Uniform Sampling Methodology to Construct Projection Matrices for Angle-of-Arrival Estimation Applications
, Marcus de Ree 3,4, Raed A. Abd-Alhameed 1,2 and Peter S. Excell 1,5Round 1
Reviewer 1 Report
Do the method and methodology have the same meaning? Do the authors propose a method or methodology? Did they present a new method or 2 new methods?
The manuscript submitted for review is somewhat similar to previous authors' articles:
Al-Sadoon, M., Ali, N., Dama, Y., Zuid, A., Jones, S., Abd-Alhameed, R., & Noras, J. (2017). A new low complexity angle of arrival algorithm for 1D and 2D direction estimation in MIMO smart antenna systems. Sensors, 17(11), 2631.
Al-Sadoon, M. A., Abd-Alhameed, R. A., & McEwan, N. J. (2019). The Impact of the Covariance Matrix Sampling on the Angle of Arrival Estimation Accuracy. Inventions, 4(3), 43.
The similarity can be seen in the case of drawings and the whole set of mathematical formulas. In this case, it would be good to clearly indicate how this manuscript differs from previous authors' work.
The article contains numerous mathematical relationships, which is characteristic in this type of work, however, a clearer explanation and distinction between the current state and the progress that has been made would be useful.
Can you present individual elements of the analyzed algorithms and signal processing process in the form of a graph or diagram? With an indication of the place where was the signal processing modified by the authors?
Did the authors in their works carry out calculations and analyzes on experimental data?
Can the proposed solution be confirmed practically?
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors present a new methodology to construct projection matrices for Angle-of-Arrival (AoA) estimation applications. The paper consists of problem specification, methodology introduction and a proposal of novel methods. The proposed methods are analysed and evaluated based on computational complexity, execution time comparison, SNR variations and a different number of snapshots.
The paper is well structured and prepared entirely understandable. The problem is up-to-date; the paper should be interesting for the community.
Minor Comments:
1) Abstract: The abstract is written too generally. The main results and outcomes should be presented in more details, not only in the text but also in a brief summary in the abstract.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 3 Report
1. Please show the reference of eq. (3) and eq. (4).
2. Please show the reference of eq. (5).
3. Please show the reference of eq. (7).
4. Please show the reference of eq. (9).
5. Please show the reference of eq. (13)-(17).
6. The author manuscript said “The projection matrix can be computed as follows: eq.(21).”
Please show the reference of the eq.(21).
7. The author manuscript said “Then, the spatial spectrum of the PM method can be formed using the below formula. Eq.(22)”
Please show the reference of the eq.(22).
8. The author manuscript said “Then, the spatial spectrum of the PM method can be formed using the below formula. Eq.(22)”
Please show the reference of the eq.(22).
9. The author manuscript said “It is clear from this figure that the size of the obtained aperture array of ???? is wider than that with ?? as illustrated in Figure 2. Eq.(23)”
Please show the reference of the eq.(23).
10. The author manuscript said “Based on the uniform selecting criterion, the projection matrix can be computed as follows:.eq.(24)”
Please show the reference of the eq.(24).
11. The author manuscript said “Now, the psudospectrum of the USM approach can be formed as follows: eq.(27).”
Please show the reference of the eq.(27).
12. The author manuscript said “The Root-USM technique can be described as follows: eq.(28).”
Please show the reference of the eq.(28).
13. Please show the definition of eq. (29) about the β, d, and θ.
14. Please show the equation of the Mmn in the eq.(30).
15. Please show the xi equation from eq. (32).
16. Please show the detail equation θi from eq. (33).
17. Please show the equation about eq. (36).
18. The author manuscript said “For uniform sampling, the space between each two adjacent sampled columns is set as U = round (M/L), where U is the uniform sampling factor.”
Please show the definition of M, L and example.
19. Please show the detail equation in the eq. (40).
20. Please show the detail equation about eq. (42).
21. The author manuscript said “The number of measurements to construct the CM was set as N = 100 and SNR at the array output was set at 10 dB. ”
Please show the equation of SNR.
22. The author manuscript said “The searching step angle is δθ= 0.5°.”
Please show the equation of searching step angle.
23. The author manuscript said “The USM and Root-USM methods in addition to four other different AoA techniques, are considered here and used to estimate the directions of the incident signals.”
Please show the detail equation of USM and Root-USM methoes.
24. The author manuscript said “The reduction projection matrix parameter of the USM method is set to G = 5.”
Please show the equation of the reduction projection matrix parameter.
25. Please show the PM, Propgator, OGSBI, Rooot-SBL, USM, Root-USM in the references.
26. The author manuscript said “A MATLAB simulation programme for each method was run under the same computer situations with one hundred iterations; the total time of execution of each method was recorded and given in Table 3.”
Please show the equation of the AOA in PM, Propgator, OGSBI, Rooot-SBL, USM, Root-USM.
27. The author manuscript said “The percentage of the reduced execution time of the Root-USM compared to the USM, propagator, PM, OGSBI and Root-SBL methods is 48%, 49%, 86%, 99.74% and 99.96% respectively.”
Please show the percentage of the reduced execution time.
28. Please show the AOA method in the Table 3.
29.Please show the AOA techniques in Fig. 6.
30. Please show the equation of Number of snapshots in Fig. 6.
31. The author manuscript said “The reason for the OGSBI gives poor estimation is this method based on sparse signal reconstruction to deal with such an off-grid DOA estimation problem.”
Please show the equation of the off-grid DOA estimation problem.
32. The author manuscript said “ reduced execution time percentage of the Root-USM compared to the propagator, PM, OGSBI and Root SBL methods is 49%, 86%, 99.74% and 99.96%, respectively”
Please show the equation of percentages.
Please show the Figure using percentages.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
I do not understand why AFc（θ）in equation（34）is a list, but AFc（θ） in equation（36）is a result. Please explain.
Author Response
Comments and Suggestions for AuthorsI do not understand why AFc（θ）in equation（34）is a list, but AFc（θ） in equation（36）is a result. Please explain.
We thank the reviewer for the comment, this is because of eq. (35) has been subtracted from eq. (34) and the result of subtraction is given in eq. (36). For clarity purposes, we have attached the subtraction details.
Author Response File: Author Response.pdf
