Parametric Analysis of Linear Periodic Arrays Generating Flat-Top Beams
Round 1
Reviewer 1 Report
The paper presents an analytic analysis of a linear periodic antenna array generating flat top beams. The approach is interesting and some analysis examples are presented. In order for the paper to be of interest to the readers of this journal, it must include a real life antenna with its parameters (like directivity) and results for different inter-element spacings. The targeted applications should be mentioned.
Author Response
We thank the reviewer for her/his suggestions.
The introduction of the paper has been extended to refer to typical application of flat-top beam arrays.
The research work tried to address key benchmarking issues related to trade-off between the design parameters related to the array factor design, rather than to a specific antenna design. In this respect, inter-element spacing has a zooming effect on the radiation pattern and was not considered for the array factor analysis which assumes a normalised spacing of half wavelength.
An assessment of the effect of the inter-element spacing together with an optima design of the radiating elements for such spacing would be certainly of interest and may be the subject of future research.
Reviewer 2 Report
The paper presents a parametric study of the power pattern of an array. The power pattern is well studied and published in textbooks and papers. For example, Phased Array Antennas book by R. C. Hansen explains the power pattern in detail and provides methods of synthesis. The proposed method is a simple search and will not be efficient in large arrays. Authors are referred to methods of synthesis of the arrays, which are much more efficient and fast ways of finding arrays that provide the desired patterns.
Author Response
We thank the reviewer for her/his suggestions.
The linear programming method analysed in the paper is known to provide the truly optimal solution to the mask problem and for this theoretical property (global optimum) it can be considered superior (or at most equal) to any known method in the literature.
In addition, concerning the speed of synthesis, linear programming can rely on well established commercially available routines (e.g. in MATLAB).
To clarify these points some more explanation has been added in the introduction.
Thanks to the reviewer for indicating some of the points that needed to be better clarified.
Reviewer 3 Report
This manuscript studied the parametric analysis of linear periodic arrays that can generate flat top beams. By employing linear programming techniques, the design parameters can be optimized efficiently.
- In general, the manuscript gave a good guideline for the engineer to design a flat top beam array with linear periodic array. However, as a research paper, it seems that the paper didn’t include enough scientific contributions. Thus, I guess that the manuscript is more suitable for some other journals which focus on the engineering training.
- A quite difficult problem in the modern array synthesis is the coupling between the elements, which makes the radiation pattern of each element is different from each other. The authors are encouraged to discuss this problem.
Author Response
We thank the reviewer for her/his suggestions.
The main scientific contribution and the main objective of the paper is to present useful guidelines and rules of thumb for the synthesis of periodic array antennas generating a flat top beam, and to show the relations between the main design parameters. As design algorithm, we have been implementing the linear programming method which is known to provide the truly optimal solution to the mask problem. To the best of our knowledge these results are completely new and have not been previously presented in the literature. At the same time, the design of rectangular beams represents a target and reference case considered often not only in theoretical studies but also in practical designs. The curves show that, also for the simple case of linear equally-spaced arrays, the relations between the design parameters can be non-linear. This is an interesting, and not completely expected result, which must be taken into account in the array design.
It is true that coupling contributions have not been included in this work. However, for arrays with moderate dimensions it can be evaluated adopting full-wave commercial solvers. For electrically large arrays the impact of the coupling contributions and the different behaviour of the inner and edge radiating elements is having a lower effect. In several papers (for instance the ones authored by D. A Neto and D. Cavallo) elegant and analytical solutions to include these contributions have been implemented. We believe that coupling contributions could be added in a follow-on work and that this paper is already quite complete and contains already a number of guidelines useful for the preliminary design of linear periodic arrays generating a flat-top beam. The final part of the Conclusions contains now a paragraph on this point with a new reference paper.
Round 2
Reviewer 1 Report
Can be accepted
Author Response
We express our gratitude to the first reviewer for her/his support and for accepting the changes implemented.
Reviewer 2 Report
It is appreciated that the author provided some revisions, however, the major concern that I had is not answered. The authors just added a few references and claimed those methods are complex and not good, without showing any evidence or comparison. Unfortunately, the argument is not convincing to me. Until the method is not compared with already available methods and tools it is not evident the method has advantages.
Author Response
We thank the second reviewer for the suggestion to add a clear explanation on the superiority of linear programming for the solution of the flat-top-beam problem. We have duly taken into account the reviewer comment adding a summary explanation as well as new references in the paper.
The auxiliary space of the real and imaginary part of the autocorrelation of the excitations offers the key advantage to formulate the mask problem as a convex linear programming problem which, as well known, admits a unique global solution.
Although our formulation leverage on the framework developed by L. R. Rabiner in 1972 for Finite-Impulse-Response (FIR) filters [1-2], application to array antennas and optimality aspects are discussed in Isernia, Bucci and Fiorentino [3].
[1] Rabiner L R. Linear program design of finite impulse response (FIR) digital filters. IEEE Trans. Audio Electroacoust. 1972; AU-20(4), pp. 280–288.
[2] Rabiner L R. The design of finite impulse response digital filters using linear programming techniques. The Bell System Technical Journal. 1972; 51(6), pp. 1177–1198.
[3] Isernia T, Bucci O M, Fiorentino N, Shaped beam antenna synthesis problems: Feasibility criteria and new strategies, J. Electromagn. Waves . Applicat. 1998, 12(1), pp. 103–138.
Reviewer 3 Report
The authors have revised the introduction and the conclulsion to reply my comments.
Author Response
We express our gratitude to the third reviewer for her/his support and for accepting the changes implemented.
Round 3
Reviewer 2 Report
My comment from the last round is still not answered. The authors need to show through examples how their method compares with the commonly practiced method. A specific example comparing the pros and cons of the method with other methods used is needed to show the correctness and effectiveness of the proposed method.
Author Response
We thank the second reviewer for her/his new feedback. We have been numerically comparing the Linear Programming method with two others well known in the antenna community. The results are presented in the attached file. The paper text has been modified accordingly with a new sentence added at the beginning and a sub-section added at the end of the numerical results.
Author Response File: 
Author Response.pdf
