Multi-Target Localization of MIMO Radar with Widely Separated Antennas on Moving Platforms Based on Expectation Maximization Algorithm
Round 1
Reviewer 1 Report
The authors focus on solving the practical problems encountered in the parameter estimation of MIMO radar with widely separated antennas on moving platforms. Specifically, the paper addresses problems of target localization in MIMO radars, such as dense multi-target and signal-to-noise ratio (SNR) fluctuations. To estimate the echo delay/Doppler shift and SNR, the Q function of Expectation Maximization (EM) algorithm is derived. The gradient descent is used to reduce the computational complexity (generalized adaptive EM - GAEM). A weighted iterative least squares (WILS) algorithm is used to estimate the target positions and velocities based on the results of the GAEM algorithm. In addition, the Cramér-Rao bound (CRB) in the practical environment is derived. Numerical simulations are carried out to validate the effectiveness of the proposed algorithms.
The paper deals with a current and relevant application. The formulation of the problem, as well as the description of the signals involved in it, are fundamental to the understanding of both the existing solutions in the literature and the solution proposed by the authors. The simulation results suggest that there is, in fact, a contribution in this work.
However, Section 2 does not make for a pleasant reading: the sequence of the sentences is not adequate and they are not very well articulated; the equations could be better edited, especially the ones presented in Section 2.4 (Cramér-Rao Bound in the non-ideal environment). In my opinion, Section 2 (Materials and Methods) is overall not very well structured.
Here are some suggestions that, in my opinion, can improve the quality of the manuscript and its overall clarity:
- p. 2/19, line 44: gird point or grid point?
- p. 3/19, line 95: the sentence "The simulation of ... Fig. 5." seems to be out of place.
- The sentences in lines 100-105 seem to be repeated.
- Eq. (4) should be better edited.
- The sentence in line 111 is not understandable.
- Instead of "we set", shouldn't it be "we denote" or "we define"?
- The letter E is used in Eq. (4) to denote "the total energy transmitted by MIMO", however "E_y" appears in Eq. (14) with another meaning. The authors should state what "E_X" means in Eq. (14).
- The text in lines 113-114 is not clear and should be rewritten.
- p. 4/19: The sentence after Eq. (8) also needs to be rewritten.
- In Eqs. (15) and (17), does the "*" mean complex conjugate?
- The passage from Eq. (21) to Eq. (22) is not clear.
- Indicate that Eq. (23) is an approximation of Eq. (19).
- In the sentence after Eq. (22): note that Eq. (22) appears in Eq. (20). So, it is confusing to state: "Next, by substituting (20) and (22) into (19)"
- Is Eq. (25) an approximation or an exact representation?
- p. 10/19, line 170: ".. is denoted by ..." -> "... is denoted by the vector ..."
- p. 11: The sentences between Eqs. (32) and (33), and between Eqs. (33) and (36), seem to be meaningless.
- It is almost impossible to follow the equations on page 12. Try to find a nicer way to represent them. Note that there are several terms repeated in these equations. The authors should take advantage of this in order to rewrite the equations in a clearer and more concise way.
- What is the meaning of beta in Eq. (49)?
- In my opinion, it would be interesting to include the expression used to obtain the MSE curves in Figures 6a and 6b.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In overall the paper recommend for publication with minor revision, as mention in result section the distance between the four targets and first radar node is 2000 m, 2010 m, 2020 m and 2030 m. Both radar nodes and targets are moving. Since the MIMO system with separate antenna with long distance between each nodes, how is the coordination of the system among nodes and impact for the performance because long distance, as well as the average speed of moving object.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The proposed paper is interesting and the focus deals with actual issues.
However the paper needs to be improved on many point of view.
Introduction:
Has to be improved. A deeper discussion about the state of art has to be supplied with much clear description of drawback and benefits. Also the application scenario has to di described with more detail with respect of the available lecterature.
Line 25 – 34 Has to be improved
Line 28 “which is names as spatially-non-white noise.” (?)
Materials and Methods
I appreciate author’s will to illustrate all the mathematical features of the proposed problem but the presentation has to be improved as well as readability of the mathematical formula. (Perhaps an appendix)
Results:
I suggest to introduce, if possibile, a comparison of the results obtained in the present work with the one presented in similar scenario and in different work.
My personal conclusion:
The paper is interesting but must be more accurate in the presentation and in readability
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
This is a second review of the manuscript entitled
"Multi-target Localization of MIMO Radar with Widely
Separated Antennas on Moving Platforms Based on Expectation
Maximization Algorithm".
In my opinion, the suggestions and changes were adequately carried out by the authors in the current version of the paper.
Reviewer 3 Report
The authors responded positively to all the observations made in the first review.
The improvements introduced in the presentation of mathematical relationships as well as in the introduction and in the description of the results significantly improve the quality of the paper.
The addendum of the an appendix to better explain matematichal processing is also positive.
My opinion on the paper is positive and i suggest the pubblication
