Beamforming Based on a SSS Angle Estimation Algorithm for 5G NR Networks

Round 1

Reviewer 1 Report (Previous Reviewer 1)

In relation to my comment last time, authors have not taken this in to consideration. For this study, characterize and compare the study with PRS or TRS with the same and higher bandwidth.

Include the following results:

1. Correlation
2. ToA
3. Power Delay Profiles showing first path or strongest path with LOS and Non LOS (TDL A to TDL D)

Authors have explained that they have used spatial scattering channel model. My impression is that they should take in to consideration the case of TDL channels as well. Indeed, what they have said is correct, but evaluating TDLs for LOS and Non-LOS will be a benchmark study that can be comapred with other works that have used TDLs instead of SS channel model. 

Moreover, for both types of channel model, the said metrices should be evaluated. 

As far as modulation rate is considered, I haven't fully understood that why it can't be done? What makes the evaluation of a higher modulation an issue that it will take 3 months? If this is the case, a analytical study should be taken in to place. 

This also makes me come to the conclusion that how is the complexity of this setup proposed? Can authors compare the complexity of the proposed vs the benchmarked methods? 

Author Response

Point 1: In relation to my comment last time, authors have not taken this in to consideration. For this study, characterize and compare the study with PRS or TRS with the same and higher bandwidth.

Include the following results:

1. Correlation
2. ToA
3. Power Delay Profiles showing first path or strongest path with LOS and Non LOS (TDL A to TDL D)

Authors have explained that they have used spatial scattering channel model. My impression is that they should take in to consideration the case of TDL channels as well. Indeed, what they have said is correct, but evaluating TDLs for LOS and Non-LOS will be a benchmark study that can be compared with other works that have used TDLs instead of SS channel model.

Moreover, for both types of channel model, the said metrices should be evaluated.

Response 1:  Please note that the proposed BSAE algorithm focuses on the initial acquisition stage based on SSB for a UE in idle mode. Once connected, the beams are refined using other reference signal, as CSI-RS (for downlink) and SRS (for uplink). We would like to point out that procedures after the initial acquisition stage are outside the scope of the proposed algorithm, since we do not have the PRS or TRP available to carry out the suggested study.

Please not that, as explained before, we used a more accurate spatial scattering channel model (used by several authors) and thus the results are closer to the ones obtained in practical scenarios than just using TDLA/D.

We would also like to point out that in 10 days is not possible to obtain such results due to the simulation chain complexity. We took about 3-4 months to obtain the results presented in this paper. We are open to share the simulation chain with the reviewer so that he/she can confirm that.

Point 2: As far as modulation rate is considered, I haven't fully understood that why it can't be done? What makes the evaluation of a higher modulation an issue that it will take 3 months? If this is the case, a analytical study should be taken in to place.

Response 2:  Please note as we mentioned the simulation chain replicates a real-world implementation scenario, and hence, it is complex and takes a lot of time to obtain the simulated results. The complexity cannot comes from changing QPSK to 16/64-QAM but from overall chain that implements all TX and Rx functionalities and also includes the channel model. In 10 days (given by MDPI to resubmit the paper) is completely impossible to obtain such results. As mentioned previously, we are open to share the simulation chain with the reviewer so that he/she can confirm that.  In such a complex scenario is not possible to make an analytically study. Please note that the conclusions will be basically the same using QPSK or for example 16-QAM. It is well known that the penalty of 16-QAM regarding QPSK is approximately 4dB. Basically we will observe a 4dB shift in all curves but the conclusions of this work remains the same since the beamforming is not jointly designed with the modulation.

Point 3: This also makes me come to the conclusion that how is the complexity of this setup proposed? Can authors compare the complexity of the proposed vs the benchmarked methods?

Response 3: Thank you for your suggestion. In this new paper version, a complexity analysis comparison between the proposed BSAE algorithm and the algorithm present in [30] was added to the 3.1 section.

Reviewer 2 Report (Previous Reviewer 2)

In this revised version, the authors seem to revise and edit some paragraphs, but still, the paper requires a lot of English editing and presentation.

However, my main concern is only about the novelty and contribution of the paper and I'm still not sure what the authors are actually proposing. The problem formulation in (5) in my opinion is not correctly formulated. An absolute function should be added to the cost function. Moreover, the problem formulation is very straightforward and should not be counted as a contribution. 

Please note that the authors use a set of analog beams to receive some measurements. Then, the authors assume that the number of receive beams, S, is equal to the number of receive antennas so that the left filtering, i.e., LS can be ideally applied to remove the effect of the analog beams. After that, the authors formulate the problem in (5) with the objective of maximizing the received signal at the user by selecting an analog beam from a codebook of beams. Since the solution to the problem ib (5) is not given, I would assume that the authors used a greedy approach by evaluating the cost function using every beam in the codebook and then selecting the one corresponding to the maximum cost function. This solution approach is used by several works as a baseline method for any newly proposed low-complexity solution method to (5). 

Please also note that the solution, i.e., the selected beam can be, in some scenarios, a beam used in the measurement phase, since the authors didn't make it clear that the analog beams used in the measurement phase are different from the ones in the codebook Omega.

Author Response

Thank you for your comments,
Please see the attachement with the responses.
Regards

Author Response File: Author Response.docx

Reviewer 3 Report (Previous Reviewer 3)

Most of the concerns have been addressed except the following. The authors need to review the use of big-oh notation, which usually does not include constants like 127.

Author Response

Point 1: Most of the concerns have been addressed except the following. The authors need to review the use of big-oh notation, which usually does not include constants like 127.

Response 1:  Thank you for your positive comments. The new version was carefully revised and this issue and others were fixed.

Round 2

Reviewer 1 Report (Previous Reviewer 1)

All suggestions have been taken in to account. Paper can be accepted in its present form.

Author Response

Thank you for the approval.
Regards,
Daniel Andrade

Reviewer 2 Report (Previous Reviewer 2)

As the authors indicated in their point-to-point response letter "Thus, when \theta_s = \theta_p, the array response vectors are correspondent.", it actually proves my point that the selected beam can be, in some scenarios, a beam used in the measurement phase, which shows that the design algorithm, in these scenarios, is not appropriate and can only add extra complexity to mobile stations and, therefore, should be considered in the design algorithm. 

The authors, unfortunately, do not comment further on this matter in the response letter. 

One hint to improve the proposed algorithm is to design the codebook candidate beams while considering the RSRP values obtained from the measurement stage, which could reduce the search space of the greedy algorithm.

Another hint is to use compressed-sensing (CS)-based methods, where the number of measurements S can be significantly reduced, i.e., no need to use S = N_r in the measurement stage. 

I encourage the authors to invest more time in their paper to improve its presentation, and more importantly, the novelty of the proposed method.  

Author Response

Hi there,
Please see the attached file.
Regards,
Daniel Andrade

Author Response File: Author Response.docx

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

The introduction of this article is quite weak. I am unable to apprehend that what is the moitivation of this work?

This seems to be a simulation study of mathworks already shown in: https://uk.mathworks.com/help/5g/ug/nr-cell-search-and-mib-and-sib1-recovery.html

Please explain what is new in it? How does it differ from what already has been shown in mathworks tutorial. Specifically Sec 2.3 is exactly taken from the link above. 

Another important thing is that according to 3GPP compliancy, why other NR standardized signals were not selected? what made you select SSS?

Equation 5 is unclear

Why QPSK modulation is used? Is there any effect of higher modulations on the simulation study? Please evaluate. 

Have you evaluated the study with changing bandwith of the SSS reference?

For this study, characterize and compare the study with PRS or TRS with the same  and higher bandwidth. 

Include the following results:

1. Correlation

2. ToA 

3. Power Delay Profiles  showing first path or strongest path with LOS and Non LOS (TDL A to TDL D) 

Quality of figures is very low and expanded (e.g see Fig. 2)

Author Response

Point 1: The introduction of this article is quite weak. I am unable to apprehend that what is the motivation of this work?

Response 1: Please note that the main goal consists in the design and subsequent performance evaluation in terms of BER of a new 3GPP-standard compliant beam pair selection algorithm based on the SSSs angle estimation (BSAE). This BSAE algorithm is implemented in a NR system model that uses BM techniques at both TX and RX ends to establish the beamformed connection in the DL direction by choosing the best beam-pair available for further synchronization, demodulation and decoding of a live gNB signal. In this new version we did our best to improve the writing quality of this paper, providing additional efforts to present a clearer view of the proposed algorithm as well as its formulation context.

Point 2: This seems to be a simulation study of mathworks already shown in: https://uk.mathworks.com/help/5g/ug/nr-cell-search-and-mib-and-sib1-recovery.html. Please explain what is new in it? How does it differ from what already has been shown in mathworks tutorial. Specifically Sec 2.3 is exactly taken from the link above.

Response 2: Please note that the referred mathworks simulation study follows the 3GPP standard procedures for the synchronization and demodulation of the received waveforms [32] and was indeed used in this work along with the one shown in: https://www.mathworks.com/help/5g/ug/nr-ssb-beam-sweeping.html, for comparison purposes. However, as you can notice from the described mathworks algorithm present in the mentioned link the beam-pair selection was achieved by a dual-end beam sweeping and RSRP measurements between every beam-pair candidate (TX-RX), where the one that presents the higher RSRP value is selected as the most adequate for the connection establishment, excluding any other information related to the other possible beam-pair candidates. Since these beams are generated for fixed directions in this scenario and most of the times they are not aligned between the TX and RX sides (optimal case), the beam-pair selection process can be enhanced in terms of performance. Thus, to achieve better performance levels, we designed a novel algorithm that bears in account more information of other beam candidates in the beam selection process, besides just the beam-pair, that leads to a maximum RSRP value. In this way, it is possible to optimize the receiver-side beam by aligning it with the already gNB selected beam without adding significant complexity to the system, since the channel estimation operation is already performed, leading to the better results as demonstrated in our paper.

Point 3: Another important thing is that according to 3GPP compliancy, why other NR standardized signals were not selected? what made you select SSS?

Response 3: Thank you for your question that allowed us to clarify the things. Using the channel estimation based on DMRS signals, first, we must search for the PSS and SSS to get the PCI and thus, we are finally able to obtain the DMRSs. In this way, we always need to obtain firstly the SSS before the DMRSs and hence, a more complex process with additional processing time is needed rather than just utilising the SSS. Moreover, we concluded, by evaluation of obtained simulation results, that performing the Rx beam angle estimations with SSS provided identical results to the optimal angle (as you can verify in the results section 4) without additional processing requirements, which is particularly important for real-time scenarios. Therefore, the use of SSSs to perform channel estimation led to the same BER performance but, with a more computational efficiency.

Point 4: Equation 5 is unclear.

Response 4:  Thank you for pointing that, in this new version we did our best to provide a clearer explanation.

Point 5: Why QPSK modulation is used? Is there any effect of higher modulations on the simulation study? Please evaluate. 

Response 5: Regarding the use of higher order modulations, the main conclusions are expected to be the same as to the QPSK modulation used. However, please note that the simulation chain tries to replicate a real-world implementation scenario, and hence, it is complex and takes a lot of time to obtain the simulated results. Having this in mind, it is impossible to perform any new simulations for 16QAM and 64QAM till the resubmission deadline because, even for 10000 symbols, the total estimated simulation time is about 4 months for each simulation.

Point 6: Have you evaluated the study with changing bandwith of the SSS reference?

Response 6: Please note that in our simulations we used the 2 different 5G frequency ranges. For FR1 simulation, a SCS of 30 kHz was used. On the other hand, for FR2, a SCS of 120 kHz was utilised instead. Having in mind that the SSS is mapped onto 127 subcarriers into the SSB, we have a total SSS bandwidth of 3.81 MHz (127x30 kHz) and 15.24 MHz (127x120 kHz) for FR1 and FR2 scenarios, respectively.

Point 7: For this study, characterize and compare the study with PRS or TRS with the same and higher bandwidth. 

Include the following results:

1. Correlation
2. ToA 
3. Power Delay Profiles showing first path or strongest path with LOS and Non LOS (TDL A to TDL D)

Response 7: Thank you for the suggestion, it would be an interesting comparison, however, the proposed BSAE algorithm focuses on the initial acquisition stage based on SSB for a UE in idle mode. Once connected, in the following stages, the beams are refined using other reference signal, as CSI-RS (for downlink) and SRS (for uplink). Procedures after the initial acquisition stage are outside the scope of the proposed algorithm, so we do not have the PRS or TRP available to carry out the suggested study.

Regarding the channel model, there are two types of channel models: the stochastic channel models as TDLA to TDLD, and the physical channel models as the spatial scattering channel model which we used in this paper. On the one hand, the TDLA to TDLD models are the ones used in 3GPP. The computation of the TDLA to TDLD models is less complex, does not depend on the physical parameters of the scenario (and that is probably why it is used in 3GPP), but it is less accurate. Oppositely, the physical models are more accurate, and that is why we decided to use the spatial scattering channel model.

Point 8: Quality of figures is very low and expanded (e.g see Fig. 2).

Response 8: We agree with the reviewer that in fact the quality of some figures can be improved. Therefore, in this new version we did our best to improve the quality of all figures.

Reviewer 2 Report

This paper considers single-user MIMO systems and proposes a receive beamforming algorithm called BSAE. 

The paper in general is very badly written and requires expensive review. The authors in Section 2 describe the system model and review the transmitter and receiver models and functions using 3GPP terminologies. However, the review is not well written, not coherent, and still requires a lot of editing.

More importantly, the proposed algorithm BSAE is not clear and I'm not sure what the authors are actually proposing. After estimating the equivalent channel at the receiver, which is done using the classical LS method, the authors propose a problem formulation in (5) to maximize the received signal power by designing the receive beamforming vector without showing its solution. More importantly, the problem formulation is very straightforward and should not be counted as a contribution. 

Author Response

Please see the attachment.
Best Regards,
Daniel Andrade

Author Response File: Author Response.docx

Reviewer 3 Report

This paper presents a beamforming method based on the secondary synchronization signal (SSS) angle estimation. The following concerns need to be addressed.

1.      From the title, “proposed” needs to be removed.

2.      Every word in acronyms does not need to be capitalized.

3.      In line 166, matrix A and vector a are not boldfaced as stated.

4.      Eq. (5) is not encoded properly. It includes some Chinese characters.

5.      A simple step-by-step example can be presented for the proposed algorithm.

6.      The computational complexity of the proposed method can be analyzed and compared with others.

7.      Please specify the reference numbers for the RSRP maximization and the optimal algorithms in Figures 4-11

8.      More of the recent works need to be included in the list of references and reviewed.

Author Response

Point 1: From the title, “proposed” needs to be removed.

Response 1:  Thank you, the new version of this paper has this mentioned correction into account.

Point 2:  Every word in acronyms does not need to be capitalized.

Response 2: Thank you for pointing that out, the new version of this paper has this mentioned correction into account.

Point 3: In line 166, matrix A and vector a are not boldfaced as stated.

Response 3: Thank you for the revision, the new version of this paper has this mentioned correction into account.

Point 4:  Eq. (5) is not encoded properly. It includes some Chinese characters.

Response 4: Regarding this matter, we could not find any issue on our side, maybe this raised due to different software version. Nevertheless, this time we will submit a pdf version of the paper to avoid formatting problems.

Point 5: A simple step-by-step example can be presented for the proposed algorithm.

Response 5: Thank you for your suggestion. In this new version a new illustration is presented in the Figure 3 (Section 3) alongside with a short description of the main algorithm steps. These steps are also explained further in the referred section, which ends with the presentation of a simplified version of the proposed algorithm.

Point 6: The computational complexity of the proposed method can be analyzed and compared with others.

Response 6: Again, thank you for this good suggestion.  A computational complexity analysis was added in the new paper version.

Point 7: Please specify the reference numbers for the RSRP maximization and the optimal algorithms in Figures 4-11.

Response 7: Please note that the considered optimum beam-pair selection algorithm was also designed by us for comparison purposes, it corresponds to the case where the real channel matrix is used to compute the optimal RX angle, however, since this matrix is not known in practical implementations, this algorithm is not feasible in real-time scenarios. On the other hand, the RSRP maximization algorithm is discussed in [24] and was used by us also for performance comparison purposes. A reference number for the RSRP maximization algorithm was added in the section 4, before the enunciation of the 3 algorithms simulated.

Point 8: More of the recent works need to be included in the list of references and reviewed.

Response 8: In this new paper version we did our best to include additional references and revisions.