Shape and Weighting Optimization of a Subarray for an mm-Wave Phased Array Antenna

Round 1

Reviewer 1 Report

This paper proposed an optimization method of subarrays and their weights for mmWave phased arrays. Authors well explained their optimization approach with detailed equations and presented simulated data that show clear improvements with some benefits of using subarray configurations. In addition, the results agree well with the calculation. However, there are some major/minor comments to be confirmed before its publication in Applied Science. Thus, I recommend the authors to revise their paper in accordance with my comments below:

1. Please address why the authors decided to cluster six elements as a subarray in the first place.
2. Please clarify if the phase excitation to the six elements should be in-phase for each subarray.
3. Based on the proposed design criteria, each subarray is subject to have different configurations. This implies that the feeding line to each element within the subarray can be different with each other. So, please explain how the in-phase condition can be realized in actual prototyping.
4. Some abbreviations are used without definitions, e.g., TRM, SLL, and QP. Please provide what those words stand for. (They are provided only in the abstract, not in the main body)

Author Response

Dear reviewer,

I would like to thank you very much for your disposition on my paper (applsci-1285791, title: "Shape and Weighting Optimization of a Subarray for an mm-Wave Phased Array Antenna"). Based on the reviewer’s comments, the paper has been revised. The revised sections are notated in highlighted text in the PDF file. The detailed responses for the review comments are attached in a separated file. We greatly value this chance to revise our manuscript.

Your consideration is very much appreciated.

Author Response File: Author Response.pdf

Reviewer 2 Report

Please check reference [1] year and details.

Regarding formula (1) the concept of “average subarray pattern” should be introduced with a short sentence [Properties of Digital Beamforming with Subarrays, Nickel 2006]. Also, the notation of equation 3a-e should be clarified.

Regarding (2) please state that fk is the array factor provided that the weights in each sub-element are identical (?)

The notation of equation (4) can be understood but is imaginative.

Please check equation (5): x is a subscript.

The objective function should be evaluated at some angles (u,v) ?

The optimization procedure is not explained in a didactic way and is not well detailed with reference to the real array constraints. The mathematical derivation from equation (1) to equation (22) should be well commented and substantially rewritten.

3.1. Cavity-backed type single radiating element design and mm-Wave analysis

Please provide the cavity fillet radius, the post diameter and position and all details to make the single element reproducible.

The active element patterns (AEPs) depend on the particular element position in the array. Here only the central element fed by port 300 is considered. This particular pattern should be compared with other AEPs to derive some conclusion on the possibility to consider the central-element AEP an average AEP.

AEPs can be shown and compared each other with respect to amplitude and phase.

Author Response

Dear reviewer,

I would like to thank you very much for your disposition on my paper (applsci-1285791, title: "Shape and Weighting Optimization of a Subarray for an mm-Wave Phased Array Antenna"). Based on the reviewer’s comments, the paper has been revised. The revised sections are notated in highlighted text in the PDF file. The detailed responses for the review comments are attached in a separated file. We greatly value this chance to revise our manuscript.

Your consideration is very much appreciated.

Author Response File: Author Response.pdf

Reviewer 3 Report

COMMENTS FOR THE EDITOR:
The paper presents a method for the optimization of the subarray shapes and weights in large phased array antenna. The topic is of great interest to the scientific and industrial communities due to the growing number of dual-use applications in which phased arrays are and will be used. In the manuscript, there are in my opinion some critical aspects (as pointed out in the comments reported below) and other flaws that make is not suitable for publication in its present form. The reasons are detailed in the comments to the Authors. I recommend a deep work of revision before a new resubmission.

COMMENTS FOR AUTHORS:
The paper presents a method for the optimization of the subarray shapes and weights in large phased array antenna. The topic is of great interest to the scientific and industrial communities due to the growing number of dual-use applications in which phased arrays are and will be used. In the manuscript, there are in my opinion some critical aspects (as pointed out in the comments reported below) and other flaws that make is not suitable for publication in its present form.

MAJOR TECHNICAL ISSUES
- formula (1) reports the expression of AF (the array factor) with the absolute values for the array factor of the subarray and of the superarray. Since AF is a complex function, the absolute value has to be removed;
- since w_k are assumed complex in Fig. 1, the real and imaginary parts derived in Eq. (8) and (9) are not correct;
- the definition of the QP design problem as in Eq. (10) and (11) is not correct. The real and imaginary parts of the array factor [not correctly derived in Eq. (8) and (9)] are separated and each has an independent constant upper-bound value over the whole SLL. However, both the real and imaginary parts simultaneously contribute to the AF, and thus to the pattern, in each angular direction. Finally, the absolute values in (11) make the constraints to be no more linear.

As for the definition of the QP or CP (convex programming) or LP (linear programming) synthesis problem, I would suggest to refer to the following contributions [1]-[7].

ADDITIONAL COMMENTS are reported as they appear in the text:
- the literature on the design of subarray array antenna is wide and the literature review has to be extended (please see [8]-[14] and the references cited therein);
- the GSO used to optimize the subarray organization is not described. Please report a detailed description of the design method;
- in the sentence “the subarray shape was  optimized to avoid grating lobes when scanning on the condition of uniform weighting (w_k = 1).”, it is important to highlight that the angular positions of the GLs is not function of the subarray weight but only of the array lattice and of the subarray layout;
- it is true that QP allows considering linear equalities and inequalities but other QP allows also including quadratic (convex) constraints (see examples [1]-[4]) that are more suitable to include a power mask constraints for the SLL minimization;
- in Tab. 1, “w/o subarray )” should be “w/o subarray”, namely there is a round bracket to be removed;
- the text in Figure 6 (and similar ones) are difficult to read and should be increased.

Finally, a careful proofreading of the writing is recommended since in some parts the manuscript is difficult to read.

References:
[1] H. Lebret and S. Boyd, “Antenna array pattern synthesis via convex optimization,” IEEE Trans. Signal Process., vol. 45, no. 3, pp. 526-532, Mar. 1997
[2] L. Manica, et al., “Design of subarrayed linear and planar array antennas with SLL control based on an excitation matching approach,” IEEE Trans. Antennas Propag., vol. 57, no. 6, pp. 1684-1691, Jun. 2009.
[3] B. Fuchs, et al., “Optimal Narrow Beam Low Sidelobe Synthesis for Arbitrary Arrays,” IEEE Trans. Antennas Propag., vol. 58, no. 6, pp. 2130-2135, Jun. 2010.
[4] B. Fuchs, “Shaped beam synthesis of arbitrary arrays via linear programming," IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 481-484, 2010.
[5] N. Anselmi, et al., “Design of simplified array layouts for preliminary experimental testing and validation of large AESAs,” IEEE Trans. Antennas Propag., vol. 66, no. 12, pp. 6906-6920, Dec. 2018.
[6] F. Yang, et al., “Synthesis of low-sidelobe 4-D heterogeneous antenna arrays including mutual coupling using iterative convex optimization,” IEEE Trans. Antennas Propag., vol. 68, no. 1, pp. 329-340, Jan. 2020
[7] S. Fofana, et al., “Reconfigurable antenna array with reduced power consumption - Synthesis methods and experimental validations in S-band,” IEEE Trans. Antennas Propag., vol. 69, no. 4, pp. 2023-2030, Apr. 2021
[8] R. J. Mailloux, et al., “Wideband arrays using irregular (polyomino) shaped subarrays,” Electron. Lett.., vol. 42, no. 18, pp. 1019-1020, Aug. 2006.
[9] M. C. Vigano, et al., “Sunflower array antenna with adjustable density taper,” Int. J. Antennas Propag., vol. 2009, Article ID 624035, 2009.
[10] R. J. Mailloux, et al., "Irregular polyomino-shaped subarrays for space-based active arrays," Int. J. Antennas Propag., vol. 2009, Article ID 956524, 2009.
[11] P. Rocca, et al., “Unconventional phased array architectures and design methodologies - A review,” IEEE Proc., vol. 104, no. 3, pp. 544-560, March 2016.
[12] N. Anselmi, et al., “Irregular phased array tiling by means of analytic schemata-driven optimization,” IEEE Trans. Antennas Propag., vol. 65, no. 9, pp. 4495-4510, Sep. 2017.
[13] P. Angeletti, et al., “Unequal polyomino layers for reduced SLL arrays with scanning ability,” Prog. Electromag. Res., vol. 162, pp. 31-38, 2018.
[14] P. Rocca, et al., “An irregular two-sizes square tiling method for the design of isophoric phased arrays,” IEEE Trans. Antennas Propag., vol. 68, no. 6, pp. 4437-4449, Jun. 2020.

Author Response

Dear reviewer,

I would like to thank you very much for your disposition on my paper (applsci-1285791, title: "Shape and Weighting Optimization of a Subarray for an mm-Wave Phased Array Antenna"). Based on the reviewer’s comments, the paper has been revised. The revised sections are notated in highlighted text in the PDF file. The detailed responses for the review comments are attached in a separated file. We greatly value this chance to revise our manuscript.

Your consideration is very much appreciated.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have effectively addressed all of the concerns raised in the first review. The authors have made the necessary changes on this manuscript, personally I think this is a better version now and it can be published as is.

Reviewer 2 Report

I went through the paper and the answer of the authors.
My previous comments have been addressed.
I still have may doubt on the overall quality of the paper. 
The manuscript in the present format (applsci-1285791-peer-review-v2.pdf) cannot be read since the pdf is generated with “track changes on” and many parts are badly formatted, mathematical formulas cannot be read. This fact alone is a good reason to reject the paper (since is not well formatted).
Moreover, the other reviewer underlined other errors that are evidence of poor quality.
The only think that can I say, based on the document “Reviewer Answer 2.docx” that my previous comment have been mostly addressed.