A Variable-Scale Coherent Integration Method for Moving Target Detection in Wideband Radar

Round 1

Reviewer 1 Report

 

General Comments

This paper addresses the problem of detecting distributed targets with a pulsed Doppler radar. The range rate induced by the target’s relative velocity is such that range migration can occur over the coherent processing interval (CPI).  The radar is wideband in the sense that the Doppler shift varies significantly across the bandwidth of the transmitted signal,  equation (6).  The Radon Fourier transform, refs [16-18], offers a solution to this problem for single-scatterer targets and, as the authors here point out, the RFT could be modified to address distributed targets by applying a “sliding window” at its output. In common with refs [16-18] this paper only considers a linear FM transmit signal and the reflection coefficients of the target are assumed to be constant over the CPI.

In this paper, a polyphase filter-bank is applied to the fast-time signal. There are several advantages to this; (i) it exploits the computational benefits of long established work of such filter-banks; (ii) the effective range resolution at the output of each filter is reduced which may avoid range migration; (iii) the pulse to pulse coherent integration is based on the centre-frequency of each filter and thus can approximate the variation of Doppler shift with frequency. The authors also provide system design equations and computational analysis of their algorithm with respect to RFT and standard coherent integration.

I think that the authors have provided convincing arguments about the computational advantages of their approach with respect to RFT and as such it is novel.  However I think they need to:

·       compare the performance of their algorithm with RTF with a sliding window.

·       Alter the conclusions to reflect the outcome of this.

Specific points are described below.

Detailed Comments

Line 59, “For the detection of moving extended targets, a variable-scale moving target detection (VSMTD) method based on subband coherent integration is proposed in this paper. The bandwidth of a signal processing system dictates its processing rate (calculation scale),  whereas the bandwidth of a radar system determines its resolution (observation scale).” - You make much use of the term “scale”. Is this really necessary? Multi-rate filter banks have been around for a long time and have not needed the concept of scale when the filters share the same output sampling rate (as they do here). The term “scale” is used in wavelet analysis, where the filters may have different output sampling rates.

Line 94, eqn(4), Is there a subscript missing on R? Should be R_l (R subscript l) – otherwise the summation does not make sense.

Line 99, “This paper defines .. as a constant in the time of coherent integration” – this is an important point and should be made in the introduction.

Line 101, eqn(6) the right hand side should be frequency, f, rather that carrier frequency, f_c.

Line 108, Is the POSP ireally needed here? The Fourier transform of a sinc function is a standard results; if you are using the approximation please be clear what it is you are approximating, i.e. the fast-time Fourier transform of eqn(5).

Line 111, “on average” – what does this mean here?

Line 113, eqn(7) & (8), - the notation is could be more consistent here. In (7) we have S(.,.) which is a functions of  fast-time-frequency and slow-time, both continuous variables. Then in (8) you change the order, slow-time is now a subscript and the second variable m is the frequency band number. Latter in the paper when you sample in fast time and slow time we have three variables s(., ., .).

Line 113, eqn(8)  - this equation is important for the readers understanding. It might be better to be more explicit. You are basically expressing the rect{} in (7) as a summation of narrower rect{} functions in (8) - summed over m? – summing (8) over m then gives (7)?

Line 115, “The scale-transformed signal..” – This the inverse (fast-time) Fourier transform of (8) – there is no need to invent a new transform.

Line 122, “It should be noted ..” – it is a bit late in the paper to make this remark – this should be made clear in the introduction – more specifically, what do you mean by a wideband radar. In your simulation section the ratio of bandwidth to carrier frequency is only 1/20?   

Line 149, “And the different scale transformation..” – again the use of the word scale is not helpful – Figure 3(b) clearly shows the frequency responses of the filters in a fast-time filterbank. In the figure legend “DFT filter bank” is not helpful at this point as you have not yet introduced the efficient implementation of Fig 12.

Line 153, figure 4, At this point in the paper it difficult for the reader to interpret. You need to specify how exactly it was calculated. I suspect it might be easier latter in the paper.

Line 190, eqn(17), should this be magnitude-squared rather than just magnitude?

Line 191, figure 7, - Can the Doppler filtering be implanted with an FFT? Either way please explain this point.  I am assuming the outputs of the Doppler filterbank are combined as per equation (17) – is that correct.?

Line 318, Table 2 – Is the fast time signal samples at the Nyquist rate – don’t think that you mentioned it. N_a is defined twice. Am I correct in thinking that the no. of samples in a PRI is much larger than the Filter order L_n?  - and after downsampling you have about 1000 samples in a PRI?

Line 367, “sliding window” and RFT – this really needs to be mention earlier in the paper.

Line 371, “The high resolution is not lost..” – this needs to be introduced and described in detail earlier in the paper when you are describing the algorithm.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper proposes a coherent integration method (VSMTD) for wideband radar to resist the range migration and Doppler broadening. On the other hand, it increases the coherent integration time by mitigation the range migration in a sufficiently narrow sub-band. On the other hand, it increases the coherent integration time by mitigation the range migration in a sufficiently narrow sub-band. Overall, the paper is interesting and the organization is well. Thus, the reviewer thinks the paper could be accepted after some necessary revisions. Please consider the follow points:

 

1. How to understand the sentence “Since there is no coherence across the range cells for extended targets…”? Is there no coherence between multiple scattering points at different range cells or is there no coherence between single scattering points at different range cells?

2. For coherent integration and detection with wideband radar, the traditional “stop-go” motion model maybe difficult to describe the real motion state [r1]. And the scale effect may occur and should be considered. The corresponding comments or description should be given.

3. How to derive formula (8) to formula (9)? Sub-band division is recommended for more detailed derivation and analysis.

4. Figure clarity needs to be improved. Also, what does the rise and fall of D mean? Please explain Figure 5 in detail.

5. What are the principles of filter bank segmentation design? How to reasonably determine the number of channels of the filter?

6. The description of schematics and flow charts needs to be strengthened.

7. RFT can coherently accumulate multiple scatter points, so what is the reason why it cannot be effectively accumulated for extended targets? please explain.

8. What’s the energy of each of the multiple scattering points of the extended target in the broadband case of Section 6? How to set it during simulation?

9. How to solve the problem of Doppler broadening when the target’s maneuverability enhances?

 

[r1] Hypersonic Target Detection and Velocity Estimation in Coherent Radar System Based on Scaled Radon Fourier Transform. IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 6, 2020.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Nice paper.