’t have any labels.
8. The Trellis coded QPSK constellation shown in Fig. 3 should also have the dots labeled with binary data the way it has been done for the QPSK constellation.
9. After the ORIM operation, the two dots in the constellation of Fig. 4 are transformed into four dots. If we are transmitting two symbols for each one original symbol, aren’t we increasing the computational burden and won’t it require additional power? This needs to be explained in the text.
10. The Comment 9 given above applies to Fig. 5 as well. When explaining Fig. 4 with reference to Comment 9, Fig. 5 should also be explained on the same lines.
11. Regarding Fig. 6, I have the following observations and questions:
    1. How many subcarriers were used to generate the CCDF curve?
    2. What was the IFFT size employed in generating the CCDF graph?
    3. Since BPSK transmits one bit per symbol and QPSK transmits two bits per symbol, comparing their performance on the same graph may not be entirely fair.
    4. The yellow curve in the plot is difficult to distinguish. It is recommended to replace it with a more visually distinct color to improve readability.
12. Regarding Fig. 7, I have the following questions:
    1. How many subcarriers were used to generate the CCDF curve?
    2. What was the IFFT size employed in generating the CCDF graph?
13. The abbreviation “RB” has been used at two places in the paper. However, nowhere has it been explained as to what is “RB”.
14. Given the complexity of proposed algorithm – both in modulation and demodulation – what is the justification of using this scheme when one of the objectives is to lower the power consumption?
15. The authors should derive the complexity of their algorithm and compare it with that of the existing techniques.

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Regarding the author's responses, I have decided to accept this manuscript for publication.

Author Response

We would like to thank the reviewer again for the constructive comments, which helped us to improve the quality of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors' explanation does not make sense to me yet. It is unclear to me both:

• how the smaller phase transitions lead to such substantial improvements in the PAPR. I would also expect the authors to explain why their I-BPSK scheme performs better in terms of PAPR compared to their I-pi/2 BPSK scheme when it is vice versa for traditional pi/2-BPSK and BPSK.
• how there are smaller phase transitions given the mode of modulation. Doing out the I-QPSK modulation scheme as an example, the phase transitions between adjacent symbols can still be up to the same amount as they would be for regular QPSK.

If they can fully explain this, I think it is a great work, but their response and revisions were not sufficiently explained to help me understand how their proposed scheme actually improves the PAPR. Since they are claiming such substantial improvement, it would improve the work to spend time in the manuscript making this very clear and explicit.

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I have two major concerns with reference to the replies given by the authors:

A) In response to my comments 11 and 12, the authors mention that the number of subcarriers used for simulations was only 12. There are two major issues here:

1) The number of subcarriers is almost always kept in powers of 2 for efficient FFT implementation. What is the justification for using a number that is not a power of two?

2) 12 subcarriers is a tiny number. I don't think we can locate any published work that has used such a small number of subcarriers. In fact, the advantage of the scheme would diminish unless a higher number of subcarriers are used, e.g., 64, 128, 256, etc. The authors should provide a justification along with references to justify the use of such a small number of subcarriers.

B) When compared with the number of subcarriers (12), the IFFT size has been kept very high at 8096. What is the justification of taking an IFFT size of such a high value, as it will waste the resources? It has long been established that taking the IFFT four times the number of subcarriers is sufficient to capture the peaks. (Another name for the same thing is "oversampling.") Please refer to the following reference: Section III, para 2. 

L. J. Cimini and N. R. Sollenberger, "Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences," in IEEE Communications Letters, vol. 4, no. 3, pp. 86-88, March 2000, doi: 10.1109/4234.831033

 

Author Response

We thank the reviewer for the comments. In the appendix, we provide detailed answers
to each comment of the reviewer.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

Given the minimal changes to the manuscript and the lack of a clear explanation for the improvement of the PAPR, I cannot recommend accepting this paper in its current state.

In the report, the authors claim that modulating using I-QPSK eliminates phase transitions between adjacent symbols equal to pi, but as far as I can tell it, only moves them around or perhaps makes them less frequent?

For example, consider the original data stream: 

1 + 1i ; -1 + 1i, -1 -1i

According to the paper, the second stream (with the shifted in-phase components) would be

-1 + 1i ; 1 + 1i; -1 - 1i

Resulting in the final, interleaved stream of 

1 + 1i; -1 + 1i; -1 + 1i; 1 + 1i; -1 - 1i; 1 + 1i

The pair of red adjacent symbols has a shift of pi between them.

Perhaps a diagram to demonstrate how exactly the modulation process works would have been helpful. 

Reviewer 3 Report

Comments and Suggestions for Authors

The paper could be accepted.