Hybrid Sparse Array Design Based on Pseudo-Random Algorithm and Convex Optimization with Wide Beam Steering

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper addresses the challenge of grating lobe suppression and side lobe level (SLL) control in planar sparse arrays, which is a critical issue in phased array systems. The authors propose a hybrid optimization method that combines pseudo-random distribution for element positioning with convex optimization for element excitation coefficients. The research is well-motivated by the need for improved performance in kinds of applications. I think the proposed method has the potential to impact the field of antenna design. After reviewing the paper, here are some points that could be clarified or may contain areas of concern.

1.     The paper mentions the use of a pseudo-random algorithm for element distribution, which is computationally efficient. However, it does not discuss the computational complexity of the Convex optimization part of the hybrid method. It would be beneficial for the readers to understand the computational resources required, especially for large-scale problems.

2.     The choice of the standard deviation δ in the pseudo-random algorithm is mentioned, Can the authors give a discussion on how different values of δ affect the outcome could provide deeper insights.

3.     The element pattern is assumed to be Gaussian with a full width at half maximum (FWHM) of 75°.  I want to know why this specific pattern was chosen and how it affects the overall array performance.

4.     While the paper mentions the advantages of the proposed method over regular arrays, it could be improved by including a comparison with the state-of-the-art methods in the field. This would help readers understand how the hybrid method performs relative to other existing techniques.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a hybrid optimization method that leverages both pseudo-random and convex optimization to design a sparse array with grating lobe suppression and side lobe level control. Additionally, beam scanning is introduced to demonstrate the effectiveness of the design procedure. The use of two different methods is particularly interesting, as it represents a sort of 'multi-method for multi-objectives': with pseudo-random optimization, the authors control the element positions, while convex optimization is used to control the excitations. The wide beam scanning is also noteworthy, achieving a range of 80°.

The paper is well-written and presents some interesting results; however, I have some concerns about the work, and a revision is needed. 

Below, I provide my comments with the aim of improving the manuscript:

1) Please enrich the literature review. It would be beneficial to expand on both the array antenna literature (lines 12-14) and the optimization algorithms discussed in lines 31-34. Specifically, consider also introducing more recent optimization algorithms for antenna array design, which are used for controlling SLLs and improving radiation characteristics. For example:

- Alnahwi, F.M.; Al-Yasir, Y.I.A.; Sattar, D.; Ali, R.S.; See, C.H.; Abd-Alhameed, R.A. “A New Optimization Algorithm Based on the Fungi Kingdom Expansion Behavior for Antenna Applications.” Electronics 2021, 10, 2057. https://doi.org/10.3390/electronics10172057.

- Niccolai, A.; Zich, R.; Beccaria, M.; Pirinoli, P. SNO Based Optimization for Shaped Beam Reflectarray Antennas. In Proceedings of the 2019 13th European Conference on Antennas and Propagation (EuCAP), Krakow, Poland, 31 March–5 April 2019.

and some Others. 

2) In line 108, you state that "If no solution is found, the value is increased to another one." How much is it increased? Please clarify this point, particularly in relation to the diagram on page 4, where you mention "increase mask level."

3) What about the convergence of the proposed example in paragraph 4.1? Can you provide some results? How fast is your algorithm?

4) What are the specifications of the masks used to control SLLs in relation to beam steering? Please provide superimposed masks in the figures 6-7-8, and include informations about the convergence in this case as well.

5) In the conclusions, you state that "This hybrid optimization algorithm proves to be an effective and capable solution for sparse array design." To better demonstrate the feasibility of this approach and provide a comparison to traditional methods, it would be helpful to include results from a couple of classical optimization approaches and highlight the differences in performance with respect to yours.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed all the issues that arose during the revisions. For this reason, I recommend accepting the paper for publication in the journal.