Reduction of the Line-of-Sight Equivalence Principle

Round 1

Reviewer 1 Report

This paper shows how to calculate the Far-field with a LoS approximation using only one type of equivalent currents. The article is well presented and the results are interesting.

I have one suggestion and some minor language clarifications:

This paper deals with improving the efficiency of a numerical method. However, there is no quantification of how much more efficient the method is compared to conventional techniques. Please include a table (or similar) with comparison in computational time/resources.

1. on page 1, line 39. It is stated that the shadow region is transformed to an "infinite surface" What is meant by this?
2. Page 5. Paragraph starting on line 126 is quite confusing. Please rephrase so that each reference is clear. For example:  "Every point on the LoS surface, together with the observation point, defines a line." Here, I assume you mean "Each point..."
3. Page 7, line 172. If the above theory is iterated for clarity, please state so in the previous section, not here.
4. Page 7, line 176-177: "If the field in region 2 were to be zero, then even for an elemental contribution, the field should be zero in region 2". What is meant by an "elemental contribution" ?
5. Page 7, last sentence. What is meant by "there are many point-of-symmetry in region 2 and field at all point-of-symmetry is zero,"?

Author Response

Thank you very much for reviewing our manuscript. We sincerely appreciate all your valuable comments and suggestions, which helped us to improve the quality of the article. The manuscript has been updated to meet all specific recommendations made by the three reviewers.

Our responses to your comments are described below in a point-to-point manner. Appropriated changes, suggested by you, has been introduced to the manuscript (highlighted by tracking changes within the document).

 

Reviewer's comments:

This paper shows how to calculate the Far-field with a LoS approximation using only one type of equivalent currents. The article is well presented and the results are interesting.

I have one suggestion and some minor language clarifications:

This paper deals with improving the efficiency of a numerical method. However, there is no quantification of how much more efficient the method is compared to conventional techniques. Please include a table (or similar) with comparison in computational time/resources.

Answer from Authors:

With the proposed solution, far-field computation (time/resources) is reduced by half. This was stated in the introduction, discussion, and conclusion sections of the paper. We are not sure if this needs to be elaborated further. The reduction in computational resources by a half is due to the reduction of the computed quantities by a half. We have also added a line the conclusion to emphasize this.

 

Reviewer's comments:

1 .on page 1, line 39. It is stated that the shadow region is transformed to an "infinite surface" What is meant by this?`

Answer from Authors:

The statement near line 39 has been rephrased to address this question.

 

Reviewer's comments:

2. Page 5. Paragraph starting on line 126 is quite confusing. Please rephrase so that each reference is clear. For example:  "Every point on the LoS surface, together with the observation point, defines a line." Here, I assume you mean "Each point..."

Answer from Authors:

Yes, it should say "Each point" and not "Every Point", this has been corrected. The paragraph near line 126 has been changed for better clarity.

 

Reviewer's comments:

3. Page 7, line 172. If the above theory is iterated for clarity, please state so in the previous section, not here.

Answer from Authors:

We used the wrong choice of words; this is now corrected to state "The above derivations are summarized here." In the modified manuscript, line 177 corresponds to line 172 of the older version.

 

Reviewer's comments:

4. Page 7, line 176-177: "If the field in region 2 were to be zero, then even for an elemental contribution, the field should be zero in region 2". What is meant by an "elemental contribution" ?

Answer from Authors:

Perhaps it would be clear if the statement is rephrased with "elemental surface current contribution" instead of "elemental contribution". In the modified manuscript, line 182 corresponds to line 177 of the older version.

The far-fields are calculated by integrating the elemental surface current contributions. Most of the derivations are based on elemental surface currents.

 

Reviewer's comments:

5. Page 7, last sentence. What is meant by "there are many point-of-symmetry in region 2 and field at all point-of-symmetry is zero,"?

Answer from Authors:

The statement has been rewritten for better clarity.

Reviewer 2 Report

In this paper, the authors show an improvement to the LoS approximation technique introduced by the authors themselves in the quoted paper [8] in order to halve the resources required for the numerical evaluation of the radiation pattern. In the opinion of this reviewer, the proposed approach sounds interesting and can be accepted for publication providing the following modifications/clarifications:

1) On lines 110-113, the authors claim that "the condition of zero fields inside region 2 can also be obtained by setting" the conditions (19) and (20). In the opinion of this reviewer this sentence should be clarified adding more details. As a matter of fact, Love's equivalence principle allows to state that the integrals (17) and (18) vanish inside region 2. And this does not imply that the integrands of those integrals vanish. Moreover, the authors write that "zero fields inside region 2 can also..." meaning that there exists an extra degree of freedolm to be used. This sounds strange because if they are using the free space Green function, which includes the radiation conditions, by imposing the boundary conditions on the equivalent surface, the uniqueness of the solution in the external problem should be guaranteed.

2) Since different approximations give different results, an error analysis should be added.

3) The Appendix is superfluous and suitable for a book, which usually include even simple and well known algebraic manipulations.

Author Response

Thank you very much for reviewing our manuscript. We sincerely appreciate all your valuable comments and suggestions, which helped us to improve the quality of the article. The manuscript has been updated to meet all specific recommendations made by the three reviewers.

Our responses to your comments are described below in a point-to-point manner. Appropriated changes, suggested by you, has been introduced to the manuscript (highlighted by tracking changes within the document).

 

Comments and Suggestions for Authors

In this paper, the authors show an improvement to the LoS approximation technique introduced by the authors themselves in the quoted paper [8] in order to halve the resources required for the numerical evaluation of the radiation pattern. In the opinion of this reviewer, the proposed approach sounds interesting and can be accepted for publication providing the following modifications/clarifications:

 

Reviewer's comments:

1) On lines 110-113, the authors claim that "the condition of zero fields inside region 2 can also be obtained by setting" the conditions (19) and (20). In the opinion of this reviewer this sentence should be clarified adding more details. As a matter of fact, Love's equivalence principle allows to state that the integrals (17) and (18) vanish inside region 2. And this does not imply that the integrands of those integrals vanish. Moreover, the authors write that "zero fields inside region 2 can also..." meaning that there exists an extra degree of freedolm to be used. This sounds strange because if they are using the free space Green function, which includes the radiation conditions, by imposing the boundary conditions on the equivalent surface, the uniqueness of the solution in the external problem should be guaranteed.

Comments from Authors:

To avoid confusion, we have modified the text in lines 111 to 116 with the following statement:

"In terms of the elemental vector potentials, the condition of zero fields inside region 2 is obtained by setting the following conditions:

Eq. 19,

Eq. 20,

which ensure the fulfilment of equations (17) and (18) regardless of the shape of the enclosed surface. Here….."

It is correct that Love's equivalence principle allows the integrals (17) and (18) to vanish inside region 2. However, it does not impose any restrictions on the integrands.  In fact, many scenarios can be envisioned in which the zero-field can only be achieved by imposing the integrands to be zero. Furthermore, our proposed concept also validates the well-known image theory.

Regarding the reviewer's comment on Free Space Green function. We are not imposing any boundary conditions on the extended equivalent surface. It is extended further enough so that the point-of-symmetry falls within the zero-field region for any observation point in the far-field. The confusion might have been due to the wrong notation we used in Figure 1; it has been changed. Also, some of the text has been updated to reflect this.

 

 

Reviewer's comments:

 2) Since different approximations give different results, an error analysis should be added.

Comments from Authors:

In the simulation example, in an effort to keep it simple and practical, we used first-order boundary condition and also used a low number of nonuniform cells. The errors observed would also include the numerical errors due to the boundary condition, and errors due to the size variation of cells. It will be very difficult to separate the numerical errors from some of the errors due to the approximation. Furthermore, the errors are also highly dependent on the type of antenna, which further completes the analysis. Our central goal was to demonstrate our proposed theory with a simple example. Since the errors are below -21 dB, and even in that level, the variation was only a few dB, error (~1%); the simulation validates the proposed theory. Further detail error analysis will substantially expand the scope of the paper, and it falls beyond the primary goal.   

 

Reviewer's comments:

3) The Appendix is superfluous and suitable for a book, which usually include even simple and well known algebraic manipulations

Comments from Authors:

We agree that the derivations in the Appendix are fairly straightforward manipulations using vector calculus. Thus, the Appendix has been removed.

 

Reviewer 3 Report

The authors have studied and proposed an improvement to the line-of-sight approximation of the equivalence principle. They demonstrate that the integration over one type of surface current on the line-of-sight surface and edge currents is sufficient. Their achievement reduces the resources required for the computations.

Overall, the manuscript seems technically correct and presents a very nice theoretical discussion. More importantly, they have validated their predictions with an example of computation of the radiation pattern of a microstrip patch antenna.

For these reasons, and since there is a growing interest in optimized and fast computational methods, this reviewer believes that the contents of the manuscript is of interest to the readers of Electronics and does recommend its acceptance for publication.

Author Response

Thank you very much for reviewing our manuscript. We sincerely appreciate all your valuable comments and suggestions, which helped us to improve the quality of the article. The manuscript has been updated to meet all specific recommendations made by the three reviewers.

 

Comments and Suggestions for Authors

The authors have studied and proposed an improvement to the line-of-sight approximation of the equivalence principle. They demonstrate that the integration over one type of surface current on the line-of-sight surface and edge currents is sufficient. Their achievement reduces the resources required for the computations.

Overall, the manuscript seems technically correct and presents a very nice theoretical discussion. More importantly, they have validated their predictions with an example of computation of the radiation pattern of a microstrip patch antenna.

For these reasons, and since there is a growing interest in optimized and fast computational methods, this reviewer believes that the contents of the manuscript is of interest to the readers of Electronics and does recommend its acceptance for publication.

Round 2

Reviewer 2 Report

In the opinion of this reviewer, this paper can be accepted in its present form.