Dynamic Phase Comparison Planar Direction-Finding Algorithm on Satellite Radio Receiver

Round 1

Reviewer 1 Report

Editorial comments:
- Before opening brackets, there should be a space, otherwise it is a klemp (see https://en.wikipedia.org/wiki/Klempen).
- Before opening parentheses, there should be a space, otherwise it is a klemp (see https://en.wikipedia.org/wiki/Klempen).
- The more typical abbreviation for "electromagnetic waves" is "EM waves" and not "EMW", which is not considerably shorter, but much more confusing.
- Some articles are missing in the text. Please ask a native speaker for support in improving the language.
- When referencing equations, you should write e.g. 'The Pythagorean theorem is given in Eq.~\eqref{eq:pythagoras}.' or 'The Pythagorean theorem is given in Equation~\eqref{eq:pythagoras}.' but not 'The Pythagorean theorem is given in the Eq.~\eqref{eq:pythagoras}.' nor 'The Pythagorean theorem is given in the Equation~\eqref{eq:pythagoras}.'.
- Please align the equality signs one below each other in Eqs. (10) to (12).
- The authors might use the subequations environment in LaTeX to group this equation set together, see: https://www.baeldung.com/cs/latex-subordinate-equations
- Eq. (17): Please enlarge and adjust the size of the parentheses and brackets to fit the height of the enclosed terms.
- Fig. 3: Figures like diagrams, plots, circuit schematics, block diagrams, flow charts and other line art graphics should be inserted as a vector graphic, not as a raster graphic, see https://en.wikipedia.org/wiki/Raster_graphics and https://en.wikipedia.org/wiki/Vector_graphics for a discussion on this.
If a raster graphic has to be used for any reason, no lossy JPEG compression should be used, as it creates nasty compression artefacts, see https://en.wikipedia.org/wiki/JPEG.
- Caption of Fig. 3: The reviewer suggests to write out the abbreviation RPI here for better understandability.
- Fig. 3: Please delete the word "The" at the beginning of the figure captions. It is usually not necessary for the understanding.
- When writing physical quantities, there should be a space between the number and the unit.
See the SI brochure at https://www.bipm.org/en/publications/si-brochure/ in Sec. 5.4.3 "Formatting the value of a quantity" that clearly states: "The numerical value always precedes the unit, and a space is always used to separate the unit from the number."
The reviewer suggests to use the very powerful siunitx package of LaTeX to typeset units and numbers.
• number and unit like \SI{1,5e3}{\micro\ohm\per\square\meter} result in 1,5 × 10³ µΩ/m²
• only a number like \num{12345,6789} results in 12345,6789
• only a unit like \si{\kilo\volt\ampere\meter\per\cubic\hour} results in kVAm/h³
• number ranges can be given as \numrange{0.1}{5e3} which results in 0,1 to 5 × 10³
• quantity ranges can be given as \SIrange{0.1}{5e3}{\meter} which results in
0,1 m to 5 × 10³ m
• quantity lists can be given as \SIlist{1;2;3;4}{\meter} which results in 1 m, 2 m, 3 m and 4 m.
• number lists can be given as \numlist{1;2;3;4} which results in 1, 2, 3 and 4.
• see the documentation of the siunitx package
- In the list of references, some paper titles are typeset e.g. as 'Influence of Antenna Characteristics on MIMO Systems' while others are typeset as 'Influence of antenna characteristics on MIMO systems'. This should be harmonized.
- Sec. 4 and 5: Please don't use capital letters only for the headings. It looks terrible.

Technical questions and comments:
- How has noise been introduced in the simulation? What type of random number generator has been used?
- Can the authors please provide some more details on the simulation method (software, numerical algorithm, solver, computational effort, simulation time, accuracy, memory requirements, number of unknowns, stability, sensitivity with respect to input parameters, ...)
- Will the developed source code of the simulation program be made available for the use by other reseachers or for further validation?
- The authors presented a direction finding algorithm with two antennas and have demonstrated that the error might get rather large for certain angles of incidence. Would it not make more sense to use at least three antennas in a triangle orientation to be able to better find the incoming direction of electromagnetic waves from 2D directions within a plane or four antennas in a tetrahedron configuration to find the incident angle of EM waves from all 3D directions?

Comments for author File: Comments.pdf

Some articles are missing in the text. Please ask a native speaker for support in improving the language.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors are describing a dynamic phase comparison algorithm for direction finding on high-speed moving satellite radio receivers treating the single moving antenna as an antenna array. The paper is well-organized and decently well-written and the topic could be of interest to the readers of MDPI Applied Sciences. Several relatively minor issues have to be remedied before the eventual manuscript publication.

My largest concern is that almost no information is given regarding the simulation. Namely, I assume the simulations the author are referring to are just plain numerical ones. However, the information regarding how such simulations are implemented (in which programming language, which environment), what is the execution, how the noise is generated and added, what was the noise source distribution, etc. have to be provided in the paper so that those simulations should bring more meaning and insight into the presented results.

Equation (4) is not exact but an approximate one. Namely difference between two cosine functions from equation (3) yields the result in (4) only under certain conditions. Please be more elaborate on that and indicate with an approximation equality sign (≈) wherever this is the case as it is more correct that standard equality sign (=).

Why does in equation (5) stand d' instead of just d? What is d'?

Why is it taken that radiation source emits the 32kHz frequency signal? What is the background and the justification behind this? Moreover why is it assumed that the distance between the radiation source and the receiver is 20 wavelengths of the 32kHz signal? What is the background and the justification? Can you perhaps rerun the simulations for different radiation source frequencies and distances and give it as an additional comparison plot to figure 6. if the result turns out to be interesting?

Since only a planar version of the algorithm is elaborated, maybe this also must be stated in the title of the paper. In the future if the authors conduce the three-dimensional generalization that would be an obvious upgrade to this one if they decided not to give away details on that one now.

Please double-check the grammar once again since there are minor mistakes such as the one on line 25 in:

"The phase interferometer algorithm use array antennas..." where it should stand "The phase interferometer algorithm uses array antennas..."

Define SNR in your abbreviation list at the end.

In line 201 maybe it is more correct to refer to digital signal processing techniques than digital signal processing technologies as it currently stands.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have adequately addressed all of my concerns hence I recommend the paper for publication.