Distributed Phased Multiple-Input Multiple-Output Radars for Early Warning: Observation Area Generation
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors This paper presents a resource management approach for distributed MIMO radar systems with phased array antennas, which aims to generate a regularly shaped observation area for long-range detection by focusing and shaping narrow beams from all transmit and receive nodes. However, the following comments are suggested to address. 1. What is architecture of the Phased MIMO Radars? What are the benefits of this type radar? 2. The authors formulated a resource management problem, but the problem is challenging to solve. How to solve this optimization problems that are non-convex? How is the tightness of the solution of the relaxed problem? 3. What is the expression for SCNR? How the metrics SCNR and detection probability are used for resource allocation? What are the reasons of the performance improvement for the proposed method? 4. How the location of distributed radar nodes affects the performance of the system? 5. There are several novel related literatures on MIMO radar can be included for comparison as follows:[1] Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation
[2] MIMO Radar Waveform Design in the Presence of Multiple Targets and Practical Constraints
6. Some typo in line 349 of page 13.
Comments on the Quality of English Languagefine
Author Response
Comments 1: What is architecture of the Phased MIMO Radars? What are the benefits of this type radar?
Response 1:Thanks very much for your comments. A distributed Phased MIMO Radar consist of widely seperated phased array antennas. This definition can be found in lines 115 to 117:
"Consider a distributed MIMO radar system with M transmit nodes and N receive nodes, as shown in Figure 1. Each node is equipped with a phased array antenna and is widely separated from others."
These radars can combine the diversity advantages inherent in distributed MIMO radar and the beamforming capabilities of phased array antennas.
Comments 2: The authors formulated a resource management problem, but the problem is challenging to solve. How to solve this optimization problems that are non-convex? How is the tightness of the solution of the relaxed problem?
Response 2: Thanks very much for your comments. We devise a balanced SCNR strategy to divide the entire optimization process into two stages. The optimization problem for the first stage is a fractional programming problem. The fractional programming problem is transformed into a series of convex optimization problems by using the linearization method described in Section 3.2.4 and the convex relaxation method described in Section 3.2.5. With a larger feasible region, there may be more points that satisfy the relaxed constraints, which can lead to a less constrained or more loosely bound solution set. To guarantee that the solution to the convex optimization problem is also feasible for the original problem, we employ a projection algorithm. Furthermore, to ensure convergence, we incorporate the concept of trust-region algorithms into our method
The optimization problem for the second stage is a bi-objective mixed integer problem. Since the problem dimension is small, we use binary search method to construct the Pareto solution set. The process is discribed in Section 3.2.6.
Comments 3: What is the expression for SCNR? How the metrics SCNR and detection probability are used for resource allocation? What are the reasons of the performance improvement for the proposed method?
Response 3: Thanks very much for your comments. SCNR is a ratio of the target echo power and the clutter plus noise power. Its definition is given in lines 349, Eq. 16.
The receive beamforming weights are completely determined by the SCNR.
The transmit beamforming weights are determined by the SCNR and detection probability.
The pulse number is determined by the detection probability.
The performance improvement is mainly attributed to the balanced SCNR strategy described in Section 3.2.2. The reason is given in lines 353 to 361:
"Direct integration of channels with low SCNR can lead to a degradation in detection performance.
Weighting and selective techniques can be used to eliminate or reduce the detrimental effects of low SCNR channels on detection performance. The weighting technique adjusts the contribution of individual channels according to their SCNR, effectively reducing the influence of less reliable channels. The selective technique excludes channels that do not exceed a specified SCNR threshold, ensuring that the detection process only uses reliable channels. These techniques will help radar systems against the effect caused by channels with low SCNR, thus enhancing detection performance. This also indicates that channels with consistent SCNR are beneficial in improving radar detection performance."
Comments 4: How the location of distributed radar nodes affects the performance of the system?
Response 4: Thanks very much for your comments. The conclusion provided in Section 4.4 states that
" When the placement angle of the nodes is limited in a narrow range, the generated observation area exhibits enhanced directivity. This is attributed to the similarity in the direction of energy radiation from the nodes towards the observation area. In contrast, as the placement angle widens, it leads to a reduction in directivity. The mismatch between the shape of the predefined observation area and the geometric distribution of the nodes can result in wasted beam energy, which affects the radar detection efficiency."
In summary, a wider distribution of nodes is more conducive to forming non-directional observation regions, such as spheres or cubes.
A narrower distribution of nodes is more conducive to forming directional observation regions, such as ellipsoids and cuboids.
If the geometry of the nodes does not align with the shape of the observation area, the radar's energy utilization efficiency is reduced, resulting in the coverage of the generated observation area being significantly different from the predefined area.
Comments 5: There are several novel related literatures on MIMO radar can be included for comparison as follows:
[1] Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation
[2] MIMO Radar Waveform Design in the Presence of Multiple Targets and Practical Constraints
Response 5: Thanks very much for your comments. We have updated our manuscript, integrating them into the relevant sections of our paper. These literatures are cited on line 69 to clearly clarify the purpose of beamforming for collocated MIMO radar.
Comments 6: Some typo in line 349 of page 13.
Response 6: Thanks very much for your comments. We sincerely apologize for our negligence regarding this issue. To address this comment, we have identified the incorrect reference and have corrected the expression to accurately cite the source.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis manuscript elaborates on:
“..a resource management approach for distributed multiple-input multiple-output (MIMO) radar systems with phased array antennas, which aims to generate a regularly shaped observation area for long-range detection by focusing and shaping narrow beams from all transmit and receive nodes.
The problem is handled through a long and extensive mathematical formulation, but is missing the required physical interpretation or insight. In general it is written as a mathematical report rather than a technical - Engineering paper. Besides that its main drawback is the poor validation through a realistic case. Explicitly:
- The mathematical formulation must be re-organized with clear tasks and shortened. In its present enormous extension it is impossible to be followed. Do not try to write a book, concentrate on the scope and avoid repeating analysis already available in textbooks.
- Every equation must be connected to the physical structure or to the involved processing.
- Throughout the mathematical formulation a number of simplifying assumptions are considered, i.e. pulses or channels fully correlated or statistically independent. These are very serious restrictions and must be emphasized. It is also important to note which of them are in turn eliminated and which are retained up to the final expressions.
- Figures 2 and 3 illustrate a nice practical case, but the simulations (section 5) are performed for an idealized simple case. This is not convincing at all and fails to prove the validity of the presented methodology. Validation, through an example as that of Figs. 2 and 3 should be carried out.
- The example considered in section 5 is totally unclear and idealized. In view of its assumptions it can’t prove anything reliably, even if it was successful.
- For this example the aim defined in Table 2 is “threshold of detection performance equal to 0.9”. However, the results achieved probability of detection 0.44 or at best 0.79, which means that both numerical examples failed. There is no meaning to present such an extensive theory when its validation is a simple failure. You must correct anything needed to make it working successfully.
Syntactical and grammatical revision is needed.
Author Response
Comments 1: The mathematical formulation must be re-organized with clear tasks and shortened. In its present enormous extension it is impossible to be followed. Do not try to write a book, concentrate on the scope and avoid repeating analysis already available in textbooks.
Response 1: Thanks very much for your comments. We agree that the current presentation may detract from the clarity and focus of our manuscript. To address this issue, we have reorganized the mathematical formulas related to the system model. Our revisions aim to prioritize clarity, conciseness, and relevance to our research objectives.
- We have removed unnecessary details, such as some descriptions of non-essential statistical features.
- We have integrated relevant content, ensuring the echo model subsection now only introduces the relevant parameters and geometric relationships.
- Descriptions of echo correlation have been moved into the subsection on detection performance, and the specific calculation methods have been relocated to the simulation section.
The modified sections of the manuscript are now highlighted in red for easy identification
Comments 2: Every equation must be connected to the physical structure or to the involved processing.
Response 2: Thanks very much for your comments. We concur with the reviewer's suggestion, thus we also follow this suggestion when re-organizing the section of the system model. At the beginning of this section, we introduce the unified geometric relationships. In the echo model, we expand the description based on the basebond signal received in a node. The target echo received at nth node seen in lines 172, and the clutter echo received at nth node seen in lines 202. In the subsection of detection performance, we expand the description based on the output of matched filters seen in lines 225. The modified parts are highlighted in red in the manuscript.
Comments 3: Throughout the mathematical formulation a number of simplifying assumptions are considered, i.e. pulses or channels fully correlated or statistically independent. These are very serious restrictions and must be emphasized. It is also important to note which of them are in turn eliminated and which are retained up to the final expressions.
Response 3: Thanks very much for your comments. To address this comment, we have added a clear description of the correlation located at lines 238 to 246. For each assumption, we have provided a clear explanation of why it was made, its impact on the mathematical formulation, and how it affects the interpretation of the results. Specifically as follows: "Due to the orthogonality of the signals transmitted by the transmit nodes, the target echoes received from different transmit nodes are not correlated. Furthermore, since the clutter belts in different channels are spatially distinct, the echoes from different clutter belts are not correlated. Noise is assumed to be independent in both time and space. Note that our system model takes into account the spatial and temporal correlations of the target echoes as well as the temporal correlations of echoes from the same clutter belt. The specific methods for calculating the covariance of the matched filter outputs are detailed in Section 5."
Comments 4: Figures 2 and 3 illustrate a nice practical case, but the simulations (section 5) are performed for an idealized simple case. This is not convincing at all and fails to prove the validity of the presented methodology. Validation, through an example as that of Figs. 2 and 3 should be carried out.
Response 4: Thanks very much for your comments. We acknowledge that the uniform node placement scheme is overly idealistic. To validate our methodology, we have conducted additional simulations for a random node placement scheme to more closely align with practical cases.
Aside from some target-specific settings, the scenario and node configurations are consistent with those shown in Figures 2 and 3. All calculated results, including echo power and covariance matrices, strictly adhere to the system model.
To clarify the 'ideal assumptions' regarding the target, we have added content explaining the rationale for selecting the target to be detected in the worst-case scenario. This explains our choice to set the target's RCS and velocity to constant values, as detailed in lines 289 and the second footnote:
'The worst case for the targets to be detected is established based on three critical factors:
Targets with a small RCS produce a low-power echo, making them less detectable.
Targets moving at low speeds are more difficult to distinguish from ground clutter.
Small targets produce high-correlated echoes, which can degrade the performance of a non-coherent accumulation detector.'
Therefore, the target RCS and velocity parameters of all channels are set to the minimum value, which corresponds to the lower limit of radar detection capability.
Comments 5: The example considered in section 5 is totally unclear and idealized. In view of its assumptions it can’t prove anything reliably, even if it was successful.
Response 5: Thanks very much for your comments. We have revised Section 5 to provide a clearer and more detailed explanation for these examples. The purpose of each example is clearly described at the beginning, as shown in lines 505, 547, 572 and 613:
“In this subsection, we evaluate the influence of initial beamforming weights on the
optimization method for beamforming weights, as outlined in Section 3.2.5. We compare
two methods for selecting initial beamforming weights.”
"This subsection evaluates the influence of the pulse number on the power factor and the coverage of observation area."
"This subsection evaluates the influence of observation area locations on the required
time resources and the energy utilization efficiency."
"In this subsection, we compare the effects of node placement on the energy utilization
efficiency."
Comments 6: For this example the aim defined in Table 2 is “threshold of detection performance equal to 0.9”. However, the results achieved probability of detection 0.44 or at best 0.79, which means that both numerical examples failed. There is no meaning to present such an extensive theory when its validation is a simple failure. You must correct anything needed to make it working successfully.
Response 6: Thanks very much for your comments. The purpose and settings of the experiment may not have been clearly described. These two numerical examples of failure cases are produced by a monostatic phased radar, and a distributed phased radar using decentralized processing, respectively. The corresponding results serve as a baseline performance comparison for our research subjects, i.e., a phased distributed radar using centralized processing.
The focus of this paper is on the centralized processing of distributed phased array MIMO radar systems. Consequently, we have chosen to exclude results from decentralized processing approaches to maintain the clarity and focus of our study. Instead, we compare the performance of distributed phased radars under two different node placement schemes to that of a monostatic phased radar. The given performance threshold can be achieved under these two node placement schemes. The results are presented in Figure 13, as described in lines 611.
Reviewer 3 Report
Comments and Suggestions for Authors1. In the introduction, certain sentences exhibit ambiguity, particularly with the causal relationship in "Since distributed MIMO radars have widely separated antennas, the far-field hypothesis between the element interval of different nodes and the detection range cannot be satisfied. The methods in these references are not suitable for distributed MIMO radars" being unclear.
2. The title of Table 1 is incorrect. The definitions of symbols should not be called the "Table of Nations".
3. When ending a sentence and starting a new line, indentation is required. For example, lines 118, 135, 160, etc.
4. Lines 124 to 125 do not need to start a new paragraph.
5. There are symbols in the formula that are not explained, such as X☆ in formula (1).
6. The symbols in the formula do not need to be explained again, such as 𝑑 in formula (4) and target RCS, which has already been explained previously.
7. Each equation needs to be followed by punctuation.
8. For the equation in line 240, there is an error in the subscripts; they should be 𝑘,𝑚,𝑁,𝑙 and 𝑘,𝑚,𝑁,𝐿 .
9. The [?] in line 349 contains an expression error; it should be [35].
10. The numbering of Figures 8 and 9 is incorrect and needs to be adjusted.
11. More recent works concerning this topic can be reviewed, e.g.,Low Complexity MIMO-FBMC Sparse Channel Parameter Estimation for Industrial Big Data Communications, IEEE TII; EMVS-MIMO radar with sparse rx geometry: tensor modeling and 2D direction finding, IEEE TAES.
Author Response
Comments 1: In the introduction, certain sentences exhibit ambiguity, particularly with the causal relationship in "Since distributed MIMO radars have widely separated antennas, the far-field hypothesis between the element interval of different nodes and the detection range cannot be satisfied. The methods in these references are not suitable for distributed MIMO radars" being unclear.
Response 1:Thanks very much for your comments. Regarding the ambiguity in the causal relationship you pointed out in the introduction, we have made the following revisions to clarify the sentence: We compare the difference in thegeneral assumption and purpose for beamforming in collocated MIMO radars and distributed MIMO radars to explain beamforming methods for collocated MIMO radars are not applicable for distributed MIMO radars.The revision content, located at lines 70 to 79, is marked in purple in the manuscript as follows: “Collocated MIMO radars typically require the estimation of the direction of arrival, the angles of arrival, and the time delays. The elements of collocated MIMO radars satisfy the far-field assumption, which ensures that the direction from each element to the target is the same. As a result, beamforming is tasked to concentrate the beam energy in the azimuth and elevation directions of targets. However, these methods are not directly applicable to distributed MIMO radars. For distributed MIMO radars with widely separated nodes, the far-field assumption does not hold between elements of different nodes. Moreover, these systems must control the accumulation of beam energy in a three-dimensional space.“
Comments 2: The title of Table 1 is incorrect. The definitions of symbols should not be called the "Table of Nations".
Response 2: Thanks very much for your comments and we are very sorry for our negligence about this issue. The title of Table 1 is corrected as “ The Table of Notions and Symbols”.
Comments 3: When ending a sentence and starting a new line, indentation is required. For example, lines 118, 135, 160, etc.
Response 3: We acknowledge the importance of maintaining a consistent and professional document format throughout the manuscript. To address this comment, we have revised the manuscript to ensure that all paragraphs are consistently indented at the beginning of a new line, following the standard formatting guidelines. Specifically, we have corrected the lines mentioned (118, 135, 160, etc.) and have checked the entire manuscript to avoid any similar issues.
Comments 4: Lines 124 to 125 do not need to start a new paragraph.
Response 4: Thank you for your careful review and for pointing out the formatting issue. It has been corrected by removing the indentation at the beginning of lines 125. The position of the paragraph in the revised version is lines 133.
Comments 5: There are symbols in the formula that are not explained, such as X☆ in formula (1).
Response 5: Thanks very much for your comments. To address this comment, we have revised the manuscript to include a clear definition for all symbols used within the formulas. Specifically, we have added an explanation for "X☆" in the text immediately following formula (1), clarifying its meaning and context within our study. The added content located at lines 141, is marked in purple in the manuscript as follows:”X⋆ is the planar center of nodes.“
Comments 6: The symbols in the formula do not need to be explained again, such as ? in formula (4) and target RCS, which has already been explained previously.
Response 6: Thanks very much for your comments. To address this comment, we have revised the manuscript to remove the redundant explanations.
Comments 7: Each equation needs to be followed by punctuation.
Response 7: Thanks very much for your comments and we are very sorry for our negligence about this issue. We have carefully reviewed the entire manuscript and ensured that each equation is now properly punctuated.
Comments 8: For the equation in line 240, there is an error in the subscripts; they should be ?,?,?,? and ?,?,?,?
Response 8: Thanks very much for your comments and we are very sorry for our negligence about this issue. We have revised the equation to reflect these corrections and have double-checked the entire manuscript to ensure that all subscripts are accurate and consistent throughout.
Comments 9: The [?] in line 349 contains an expression error; it should be [35].
Response 9: Thank you very much for your comments, and we sincerely apologize for our negligence regarding this issue. To address this comment, we have identified the incorrect reference and have corrected the expression to accurately cite the source.
Comments 10: The numbering of Figures 8 and 9 is incorrect and needs to be adjusted.
Response 10: Thanks very much for your comments and we are very sorry for our negligence about this issue. We have reviewed all the Figures and their respective placements within the manuscript and have made the necessary adjustments to ensure the correct numbering and sequencing.
Comments 11: More recent works concerning this topic can be reviewed, e.g.,Low Complexity MIMO-FBMC Sparse Channel Parameter Estimation for Industrial Big Data Communications, IEEE TII; EMVS-MIMO radar with sparse rx geometry: tensor modeling and 2D direction finding, IEEE TAES.
Response 11: Thanks very much for your comments. These works are indeed relevant and have made significant contributions to our field. We have updated our manuscript, integrating them into the relevant sections of our paper. The first work is cited in line 60 to more clearly explain the application scenarios of phased array antennas. The second work is cited in line 72 to clearly clarify the purpose of beamforming for centralized MIMO radar.
Round 2
Reviewer 1 Report
Comments and Suggestions for Authorsfine
Reviewer 2 Report
Comments and Suggestions for AuthorsThank you for carefully addressing all of my comments and concerns.
