Plane-Wave Generation through General Near-Field In-Band Reflectarray Direct Layout Optimization with Figure of Merit Constraints in mm-Wave Band
Round 1
Reviewer 1 Report
Please see the attached file.
Comments for author File: 
Comments.pdf
Author Response
Reviewer 1
This paper proposed a general near field in-band synthesis strategy for the direct layout optimization of reflectarrays with application to the generation of plane waves for mm-wave band.
Generally, the authors seem have done a solid work, although the paper is well written, you need to be a specialist in the field to read the paper. As am I not a specialist in this field, it is hard to judge the results of the paper. Besides, some parts are not clear, and need to be further clarified. The reviewer has the following concerns:
I would like to thank the reviewer for the time taken to review the manuscript and for providing valuable comments. Here follows the response to the raised concerns.
Please note that due to the addition of new references to the bibliography, the numbers of the references cited by the reviewer have changed in the revised version of the manuscript.
- It is suggested to use past tence to introduce the existing works, such as [21], [25]-[27].
As suggested by the reviewer, I have changed the use of the present perfect tense to the past simple tense in the passive form in line 63 to introduce the existing works. Now it reads:
Recently, several synthesis techniques were proposed for the NF shaping of spatially-fed arrays [28,32–34].
- The authors should explain why the disunion feed size is different from the commonly used uniform planar array and how could it help near field in-band synthesis strategy?
I believe that the reviewer refers to the use of spatially-fed arrays (such as reflectarrays and transmitarrays, mentioned in the paper) where the array is fed by an “external” feed, most commonly a horn antenna, although other types are possible. This contrasts with conventional arrays which directly integrate a feeding network that distributes the feeding signal to each individual element of the array.
In this regard, both types of arrays are suitable for the near field synthesis with application to plane wave generators, and conventional arrays have been designed in the literature to that end [21]. However, the use of conventional arrays presents the issue of requiring complex feeding networks to control the excitation of the array elements. This in turn may make the in-band synthesis more challenging since the feeding network would ideally have to be considered in the simulations to obtain more accurate results [23].
The use of spatially-fed arrays overcomes this limitation, since the feed may be easily included in the in-band synthesis procedure simply by obtaining the incident field at the array aperture at a number of frequencies, either by means of measurements or full-wave simulations. Then, the array element may be easily simulated by assuming local periodicity with the Floquet theorem, as it is customary in the literature [35].
In order to make this point clearer in the revised manuscript, the introduction has been updated to include the following text in page 2:
The use of conventional arrays presents the issue of requiring complex feeding networks to control the excitation of the array elements [21]. This in turn may make the in-band synthesis of these arrays more challenging since the feeding network would ideally have to be considered in the simulations to obtain more accurate results [23]. Using spatially-fed arrays [24] overcomes this limitation, since the feed may be easily included in the in-band synthesis procedure simply by obtaining the incident field at the array aperture at a number of frequencies, either by means of measurements or full-wave simulations. Then, the array element may be easily simulated by assuming local periodicity with the Floquet theorem [25,26].
- It is suggested to introduce the following recent works in 5G networks [R1]-[R2], mmWave [R3], and IoT [R4] fields to highlight the state-of-the-art of this paper.
[R1] “Refracting RIS aided hybrid satellite-terrestrial relay networks: Joint beamforming design and optimization,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 4, pp. 3717-3724, Aug. 2022.
[R2] “SLNR-based secure energy efficient beamforming in multibeam satellite systems,” IEEE Transactions on Aerospace and Electronic Systems, early access, Jul. 2022, doi: 10.1109/TAES.2022.3190238.
[R3] “Joint beamforming and power allocation for satellite-terrestrial integrated networks with non-orthogonal multiple access,” IEEE Journal of Selected Topics in Signal Processing, vol. 13, no. 3, pp. 657-670, June 2019.
[R4] “Supporting IoT with rate-splitting multiple access in satellite and aerial-integrated networks,” IEEE Internet of Things Journal, vol. 8, no. 14, pp. 11123-11134, Jul. 2021.
As suggested by the reviewer, these four references have been added to the first paragraph of the introduction to improve the state-of-the-art on 5G networks and applications. Specifically, the new references in the revised manuscript are [3] ([R4]), [7] ([R1]), [8] ([R2]) and [9] ([R3]).
- The authors claimed that they adopted reflectarray, from wireless communications perspective, is the reflectarray operated in half model, full duplex model or like intelligent reflective surface?
For the application presented in this paper, the reflectarray antenna is proposed to work as a probe in compact antenna test ranges (CATR). For this to happen, the reflectarray needs to generate a plane wave (hence, plane wave generator, or PWG) in front of the array. An antenna under test (AUT) is placed in the region where the plane wave is generated such that its radiation pattern may be measured.
With this in mind, the reflectarray designed as a PWG would transmit a signal while the AUT would only receive it, and the magnitude of the received signal (as a function of the orientation of the AUT) would correspond to the radiation pattern. Although my area of expertise is not wireless communications, I believe this would correspond to a simplex model.
In order to clarify this point, and in relation with the application (PWG for CATR systems), the following text has been added to Section 3.1 of the revised manuscript:
The goal is to design a reflectarray that acts as a probe in a CATR system, where an antenna or device under test is placed in the region where a plane wave is generated in front the of the antenna. The reflectarray feed would emit a wave, which is transformed into a plane wave by the reflectarray, and then collected by the device being measured. Thus, […]
I am at the reviewer’s disposal in case that anything else needs further clarification.
- The sections on the model and the derivation of the algorithms (sections 2.2.2) are (only) meant for specialists that are familiar with this field. This reviewer is not that familiar with this area and it is therefore difficult to check the soundness of the derivations.
As the reviewer points out, this paper is mainly aimed at readers who are familiar with the analysis, design and optimization/synthesis of spatially-fed arrays (namely, reflectarrays and transmitarrays). In particular, Section 2.2.2 describes the equations for the direct layout optimization (DLO) of the reflectarray. This technique is based on the use of the Levenberg-Marquardt (LM) algorithm, whose working principle may be consulted in many books in the literature. One that has been employed by the author over the years is “Numerical Optimization”, by Nocedal and Wright, which is referenced in the revised manuscript as [42].
As explained in [42, Chapter 10], the LM algorithm is an extension of the Gauss–Newton optimization method in which a trust region is introduced. Although the notation in [42] and the present manuscript differ to some extent, the reviewer may find that some equations look very similar.
A more detailed explanation of the LM algorithm applied to the phase-only synthesis of reflectarray antennas may be found in a previous work by the author [38], which also includes multiple references that may be consulted to further clarify the concepts involved. There are also many other works in the literature that employ the LM algorithm for array synthesis, either in the near field or the far field.
Unfortunately, since most research papers build on previous knowledge, it is very difficult to show current research results from a beginner’s perspective since it would take an important portion of space. In any case, I remain at the reviewer’s disposal in case that anything else needs further clarification.
- There are too many symbols in this paper, it is better to add a Table to list them, which would improve the readability of this paper.
As suggested by the reviewer, a list of symbols used in the manuscript has been added in page 15 for a quick reference.
- The resulting power gains are substantial.
I would like to thank the reviewer for the kind words. Indeed, thanks to the developed technique, the optimized reflectarray is able to fully comply with requirements in both magnitude and phase over a 2 GHz bandwidth within the n257 band. In addition, as shown in Section 3.4, other techniques described in the literature are not able to achieve such results, confirming the suitability of directly optimizing the relevant figures of merit to achieve better results in fewer iterations.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments for author File: Comments.pdf
Author Response
Reviewer 2
The article is well written, an extensive bibliography is provided both on this technique and on other techniques. I suggest some minor review. In detail:
I would like to take this opportunity to thank the reviewer for the time taken to review the manuscript and for the kind words.
- Acronyms:
Line 45: plane wave generators (PWG), not inserted in Abbreviation table
Line 147: Levenberg-Marquardt (LM), not inserted in Abbreviation table
Line 152: DoF, first time mentioned, please write ‘Degrees of freedom’
Line 248: 5G NR, first time mentioned, please write ‘Fifth generation new radio’
PWG and LM have been added to the abbreviation table. DoF and 5G NR have been expanded the first time they are mentioned.
- Typos:
Line 67: ‘them’ -> ‘they’
Line 386: ‘relaying’ -> ‘relying’
Relying has been fixed. However, in Line 74 in the revised manuscript, “them” is used correctly in the phrase context and has not been changed.
Author Response File: Author Response.pdf
