An Image-Based Focusing Performance Improvement Method for Airborne Synthetic Aperture Radar

Highlights

What are the main findings?

• This paper proposes an innovative signal distortion compensation method based on single-look complex synthetic aperture radar (SAR) images, which effectively suppresses sidelobes in SAR images while enhancing image focusing quality.
• The general applicability of the proposed method to SAR imagery is validated via image processing and analysis of data acquired from airborne SAR and unmanned aerial vehicles SAR.

What are the implications of the main findings?

• The focusing performance of airborne SAR images can be further improved by the proposed method, thereby enhancing the quality of SAR images and contributing to the accuracy of applications such as registration and target recognition, etc.
• For simplified or low-cost SAR systems, such as UAV SAR, the imaging quality can be effectively improved.

Abstract

Synthetic Aperture Radar (SAR) is one of mainstream remote sensing techniques, offering all-weather, day-and-night operational capabilities. However, throughout the processes of signal transmission, propagation, and reception, it is difficult to ensure that the amplitude and phase of the SAR signal strictly follow a linear frequency modulation (LFM) characteristic. The resulting signal distortion often leads to main lobe broadening and sidelobe elevation, degrading the focusing performance of SAR images. Traditionally, this issue has been addressed primarily through SAR system internal calibration and pre-distortion compensation, which makes it challenging to maintain the signal in an ideal state over the long term. At the same time, many simplified SAR systems also lack an internal calibration design, such as low-cost UAV-borne SAR payloads. In this paper, we propose a novel signal distortion compensation method based on SAR image data. Without relying on SAR system calibration signals, this method estimates and compensates for signal distortion directly using SAR image data, thereby improving SAR image focusing performance, achieving a resolution closer to the theoretical bandwidth and lower sidelobe. The processing and analysis of both manned and unmanned airborne SAR image data and calibration signals demonstrate that the proposed method effectively compensates for signal distortion phases, achieving performance comparable to that of real-time calibration-signal-based methods.

1. Introduction

Synthetic aperture radar (SAR) plays an important role in the field of remote sensing and Earth observation since it can provide high-resolution remote sensing images under all weather conditions [1,2,3,4]. With the development of electronic components and system integration techniques, high-resolution imaging has become a typical feature of modern SARs. SAR’s high-resolution imaging capability enables the detailed visualization of ground features with exceptional clarity. These advantages not only facilitate precise target identification in military reconnaissance [5], but also drive transformative advancements in civilian sectors. Key applications include precise surface deformation monitoring at the millimeter scale for early warning systems [6], accurate assessment of crop growth conditions [7], and rapid generation of high-precision damage maps in post-disaster scenarios [8]. Such capacity for capturing intricate spatial details addresses the critical demand for all-weather, day-and-night acquisition of accurate geographic information [9], which is essential for domains ranging from national security and emergency response to resource management and planning.

Commonly, SAR transmits a linear frequency modulation (LFM) signal to achieve a large time-bandwidth product [10], which is essential for obtaining a high-resolution range. However, due to the inherent nonlinear characteristics of analog devices—such as signal modulation circuits, power amplifiers in the radio frequency (RF) unit, and band-pass filters—the LFM signal inevitably suffers from both amplitude and phase distortions during transmission and reception [11,12,13]. These distortions degrade the ideal signal properties, leading to broadening of the main lobe width, elevation of the peak side lobe ratio (PSLR), and deterioration of the integral side lobe ratio (ISLR) [14,15]. For high-resolution SAR systems, which require extremely large bandwidth to achieve finer range resolution, the adverse effects of amplitude and phase distortions become significantly more pronounced. As bandwidth increases, the non-ideal frequency response of analog components—such as amplitude ripple and nonlinear phase deviations—introduces more severe distortions across the wider frequency span. This exacerbates the mismatch in the matched filtering process, further broadening the main lobe and raising side lobe levels, thereby degrading image contrast and geometric fidelity [16]. Consequently, maintaining precise amplitude and phase linearity over a broad bandwidth is critical for high-resolution SAR, placing stringent demands on component design, calibration, and compensation techniques to preserve image quality [17].

To address the issue of nonlinear time-frequency relationships in SAR signals throughout the entire transceiver loop, traditional approaches primarily employ pre-distortion compensation [18]. This method records a set of signals that have passed through the complete transceiver loop and compares them with ideal linear frequency-modulation signals to obtain the amplitude and phase to be compensated. These compensation values are then written into the baseband signal generator to ensure that the transmitted signal maintains a near-ideal time-frequency relationship upon reception. Various improvements and optimizations to this method have also been proposed in the literature. To address the issue of nonlinear frequency-sweep errors in wideband linear frequency modulation sources, Kim et al. designed a hardware extraction scheme based on a physical delay-line mixer and a zero-crossing detector [19], achieving low-cost open-loop pre-distortion compensation by solving for the quadratic phase coefficient. To overcome the excessive complexity of measuring amplitude and phase distortions in ultra-wideband radar, Hu et al. employed a digital oscilloscope to capture the transmitted waveform and proposed a pre-distortion strategy based on direct time-domain subtraction between the ideal signal and the measured signal, thereby circumventing the complex modeling of the transfer function [20]. To further improve compensation accuracy in noisy environments, Wang et al. introduced multi-pulse coherent averaging to suppress background noise and achieved refined calibration of nonlinear frequency-modulated signals through deconvolution in the frequency domain [21]. To address the severe amplitude and phase distortions caused by RF components on 800 MHz ultra-wideband signals, Jiang et al. proposed an inverse compensation scheme based on direct digital waveform synthesis, enabling point-by-point pre-correction of wideband signals by fitting the instantaneous amplitude and phase errors using a power series [22]. Kim et al. developed a piecewise second-order polynomial regression algorithm based on inflection-point identification, effectively eliminating phase discontinuities caused by full-band fitting [23]. To resolve the trade-off between high-precision fitting and real-time computational complexity on FPGAs in airborne SAR systems, Chen et al. adopted a 14th-order high-order polynomial to fit complex distortion curves and optimized the parallel computing efficiency of FPGAs using a piecewise linear approximation algorithm, achieving real-time adaptive generation of pre-distortion for airborne SAR [24]. Han and Ding et al. employed the GLS method to perform a data-based compensation for errors with a sinusoidal form, which can reduce sidelobes of point targets [25,26].

Although the pre-distortion compensation method based on calibration signals can effectively mitigate sidelobe elevation and main lobe broadening caused by signal distortion, it has notable limitations. First, the extraction of error coefficients strictly depends on the high signal-to-noise ratio (SNR) environment provided by laboratory anechoic chambers or internal closed-loop calibrators. During actual SAR system operation, factors such as ambient temperature drift, component aging, and space radiation often cause pre-calibrated parameters to drift non-negligibly [27,28], leading to system performance degradation over time, and the compensation effect may deteriorate or even fail. Additionally, some simple airborne SAR systems may not incorporate an internal calibration loop, such as low-cost UAV-borne SAR payloads. Moreover, the delay lines, circulators, and other components in the calibration signal path do not fully represent the actual operating path [29,30]. Furthermore, calibration signals cannot capture signal distortions caused by factors such as the atmosphere [31]. If the reliance on the calibration link can be eliminated and error parameters can be estimated and compensated directly using SAR images, this would offer significant engineering application value [32]. Therefore, it is necessary to investigate distortion-compensation methods based on SAR image data to address the above issues.

There are currently few studies on signal distortion compensation methods based on SAR images. This paper presents an in-depth investigation into this issue and proposes a compensation method that leverages SAR image data. The approach identifies strong scatterers in the image and applies a series of signal processing techniques to accurately estimate the error phase. A least-squares method is then employed to fit the error phase using a finite-order polynomial, thereby enhancing its generalization capability for compensation. The fitted phase is further processed by removing linear components to prevent any image shift caused by the compensation phase. This allows the nonlinear frequency components of the signal to be extracted without the need for calibration signals, enabling effective distortion compensation and yielding well-focused SAR images. To validate the effectiveness of the proposed method, experiments were conducted using SAR image data acquired from both manned and unmanned aerial vehicles. The experimental results demonstrate that the proposed method effectively compensates for SAR signal distortion, reducing sidelobes and achieving main lobe resolution closer to the theoretical value.

The remainder of this paper is organized as follows. Section 2 introduces the signal model for the proposed image-based distortion compensation method. Section 3 presents the experimental results obtained from an airborne X-band high-resolution SAR and an Unmanned Aerial Vehicle (UAV) based Ka-band SAR, along with an analysis of the observed signal improvements. Section 4 discusses the experimental results. Section 5 concludes the paper with a summary of the key findings.

2. Image-Based Distortion Compensation Method

To suppress the phase errors introduced by non-ideal system characteristics, this paper proposes an image-based linear frequency-modulation signal distortion-compensation method, which is shown in Figure 1. By extracting the phase history of strong-point targets in the image domain and constructing a phase-error model, accurate compensation of residual phase errors is achieved. The proposed method is described as follows.

Firstly, for squinted single-look complex (SLC) images, if the data are not imaged under zero-Doppler conditions, a linear range walk correction should first be applied to align the range sidelobes within the same row of the data grid [33]. This makes the subsequent phase error extraction more convenient. Secondly, the strongest point in the image is selected based on the maximum energy criterion, and its coordinates are determined. To mitigate interference from neighboring points, a rectangular window of approximately eight pixels is suggested to be applied to the strongest point for windowing.

Assume the windowed strong point signal is $s_w\left(t_r\right)$, where $t_r$ is the range fast time. Subsequently, inverse LFM matched filtering is performed in the range direction to recover the original phase history.

$$s_w^{\prime }\left(t_r\right)=\mathcal{I}\mathcal{F}\left\{\mathcal{F}[s_w\left(t_r\right)]·\mathrm{e}\mathrm{x}\mathrm{p}(-j\pi {\displaystyle \frac{f_r^2}{K_r}})\right\}$$

(1)

where $f_r$ denotes the range frequency, $K_r$ denotes the chirp rate of the LFM signal. $\mathcal{F}$ and $\mathcal{I}\mathcal{F}$ represents for the forward and inverse Fourier Transform, respectively.

Extract the phase and accumulate it along the range direction to obtain the estimated phase curve ${\phi }_{est}\left(t_r\right)$. Then subtract the phase of the ideal LFM signal from this phase to obtain the differential phase curve.

$${\phi }_{diff}\left(t_r\right)={\phi }_{est}\left(t_r\right)-\pi K_r{t}_r^2$$

(2)

To ensure the generalization capability of the compensation, we fit the differential phase ${\phi }_{diff}\left(t_r\right)$ using a fourth-order polynomial for all SAR systems. The fitted phase polynomial can be expressed as follows.

$${\phi }_{fit}\left(t_r\right)=a_0+a_1{t}_r+a_2{t}_r^2+a_3{t}_r^3+a_4{t}_r^4$$

(3)

To achieve the optimal fitting performance, the least squares method is adopted here to minimize the sum of squared errors [34]. Accordingly, we formulate the following objective function.

$$J\left(\mathit{a}\right)={\left(\mathit{p}-T\mathit{a}\right)}^T(\mathit{p}-T\mathit{a})$$

(4)

where $\mathit{a}$ denotes the coefficient array ${\left[a_0,a_1,a_2,a_3,a_4\right]}^T$, $\mathit{p}$ represents for the phase array ${\left[{\phi }_{diff}\left(t_{r1}\right),{\phi }_{diff}\left(t_{r2}\right)\dots {\phi }_{diff}\left(t_{rN}\right)\right]}^{\mathrm{T}}$, $N$ denotes the number of range sampling; T is the fast-time matrix, which can be expressed as follows.

$$T=\left[\begin{array}{ccccc}1& t_{r1}& t_{r1}^2& t_{r1}^3& t_{r1}^4\\ 1& t_{r2}& t_{r2}^2& t_{r2}^3& t_{r2}^4\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ 1& t_{rN}& t_{rN}^2& t_{rN}^3& t_{rN}^4\end{array}\right]$$

(5)

When the gradient is zero, the objective function $J\left(\mathit{a}\right)$ is minimized, and the resulting optimal solution ${\mathit{a}}_{\mathit{o}\mathit{p}\mathit{t}}$ is expressed as follows.

$${\mathit{a}}_{\mathit{o}\mathit{p}\mathit{t}}={\left(T^{T}T\right)}^{-1}{T}^T\mathit{p}$$

(6)

After obtaining the five optimal coefficients, the constant term is removed to prevent any overall phase shift in the data. The fitted differential phase ${{\phi }^{\prime }}_{fit}\left(t_r\right)$ is then constructed using the remaining polynomial coefficients, and a linear detrending operation is applied to the differential phase to ensure no time shift occurs after compensation [35].

Since the edges of the signal spectrum typically exhibit certain oscillations, to reduce their impact on phase estimation, we select a time-domain region corresponding to 70% of the duration around the center of the strong point as the support domain. Based on the range chirp rate, the differential phase after linear detrending is extrapolated to obtain the corresponding differential phase in the frequency domain, which is then used to perform phase compensation in the frequency domain of the image data. Finally, range matched filtering is applied to the image data, yielding an SLC image with accurate compensation.

3. Results

In this section, experimental results of two airborne high-resolution SARs are presented to demonstrate the effect of the proposed distortion compensation method.

3.1. Airborne X-Band High-Resolution SAR Experimental Results

First, we conducted experiments using the manned airborne X-band high-resolution SAR data [36]. The system parameters are given in

Table 1. The Experimental Airborne X-Band SAR Parameters.

Parameter	Value
Carrier frequency	9.6 GHz
Velocity	126.58 m/s
Height	7605 m
Signal bandwidth	1200 MHz
Sampling frequency	1.4 GHz
Pulse duration	10 μs
Pulse repeat frequency (PRF)	1500 Hz
Range nominal resolution	0.3 m
Azimuth nominal resolution	0.3 m

.

The whole image processed without the distortion compensation is shown in Figure 2a. The 0.54-cosine window was used in image processing. The swath was 3 km (slant range) × 1.5 km (azimuth). The imaging result obtained with the distortion compensation under the calibration file is presented in Figure 2b. The imaging result obtained with the distortion compensation under the proposed method is presented in Figure 2c. In the azimuth direction, all images are focused using the same Phase Gradient Autofocus method.

Figure 3 and Figure 4 show the marked areas E and F of Figure 2, respectively. Two-point targets are selected for upsampling analysis in both areas. The range profiles of the selected point targets under different processing methods are shown in Figure 5. Seen from Figure 3 and Figure 4, it is obvious that both the image-based method and the calibration method can significantly compensate for signal distortion. As can also be seen from Figure 3 and Figure 4, the improvement in focusing performance benefits the entire swath of the image, regardless of the range position of the point target. The main lobes of the point targets are significantly narrowed, and the sidelobes are also improved to varying degrees. The point target pulse-compression performance analysis is shown in

Table 2. Point Target Pulse Compression Performance Analysis.

Point Target Area	Dimension	Parameter	Without Compensation	Compensation with Calibration File	Compensation with Image Data
E	Range	Resolution (m)	0.22797	0.16819	0.16844
		IRW (ratio)	1.825	1.3465	1.3485
		PSLR (dB)	−10.5076	−22.6621	−14.4943
		ISLR (dB)	−11.1842	−17.4372	−13.1344
	Azimuth	Resolution (m)	0.19298	0.19608	0.19242
		IRW (ratio)	1.5066	1.5308	1.5022
		PSLR (dB)	−9.8663	−12.8856	−11.662
		ISLR (dB)	−7.927	−9.6367	−8.6954
F	Range	Resolution (m)	0.2153	0.1697	0.1684
		IRW (ratio)	1.7232	1.3585	1.3479
		PSLR (dB)	−14.5122	−17.0671	−26.2121
		ISLR (dB)	−14.6292	−15.0638	−22.6091
	Azimuth	Resolution (m)	0.2072	0.2091	0.2070
		IRW (ratio)	1.6174	1.6327	1.6157
		PSLR (dB)	−14.2688	−13.8101	−13.5715
		ISLR (dB)	−10.6073	−10.8727	−10.6638

.

As shown in Table 2, the calibration method obtains the best focusing results. This is because the calibration file was recorded at a time very close to the SAR system startup, during which the system state did not undergo significant changes.

Figure 6 presents the phase compensation curves derived from the calibration file and from the proposed image-based estimation method. As observed in Figure 6, the phase error curve obtained from the calibration file exhibits significantly richer details, capturing high-frequency fluctuations and fine structures across the entire bandwidth. In contrast, the image-based phase error curve appears smoother, primarily preserving the dominant trend of the phase distortion. Nevertheless, the overall trends of the two curves are in good agreement, indicating that the image-based estimation is capable of capturing the primary components of the phase error. From a different perspective, this consistency demonstrates the feasibility of extracting distortion information directly from SAR images, although the limited detail in the image-based estimation inevitably limits its compensation effectiveness mainly to the main lobe region. Compared with strong scatterers in the image, the calibration signal benefits from a much higher SNR, enabling it to compensate for sidelobes over a broader range, particularly those far from the main lobe. Meanwhile, the proposed image-based method performs comparably well in the vicinity of the main lobe, achieving compensation performance that closely approaches that of the calibration-file-based approach, making it a viable alternative when dedicated calibration hardware is unavailable or outdated.

Figure 7 shows the range profiles of point targets at Area E under different fitting orders. From the figure, it can be seen that the focusing effect is best when a fourth-order fit is used. In fact, the fourth order is not a fixed value: too low an order leads to inaccurate fitting, while too high an order is prone to overfitting. Moreover, given the number of pixel points used to select strong point targets, the order should not be set too high. In practice, the fourth order represents an engineering optimum. The use of 70% of the main lobe region and eight pixels is primarily limited by the SNR of the point targets. When multiple sidelobes of the point target are clearly visible, this ratio can be further increased; otherwise, selecting a larger region often introduces inaccuracies in phase estimation. Therefore, this threshold is also not fixed, and 70% is an empirical value from engineering experience.

In this paper, the principle for selecting eight pixels is mainly based on the following criterion: selecting the main lobe and the first side lobe of the point target. Since SAR systems typically use an oversampling ratio of 1.1–1.4, these eight pixels approximately cover two zero-crossing points on each side of the compressed sinc-shaped response of the point target, corresponding to the complete energy of the main lobe and the first sidelobes on both sides. Selecting 70% of the bandwidth is mainly based on the following consideration: since a Hamming window (0.54 cosine window) is adopted for sidelobe suppression in the processing of this paper, under the standard Hamming window, the normalized spectrum drops to −10 dB at approximately 70% of the bandwidth region. Thus, the selection of 70% includes the energy within the 10 dB range while effectively avoiding inaccurate phase estimation at the edges of the bandwidth. In addition to phase error, the amplitude error of the signal also affects focusing, but its impact is smaller compared to phase error and can be easily compensated for by amplitude equalization in the frequency domain.

Figure 8 shows the range profiles of point targets in Area E under the compensation effects of different data-based methods.

Table 3. Range focusing performance parameters of the point target in area E with different compensation methods.

Parameter	Without Compensation	Compensation with GLS Method	Compensation with the Proposed Method
Resolution (m)	0.2279	0.1725	0.1721
IRW (ratio)	1.8250	1.3814	1.3782
PSLR (dB)	−10.5076	−12.1802	−16.2078
ISLR (dB)	−11.1842	−12.2410	−13.1547

lists the range focusing parameters under different methods. From the figure and table, both the GLS method and the method proposed in this paper can improve the focusing performance of point targets. Compared with the GLS method, which restricts the error to a sinusoidal form, the method proposed in this paper does not impose any restriction on the error form; therefore, when the error is random, its compensation effect is better.

To analyze the compensation performance under different SNR conditions, we added noise to the data at different levels before compensation. The resulting compensation effects are shown in Figure 9 and

Table 4. Range focusing performance parameters of the point target in area E under different SNR conditions.

Parameter	Without Compensation	SNR = 20 dB	SNR = 15 dB	SNR = 10 dB
Resolution (m)	0.2279	0.1765	0.2272	0.3769
IRW (ratio)	1.8250	1.4135	1.8230	2.0230
PSLR (dB)	−10.5076	−15.8078	−10.6693	−2.6693
ISLR (dB)	−11.1842	−12.7547	−11.2216	−3.5771

. From the figure and table, it can be seen that low SNR affects the accuracy of phase estimation. For the method proposed in this paper, the effective boundary of compensation is approximately at SNR = 15 dB.

To illustrate the efficiency of the proposed method, we calculated the computational cost of each compensation step, as listed in

Table 5. The Computational Cost of Each Compensation Step.

Operation	Number of Multiplications	Number of Additions
Windowing	$\mathrm{N}\mathrm{r}$	0
Range decompression	$\mathrm{N}\mathrm{r}\times \mathrm{N}\mathrm{a}$	0
Phase extraction	0	$\mathrm{N}\mathrm{r}$
4-th order phase fitting	$30\times \mathrm{N}\mathrm{r}$	$30\times \mathrm{N}\mathrm{r}$
Phase compensation	$\mathrm{N}\mathrm{r}\times \mathrm{N}\mathrm{a}$	0
Range compression	$\mathrm{N}\mathrm{r}\times \mathrm{N}\mathrm{a}$	0
Range FFT	${(\mathrm{Nr}\times \mathrm{Na}\times \log }_2 \mathrm{N}\mathrm{r})/2$	${\mathrm{Nr}\times \mathrm{Na}\times \log }_2 \mathrm{N}\mathrm{r}$
Range IFFT	${(\mathrm{Nr}\times \mathrm{Na}\times \log }_2 \mathrm{N}\mathrm{r})/2$	${\mathrm{Nr}\times \mathrm{Na}\times \log }_2 \mathrm{N}\mathrm{r}$

. As shown in Table 5, since the estimation error only considers strong points, the main time overhead lies in the full-image compensation, which primarily involves Fourier transforms and complex multiplications, both of which are highly efficient operations. Based on statistics from an Intel 8269CY processor, the average imaging time for this dataset is 268.32 s, while the average proposed compensation algorithm takes 22.58 s, accounting for approximately 8% of the total imaging time.

To demonstrate the improvement in the global focusing performance of SAR images achieved by the proposed method, we selected point targets from nine different areas for analysis. The point targets selected in each area are shown in Figure 10, and the range profiles of all point targets are shown in Figure 11. It can be seen from Figure 11 that, because the distorted phases of point targets across different areas exhibit a certain degree of similarity, the range focusing performance of all point targets is improved after compensation using the proposed method.

Table 6. Range focusing performance parameters of the nine-point targets.

Point Target	Compensation	Resolution (m)	IRW (Ratio)	PSLR (dB)	ISLR (dB)
A	Before	0.2247	1.7995	−6.9799	−8.4611
	After	0.1812	1.4508	−12.1098	−11.4684
B	Before	0.2640	2.1133	−9.5022	−8.9947
	After	0.1769	1.4158	−15.0779	−11.1499
C	Before	0.2361	1.8908	−12.0800	−12.1686
	After	0.1752	1.4029	−17.4165	−14.3782
D	Before	0.2241	1.7939	−6.5596	−8.0113
	After	0.1874	1.5004	−11.3133	−11.6982
E	Before	0.2279	1.8250	−10.5076	−11.1842
	After	0.1721	1.3782	−16.2078	−13.1547
F	Before	0.2152	1.7232	−14.5122	−14.6292
	After	0.1762	1.4113	−20.3019	−17.0365
G	Before	0.2242	1.7951	−9.3793	−10.1575
	After	0.1743	1.3961	−14.9771	−12.9398
H	Before	0.2699	2.1613	−8.9559	−10.5795
	After	0.1664	1.3324	−17.5686	−15.6926
I	Before	0.2076	1.6622	−7.8844	−6.7877
	After	0.2083	1.6677	−11.3038	−7.9568
Improvement	-	22.01%	22.01%	5.55 dB	2.72 dB

presents the focusing performance improvement for each point target and the global average improvement of the image.

As shown in Figure 11 and Table 6, the proposed method improves focusing performance at all nine selected points, indicating that the method is not limited to individual-point targets but possesses generalization capability for full-image compensation. This is mainly because the signal distortion often originates from the hardware frequency-response characteristics of the signal transmitter and receiver. Such hardware-induced distortions tend to be consistent across the entire image scene, resulting in insignificant spatial variance. Therefore, a compensation function estimated from a few representative point targets can be effectively applied to the whole image. According to Table 6, the proposed method improves the overall focusing performance of the image in three key metrics: the IRW is narrowed by 22.01%, indicating better spatial resolution; the PSLR is reduced by 5.55 dB, meaning reduced strong sidelobe interference near bright targets; and the ISLR is reduced by 2.72 dB, reflecting effective suppression of the overall sidelobe energy. These consistent improvements across all nine points further demonstrate the robustness and generalization capability of the proposed method for full-image compensation.

3.2. UAV-Based Ka-Band SAR Experimental Results

In this subsection, we present the experimental results obtained from the unmanned airborne Ka-band high-resolution SAR data. The system parameters of the UAV SAR platform are provided in

Table 7. The Experimental UAV-based Ka-band SAR Parameters.

Parameter	Value
Carrier frequency	34.1 GHz
Velocity	10.1 m/s
Height	300 m
Signal bandwidth	1788 MHz
Sampling frequency	2.4 GHz
Pulse duration	3.627 μs
Pulse repeat frequency (PRF)	2000 Hz
Range nominal resolution	0.15 m
Azimuth nominal resolution	0.15 m

. The experimental results based on the UAV Ka-band SAR data are illustrated in Figure 12. Specifically, the imaging result without distortion compensation is shown in Figure 12a, where a 0.54-cosine window was applied during image processing. The imaged swath covers 700 m in slant range and 330 m in azimuth. The imaging result after applying the proposed distortion-compensation method is presented in Figure 12b, which has the same 0.54-cosine window weighting. The Phase Gradient Autofocus method is also employed to focus the azimuth direction of the images. To more intuitively demonstrate the effectiveness of the proposed algorithm, the area marked in Figure 12 is enlarged for a detailed comparison, as shown in Figure 13.

As shown in Figure 13a,b, after applying the image-based distortion compensation, the range-focusing performance of the point target is significantly improved. This is further corroborated by the comparison of the upsampled slices in Figure 13c,d. This demonstrates that the proposed method is also effective for UAV SAR images.

Figure 14 presents a comparison of the range profiles of the selected point target under different processing conditions. It can be clearly observed from Figure 14 that after applying the proposed image-based distortion compensation method, the sidelobes around the main lobe of the point target are significantly reduced compared to the uncompensated case. This result is consistent with that obtained from the manned airborne X-band SAR experiment, where the improvement is mainly concentrated in the region surrounding the main lobe, while the suppression of sidelobes far from the main lobe remains relatively limited. However, unlike the manned airborne results, the UAV Ka-band SAR images exhibit a different trend: the improvement in range resolution is less pronounced, whereas the suppression of sidelobes is more evident. This distinction may be attributed to the low antenna power of the UAV platform. According to calculations, the image SNR is 17.546 dB lower than that of the X-band manned aircraft, and the region selected for error estimation around strong sidelobe points is reduced by approximately three pixels. As a result, the compensation effect is somewhat degraded. Overall, these results further demonstrate the effectiveness of the proposed method across different SAR platforms, while also highlighting platform-specific variations in compensation behavior.

Table 8. Point Target Pulse Compression Performance Analysis.

Dimension	Parameter	Without Compensation	Compensation with Image Data
Range	Resolution (m)	0.1097	0.1075
	IRW (ratio)	1.3085	1.2830
	PSLR (dB)	−11.3051	−17.1938
	ISLR (dB)	−10.9385	−13.0503
Azimuth	Resolution (m)	0.1307	0.1298
	IRW (ratio)	1.4448	1.4345
	PSLR (dB)	−17.6224	−17.5215
	ISLR (dB)	−14.9899	−14.8651

lists the pulse-compression performance metrics of the selected point target. As shown in Table 8, after applying the image-based distortion compensation method, the range resolution of the selected point target is slightly improved, while the PSLR and ISLR are significantly enhanced.

4. Discussion

In this study, we proposed an image-based distortion-compensation method that directly estimates and compensates for phase errors from SLC SAR images without relying on calibration files. Experimental results from both manned airborne X-band high-resolution SAR and UAV-borne Ka-band SAR data demonstrate the effectiveness of the proposed approach in improving focusing performance, particularly in terms of sidelobe suppression and main-lobe sharpening.

The results from the X-band manned airborne SAR experiment show that the proposed method achieves focusing performance comparable to that of the traditional calibration-file-based approach, especially in the vicinity of the main lobe. However, as illustrated in Table 2, the calibration-file-based method yields superior sidelobe suppression further away from the main lobe, which can be attributed to the higher SNR and richer phase detail contained in the calibration signal. Nevertheless, the consistency in the trend of the phase error curves between the two methods confirms the feasibility of extracting distortion information from image data, albeit with a trade-off in detail richness.

From the underlying principle and experimental results, it is evident that, owing to the effective data of the windowed strong point being confined to a limited number of pixels, the phase error curve provided by the image-based compensation method cannot match that obtained from the calibration file. Additionally, to ensure robustness in phase estimation, the proposed method employs a low-order polynomial for phase fitting. Therefore, in principle, its application effect cannot be entirely consistent with that of the calibration-file-based method. If the system has a higher SNR and the strong point reveals more sidelobe details, the polynomial order can be appropriately increased to capture finer details in the phase estimation, thereby achieving better compensation performance. For images with poor SNR, a larger number of strong points can be selected, and when estimating the phase error, the phase can be weighted according to the intensity of each point to enhance the robustness of phase estimation. Nevertheless, in terms of the main lobe and its surrounding sidelobes, the performance of the proposed method remains very close to that achieved with calibration-file-based compensation. Future work could explore higher-order models or adaptive filtering techniques to extend the compensation range, as well as investigate the integration of multiple scatterers to improve estimation robustness.

A key advantage of the proposed method lies in its independence from calibration hardware and its adaptability to varying system states. It is particularly valuable for SAR systems that lack internal calibration loops or operate under unstable environmental conditions, where pre-calibrated parameters may become outdated. Furthermore, the improvement in image quality benefits the entire image rather than being confined to local regions. By leveraging inherently present strong point scatterers in the scene, the method provides a practical and cost-effective solution for post-acquisition focusing enhancement.

In terms of algorithmic efficiency, since the phase estimation is confined to the echo where the strong point resides, the estimation itself is efficient. The main additional overhead lies in the range pulse compression and decompression, both of which are also efficient when implemented using fast Fourier transform (FFT)-based frequency-domain operations. Therefore, the method proposed in this paper does not exhibit excessively slow efficiency performance.

Overall, the proposed method offers a promising alternative for SAR focusing enhancement, with strong generalizability across different SAR platforms and operating conditions. Its image-driven nature makes it especially suitable for operational scenarios where real-time calibration signals are unavailable or impractical.

5. Conclusions

In this paper, we propose a signal distortion compensation method for airborne SAR based on SLC images that effectively mitigates main-lobe broadening and sidelobe elevation caused by nonlinear components of the LFM signal. By extracting the phase of the selected strong-point targets, fitting them with a low-order polynomial, and performing linear detrending, the method accurately estimates and compensates the phase error without requiring dedicated calibration hardware. Experimental results on manned airborne X-band high-resolution SAR and UAV-borne Ka-band SAR data demonstrate significant improvements in focusing quality, including reduced sidelobes and resolution closer to the theoretical value. The method exhibits strong generalizability across platforms and bands, and its image-driven nature ensures practical applicability for simplified or low-cost SAR systems where internal calibration is unavailable. It is expected to enhance image quality for most SAR systems and to benefit subsequent applications such as target recognition, image registration, interferometric processing, etc. Future work will further investigate the applicability of this method to spaceborne SAR imagery and other types of SAR data.