- Research Article
- Open Access

# Superresolution versus Motion Compensation-Based Techniques for Radar Imaging Defense Applications

- J M Muñoz-Ferreras
^{1}Email author and - F Pérez-Martínez
^{2}

**2010**:308379

https://doi.org/10.1155/2010/308379

© J. M. Mu˜noz-Ferreras and F. Pérez-Martínez. 2010

**Received:**17 November 2009**Accepted:**8 April 2010**Published:**16 May 2010

## Abstract

Radar imaging of noncooperative targets is an interesting application of all-weather high-resolution coherent radars. However, these images are usually blurred when using the standard range-Doppler algorithm, if a long coherent processing interval (CPI) is used, and motion compensation techniques are hence necessary to improve imaging quality. If the CPI is reduced enough, target scatterers do not migrate of resolution cells and their corresponding Doppler frequencies are constant. Hence, for a short CPI, motion compensation is not longer necessary, but Doppler resolution gets degraded. In that case, superresolution algorithms may be applied. Here, we compare the superresolution-based focusing techniques with motion compensation-based methods. Our conclusion is that imaging quality after employing the superresolution approaches is not improved and, consequently, the use of motion compensation-based approaches to focus the radar images cannot be circumvented. Simulated and real data from high-resolution radars have been used to make the comparisons.

## Keywords

- Motion Compensation
- Inverse Synthetic Aperture Radar
- Inverse Synthetic Aperture Radar Image
- Coherent Processing Interval
- Target Scatterer

## 1. Introduction

where is the light speed, is the transmitted bandwidth, is the transmitted wavelength, and is the variation of the target aspect angle during the CPI.

In adverse meteorological conditions (such as fog or haze) and in defense and security applications, imaging sensors based on electro-optical wavelengths may have a reduced performance [4–6]. However, the ISAR technique, because of its all-weather feature, may still provide useful target images in those conditions. These images may subsequently be exploited by Automatic Target Recognition (ATR) algorithms [7–10].

In ISAR imaging, if the processing interval CPI is not too large, target scatterers do not migrate of resolution cells and their corresponding Doppler frequencies remain constant during the CPI. Hence, for this case, the standard range-Doppler algorithm (RDA) obtains focused ISAR images. However, these images are usually not adequate for subsequent ATR algorithms, because they have a degraded cross-range resolution, according to (2). Note that it is likely that the variation of the target aspect angle is little for this short CPI.

On the contrary, if the CPI is large, the target scatterers migrate of resolution cells and the Doppler histories are complex functions. In this situation, RDA generates blurred ISAR images of decreased quality and motion compensation techniques are usually necessary to improve these ISAR products.

Moreover, the previous problem is exacerbated when the target is involved in complex motions, which is true for many practical cases. For example, maritime targets are usually involved in complex dynamics characterized by complicated yaw, pitch, and roll attitude motions [11].

Hence, in ISAR imaging of real noncooperative maneuvering targets, an important trade-off emerges; it is interesting to process a long CPI for achieving a fine cross-range resolution, but blurring effects arise for this long CPI because of the complex motion.

where is the central transmitted wavelength and is the range from the radar to the scatterer as a function of the slow-time .

Hence, according to (5), if the target motion is smooth, which is true for a reduced CPI, the Doppler frequency for each target scatterer is a constant and the standard RDA will generate a focused ISAR image. Take into account that the Doppler frequency is proportional to the cross-range position of the scatterer.

On the other hand, according to (3), if the target is involved in complex motions and the CPI is large, the range from the radar to the scatterer is a complex function and, consequently, the phase of the scatterer is also a complex function of the slow-time . This eventually implies that the scatterer Doppler frequency is not constant during the illumination interval CPI and, hence, if the standard RDA is applied, a severely blurred ISAR image is to be obtained. The problem rests in the fact that the processed CPI is too large and complex phase variations arise.

By trying to move away from motion compensation techniques, several authors have proposed to make use of superresolution techniques [12–17] to focus ISAR images. Because the blurring origin comes from a large CPI, the subjacent idea under the superresolution approach is based on reducing the observation interval CPI. As previously commented, for a reduced CPI, the target scatterers do not have enough time to experiment large variations of their Doppler frequencies or to migrate of resolution bins.

However, this CPI reduction certainly implies a loss of Doppler (cross-range) resolution. It is here where superresolution algorithms may theoretically improve the standard Fourier resolution. Hence, according to these approaches [12–17], focused ISAR images could be obtained without the necessity of processing long coherent intervals or of applying motion compensation algorithms.

In this paper, we compare the superresolution approaches with the results obtained after compensating the motion, by applying the methods to simulated and real data from complex targets. As far as the superresolution algorithms are concerned, we concentrate on the spectral estimation based on autoregressive (AR) coefficients [18], the multiple signal classification (MUSIC) estimator [19], and the Capon estimator [20].

Superresolution algorithms are based on parametric models of the signals and, consequently, they assume that the data satisfy some concrete hypotheses. In the ISAR scenario, we do not know to what extent the data match the models and, hence, the results are not as promising as expected. We have obtained images with many peaks whose positions do not necessarily correspond with the true locations of the scatterers. On the other hand, focusing indicators (such as entropy or contrast) may provide optimized values for the superresolution-based images because of their peaky nature. However, this is not indicative of an enhancement in the quality of the ISAR images, as discussed.

Our conclusion is that, when dealing with complex high-resolution radar data, the performance of the superresolution approach is not as good as expected and motion compensation methods should be applied if focused ISAR images are desired to be obtained.

Section 2 presents a brief introduction to RDA and motion compensation. In Section 3, the ISAR focusing technique based on superresolution algorithms is addressed. A brief description of the superresolution algorithms (AR, MUSIC, and Capon) is also given. Comparisons between superresolution and motion compensation-based techniques when using simulated data are presented in Section 4. Deep analyses of the obtained results in Section 4 let us derive important conclusions. After detailing the results achieved with live radar data in Section 5, some final conclusions conclude the paper in Section 6.

## 2. Range-Doppler Algorithm and Motion Compensation

- (i)
Acquire a set of range profiles by using a coherent high-resolution radar and stack them to form the matrix , where is the number of range bins, and is the total number of acquired range profiles. Hence, the columns of are the range profiles.

- (ii)
Apply a Fast Fourier Transform (FFT) to each range bin; that is, apply an FFT to each row of . The resulting matrix is the ISAR image generated by using RDA.

Target motion may be divided into a translational component and a rotational component [21, 22]. With respect to the line-of-sight (LOS), the translational motion may further be decomposed into a radial (along-LOS) component and a tangential (across-LOS) component. The rotational motion is formed by the yaw, pitch, and roll attitude components.

In this context, the obtained ISAR image is a projection depending on target dynamics and orientation. Concretely, this ISAR projection plane is a plane formed by the LOS vector and a vector normal to the effective rotation vector and contained in the plane perpendicular to LOS [22]. The effective rotation vector is the projection of the rotation vector over the plane perpendicular to LOS.

The rotational motion and the tangential translational motion may generate the desired Doppler gradient among scatterers situated in the same range bin. However, motion is also responsible for the possible appearance of blurring effects. Concretely, when the CPI is large and RDA is applied, the radial (along-LOS) component of the translational motion causes a large blurring in the ISAR images and the rest of motion may produce the so-called Migration Through Resolution Cells (MTRCs) [23].

Generally, before applying RDA, motion compensation techniques are necessary to improve the quality of the ISAR images. Thus, for translational motion compensation, two stages are often considered; range-bin alignment [1, 24–27] and phase adjustment [28–31]. On the other hand, for compensating the rotational motion, several methods may also be found in the literature [32–36].

In this paper, when dealing with motion compensation issues, we employ the extended envelope correlation method [26] for range-bin alignment, the entropy minimization approach [28] for phase adjustment, and the uniform-rate technique [36] for rotational motion compensation.

The focusing technique based on superresolution algorithms circumvents the use of motion compensation-based approaches, by reducing the CPI, as explained in the next section.

## 3. ISAR Focusing Technique Based on Superresolution Algorithms

- (i)
Consider a reduced number of range profiles of . This is equivalent to reducing the CPI. This simplified set may mathematically be expressed as , where , with . The selection of depends on the target dynamics.

- (ii)
For the th range bin, estimate its high-resolution frequency content by applying a superresolution algorithm. That is, apply a superresolution technique to each row of .

- (iii)
Repeat the previous step for all the range bins. Subsequently, construct the superresolution ISAR image , where indicates the number of Doppler bin.

Take into account that SRA may apply to the AR, MUSIC, or Capon spectral estimators, on which the paper concentrates. For completeness, in the next subsections, a brief description of these spectral estimators is provided.

### 3.1. Spectral Estimation Based on AR Coefficients

where are the filter coefficients, is the filter order, and is the white noise at the input.

Some methods to calculate the filter coefficients and the variance of the white noise have been proposed [18]. Note that these values are necessary to evaluate (7). In this paper, we have used the modified variance method, which minimizes the forward and backward prediction errors [18].

### 3.2. Spectral Estimation Based on MUSIC

The estimated number of sinusoids *N* _{
s
} is the value of *q* which minimizes expression (11).

### 3.3. Capon Spectral Estimation

where is the vector provided by (10) and is the correlation matrix (of dimensions ) of the input signal .

## 4. Comparison Results for Simulated Data

Radar parameters for the simulated target.

Radar type | Stepped frequency |
---|---|

Central Frequency | 9 GHz |

Stepped frequencies in a burst | 64 |

Number of bursts | 512 |

Pulse repetition frequency | 15000 Hz |

Bandwidth | 512 MHz |

Coherent processing interval | 2.18 s |

In the literature, it is assumed that the greater the contrast and the lower the entropy are, the more focused the ISAR images are [28, 30]. This is usually valid to make comparisons among different autofocusing methods. However, as shown next, the entropy and the contrast are not proper focusing indicators to measure the image quality of the ISAR images obtained by using a superresolution-based technique.

- (i)
The ISAR images obtained by applying the technique based on superresolution algorithms usually present spurious scatterers; that is, they have peaks whose positions do not correspond with locations of real scatterers. We attribute this behavior to the fact that the inherent parametric model assumed by the superresolution techniques may not adequately adjust to the ISAR data. Note that the ISAR data are complex; as an example, take into account that interference among scatterers is always present in complex targets.

- (ii)
Hence, the qualitative appearance of the ISAR images obtained with the superresolution-based approach is not satisfactory. Their quality may be greater than the RDA-based images (Figures 4 and 5), but it is clear that the superresolution-based approach does not outperform the motion compensation-based results (Figure 9), where the scatterers are clearly visible and localizable. Possible subsequent ATR algorithms may have problems with the spurious peaks appearing in the superresolution-based ISAR images.

- (iii)
By comparing the results provided by the AR, MUSIC, and Capon spectral estimators, the most promising output is the one given by the Capon estimator, since the target contour is more detailed. On the other hand, it is clear that, for complex radar data, the Akaike criterion misestimates the number of sinusoids existent in each range bin.

- (iv)
From a direct reading of Table 2, one may conclude that the images obtained with the superresolution-based technique are highly focused, because they have high contrast and low entropy values. However, according to the previous conclusions, we know that the superresolution approaches do not outperform the motion compensation-based techniques. The explanation for the high contrast and low entropy values must be found in the very abrupt peaks generated by the parametric approaches [18]. We admit that these focusing indicators are really useful for other ISAR contexts [28, 30], but we also conclude that they are useless for assessing the performance of ISAR focusing superresolution-based approaches.

## 5. Comparison Results for Real Data

Radar parameters for the live acquisition.

Radar type | LFMCW |
---|---|

Central frequency | 28.5 GHz |

Ramp repetition frequency | 1000 Hz |

Bandwidth | 1 GHz |

Coherent processing interval | 0.6 s |

The results obtained with real data are analogous to the ones achieved with simulated data. Consequently, the conclusions drawn at the end of Section 4 are also applicable to the real data detailed in this section.

## 6. Conclusions

The ISAR technique is a radar imaging method which may be very interesting in defense and security applications. In fact, ISAR can provide images of noncooperative targets in adverse meteorological conditions and in degraded scenarios.

Generally, it is interesting to process long illumination intervals to guarantee a high Doppler resolution. In this case, it is almost mandatory to apply motion compensation techniques, if focused ISAR images are desired. Otherwise, the radar images are highly blurred and are useless for recognition/identification purposes.

On the other hand, if the processed CPI is reduced, the target scatterers do not migrate of resolution cells and their associated Doppler frequencies may be considered to be constant. In this case, the ISAR images have a poor Doppler resolution, which may theoretically be improved by using superresolution algorithms.

In this paper, we have concentrated on the comparison between the superresolution-based approaches and the motion compensation-based methods with respect to their capabilities of focusing ISAR images. Both simulated and real data from complex targets have been used.

Our main conclusion is that motion compensation cannot be circumvented, that is, it is always necessary to compensate the motion, if focused high-resolution ISAR images are desired. The ISAR images obtained after applying superresolution approaches usually present spurious peaks, whose positions do not correspond to locations of real scatterers. These images could not be properly exploited by subsequent ATR algorithms.

The paper also provides the values of the entropy and the contrast for all the presented ISAR images. The superresolution-based images have high contrast and low entropy values, but this is not indicative of an increase in image quality.

## Declarations

### Acknowledgments

This work was financially supported by the Spanish National Board of Scientific and Technology Research under Project TEC2008-02148/TEC. The authors thank Dr. A. Blanco-del-Campo, Dr. A. Asensio-López, and Dr. B. P. Dorta-Naranjo for providing the live data of the sailboat.

## Authors’ Affiliations

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