Fast Variational Bayesian Inference for Space-Time Adaptive Processing

Round 1

Reviewer 1 Report

This paper presents a novel integration of the VBI framework into the STAP algorithm, aiming to enhance convergence speed and outperform the conventional SBL approach. The proposed rapid iterative algorithm addresses the computational burden posed by matrix inverse operations, yielding promising results. The empirical analyses conducted on both synthetic and real datasets convincingly demonstrate the algorithm's prowess in STAP and target detection tasks, coupled with its commendable ability to mitigate computational complexity. While the manuscript exhibits reasonable proofs, equations, and outcomes, there is room for further refinement and improvement. The following suggestions are offered to enhance the overall quality of the paper:

1. It is unclear how Figure 2 was constructed, and the computational complexities of different

algorithms appear to follow distributions with similar shapes but different scales.

2. In the algorithm comparison, LSMI-STAP seems to perform the poorest in both simulated

and real-case scenarios. The presence of LSMI-STAP causes the curves of other algorithms to

overlap. It is recommended to omit this algorithm and replot the figures for optimal

presentation.

3. According to the results in Figure 3, the M-VBI-STAP algorithm accurately captures the true

distribution pattern, but it underestimates the true values when the abscissa is small.

Attempting to explain the reasons behind this phenomenon could aid readers in better

understanding the algorithm. Additionally, the results in Figure 3 suggest that the

Normalized Doppler frequency and Normalized spatial frequency in the simulation

experiment seem to be independent. Introducing additional complex distribution patterns

could better illustrate the algorithm's advantages.

4. In the real-case scenario, presenting distribution plots of Normalized Doppler frequency and

Normalized spatial frequency for different algorithms can provide readers with a more

intuitive view of the estimation effects of various algorithms.

5. While variational algorithms do alleviate computational burdens, they are not without

limitations. It is suggested that the authors, in the conclusion section, discuss both the

drawbacks of variational algorithms and the applicable scenarios and potential

enhancement strategies of the algorithm proposed in this paper.

6. The fusion of variational algorithms in the context of STAP constitutes a key innovative

aspect of this paper. However, the literature review on variational algorithms still requires

further improvement. It is recommended that the authors elucidate the fundamental

principles of variational algorithms and highlight recent research accomplishments in various

fields, for example

[1] Zhou S, Xu A, Tang Y, Shen L. Fast Bayesian inference of reparameterized gamma process with random effects. IEEE Transactions on Reliability. In press. doi: 10.1109/TR.2023.3263940.

[2] Turlapaty, Anish C. "Variational Bayesian estimation of statistical properties of composite

gamma log-normal distribution." IEEE Transactions on Signal Processing 68 (2020): 6481-6492.

[3] W. Yuan, Z. Wei, J. Yuan and D. W. K. Ng, "A Simple Variational Bayes Detector for Orthogonal Time Frequency Space (OTFS) Modulation," in IEEE Transactions on Vehicular Technology, vol. 69, no. 7, pp. 7976-7980, July 2020.

Furthermore, there are areas in the writing that need further improvement:

1. Page 2, line 15, "The symbols The symbols?" - This sentence appears to be incomplete or

unclear. Clarification is needed.

2. Formulas should be punctuated appropriately based on the context.

3. Unnecessary formula numbering can be omitted.

4. Page 6, line 153, the algorithm used to estimate should be specified.

5. Page 14, line 266, the description regarding the equipment on which the algorithm runs

seems insufficient.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 2 Report

STAP approaches based on SBL have been beneficial in reducing the training sample requirement. To improve the convergence speed and the computational efficiency, the variational Bayesian inference (VBI) is introduced to STAP in this research However, the experimental part of the manuscript was not comprehensive enough to highlight the superiority of the proposed method. It is hoped that the authors will make further improvements to the manuscript. Here are my specific comments： 

1.     Avoid the first-person position, such as 'we', or 'they' in technical writing, such as in ln 73, 109...etc. Third-person singular or past tense is preferred. Please revise accordingly.

2.     The full name and content of MCARM must be introduced before the acronym is used in ln 272.

3.     The past tense of the verb was incorrect and a missing period between two sentences in ln 286.

4.     Fig 1, 4, and 9 were presented before the illustration content. Please present the illustration of figures in the content before they were introduced.

 

5.     For numerical comparison between all detection algorithms extending from Fig 9, a signal-noise-ratio comparison is a decent and clear analysis instead of the average power analysis of Table 6. Please revise.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 3 Report

In this paper, the authors deal with the problem of radar space time adaptive processing, proposing a proper modification of the VBI (Variational Bayesian inference) method in order to guarantee a reduced computational cost.

Overall the paper is sufficiently well-written and clear. Moreover, the results clearly show that the method has approximatel the same performance as the related competitor, but improving substantially the computational efficiency.

However, before publication the manuscript needs to be edited in some parts.

Firstly, some typos are present in the paper, see e.g.:

"clutter pulse noise covariance matrix" --> "clutter plus noise covariance matrix"

"chosen empiriccally" --> "chosen empirically"

"the expcatations." --> "the expectation."

Please, carefully proofread the entire paper.

On line 113, "According to the conjugate prior principle", please add a reference.

At the beginning of Introduction, some important references on STAP are missed. Hence, the manuscript is not framed in the STAP literature in the best way. Please, see the following and related references:
[1] W. L. Melvin, ``Space-time adaptive processing and adaptive arrays: Special collection of papers,'' IEEE Trans. Aerosp. Electron. Syst., vol. 36, no. 2, pp. 508509, Apr. 2000.
[2] L. Pallotta et al., (2021). Phase-only space-time adaptive processing. IEEE Access, 9, 147250-147263.
[3] S. T. Smith, ``Adaptive radar,'' in Wiley Encyclopedia of Electrical and Electronics Engineering. Hoboken, NJ, USA: Wiley, 2001.

As to the review of literature dealing with the problem of covariance estimation in the presence of a reduced number of sample data, several important papers in the field are missed. As is, the study is not fear. Please see the following papers and references therein:
[4] M. Steiner, and K. Gerlach (2000). Fast converging adaptive processor or a structured covariance matrix. IEEE Transactions on Aerospace and Electronic Systems, 36(4), 1115-1126.
[5] A. Aubry et al. (2017). A geometric approach to covariance matrix estimation and its applications to radar problems. IEEE Transactions on Signal Processing, 66(4), 907-922.
[6] A. De Maio et al. (2009). Knowledge-aided covariance matrix estimation: a MAXDET approach. IET radar, sonar & navigation, 3(4), 341-356.
[7] B. Kang et al. (2014). Rank-constrained maximum likelihood estimation of structured covariance matrices. IEEE Transactions on Aerospace and Electronic Systems, 50(1), 501-515.

As to the pseudocode of the M-VBI, is the choice of the parameters a-d equal to 10^-6 motivated somehow? Or are they empirically chosen?

At the end of conclusions some hints for future works should be provided.

The paper needs to be carefully proofread.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have revised the paper well.

Reviewer 2 Report

Thank you for your hard work and improvement. The article is qualified to be published in my opinion. Good luck!

Reviewer 3 Report

The authors have addressed all my previous comments, therefore the manuscript has been improved and can be accepted for publication.