# An Improved Multi-Frame Coherent Integration Algorithm for Heterogeneous Radar

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Heterogeneous Signal Model

#### 2.2. Improved Keystone Transform

#### 2.3. Fixed-Phase Compensation

#### 2.4. Variable Selection Criteria

#### 2.5. Algorithm Summary

## 3. Simulation Results

- Single-frame coherent integration method based on conventional KT (parameters of the single frame are shown in Table 1 as the third frame);
- The intra-frame coherent and inter-frame non-coherent integration method based on conventional KT (parameters of five frames listed in Table 1, the same below);
- Multi-frame coherent integration using the proposed method.

- Single-frame coherent integration based on the conventional KT (the parameters of the single frame are shown in Table 1 as the third frame);
- Five-frame non-coherent integration based on the improved KT, without fixed-phase compensation (the parameters of the five frames are shown in Table 1, the same below);
- Five-frame coherent integration based on the improved KT, with the fixed-phase compensation method based on the minimum image entropy [14];
- Five-frame coherent integration using the proposed method.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An example of heterogeneous echoes. During a scanning task, a phased array radar sequentially generates transmission beams of linear frequency modulation pulses with varying working parameters in three azimuths. If a target appears in the overlapping region of these three beams, its echoes will be detected in multiple frames with distinct working parameters, thereby exhibiting heterogeneity. ${F}_{c}$, $BW$, $PRF$, and $PW$ represent carrier frequency, bandwidth, pulse repetition frequency, and pulse width, respectively.

**Figure 2.**An example of the fast-time frequency and slow-time spectrums before and after conventional KT or improved KT. The heterogeneous signal consists of 3 frames with carrier frequencies of 1.5 GHz, 3.4 GHz and 2.2 GHz, respectively. (

**a**) The raw spectrum. (

**b**) The spectrum after conventional KT which kept the carrier frequencies unchanged. (

**c**) The spectrum after improved KT which aligned the carrier frequencies of each frame to 2.2 GHz.

**Figure 3.**The diagram and typical results of compensating fixed phase B based on fractional range bins. (

**a**) The diagram of compensating fixed phase B using compensation term described in Equation (25). In this example, it is assumed that the target’s reference range bin ${L}_{ref}$ is 128.3. Choosing the denominator factor ${N}_{FrR}=3$, the strongest peak in multi-frame integrated result appears at the fractional range bin 128 + 1/3, which is called the detection range bin ${L}_{det}$ and serves as an estimation for ${L}_{ref}$. (

**b**) The typical output of a point scatterer in the range–Doppler spectrum obtained with Equation (25). (

**c**) The typical output of a point scatterer in the range–Doppler spectrum obtained with Equation (29).

**Figure 4.**An example of intermediate results of the compensations of fixed phases A and B. The heterogeneous signal consists of 3 frames. (

**a**) The phase variation along slow time when only compensating fixed phase A. (

**b**) The phase variation along slow time when only compensating fixed phase B. (

**c**) The phase variation along slow time when compensating both fixed phases A and B. (

**d**) The Doppler profiles of the range–Doppler spectrums obtained under four different compensation conditions.

**Figure 5.**The flowchart of the improved multi-frame coherent integration algorithm. The solid arrows represent the steps before the Doppler ambiguity estimation, while the dashed arrows represent the steps after the Doppler ambiguity estimation. Therefore, the latter steps need to be performed after the former steps. In the end, the desired multi-frame coherent integrated result is the range–Doppler spectrum obtained from the dashed arrows.

**Figure 7.**The range–Doppler spectrum obtained by multi-frame non-coherent integration based on conventional KT. (

**a**) The amplitude of the range–Doppler spectrum in dB scale. (

**b**) The projection of figure (

**a**).

**Figure 9.**The range–Doppler spectrum obtained from multi-frame coherent integration using the proposed algorithm. (

**a**) The amplitude of the range–Doppler spectrum in dB scale. (

**b**) The projection of figure (

**a**).

**Figure 10.**Doppler profile comparison of the range–Doppler spectrums obtained from the conventional method and the proposed method.

**Figure 11.**Range profile comparison of the range–Doppler spectrums obtained from the conventional method and the proposed method.

**Figure 12.**The comparison of the detection performance of four methods. (

**a**) Input SNR and output SNR curve. (

**b**) Input SNR and detection probability curve, obtained from the cell-averaging constant false-alarm rate (CA-CFAR) thresholding with a false-alarm rate of 10

^{−6}.

Frame Number | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Carrier frequency/GHz | 2.86 | 2.94 | 3.00 | 2.92 | 2.88 |

Bandwidth/MHz | 150 | 200 | 180 | 160 | 120 |

Pulse width/μs | 20 | 18 | 20 | 30 | 22 |

PRF/KHz | 1.83 | 1.63 | 2.03 | 1.97 | 2.05 |

SNR/dB | −19 | −20 | −21 | −22 | −18 |

Pulse number | 9 | 12 | 11 | 12 | 10 |

Time interval from the previous frame/ms | 3.0 | 2.0 | 1.0 | 1.5 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Zhang, H.; Wang, X.; Dong, Q.; Lyu, X.
An Improved Multi-Frame Coherent Integration Algorithm for Heterogeneous Radar. *Remote Sens.* **2023**, *15*, 4026.
https://doi.org/10.3390/rs15164026

**AMA Style**

Liu Y, Zhang H, Wang X, Dong Q, Lyu X.
An Improved Multi-Frame Coherent Integration Algorithm for Heterogeneous Radar. *Remote Sensing*. 2023; 15(16):4026.
https://doi.org/10.3390/rs15164026

**Chicago/Turabian Style**

Liu, Yiheng, Hua Zhang, Xuemei Wang, Qinghai Dong, and Xiaode Lyu.
2023. "An Improved Multi-Frame Coherent Integration Algorithm for Heterogeneous Radar" *Remote Sensing* 15, no. 16: 4026.
https://doi.org/10.3390/rs15164026