UAV-Based Bistatic SAR-Imaging Using a Stationary Repeater

Synthetic aperture radar (SAR) is an established technique for high-resolution radar imaging relying on the ego-motion of the radar. The long coherent integration time of the radar in conjunction with a linear or circular trajectory enables the illumination of targets under different observation angles leading to robustness against short-time interference signals. The use of a bistatic setup to simultaneously acquire multiple observation angles further increases the aforementioned benefits. In this work, a bistatic SAR system using an active repeater is proposed, in the following called Bistatic Repeater-SAR (BR-SAR). In BR-SAR the repeater acts as a second observer providing a bistatic path with low system cost and hardware effort. This article discusses the BR-SAR approach with all signal processing and hardware considerations necessary to build the bistatic radar system. This includes a description of the full system and signal chain with a focus on the signal separation and evaluation of both monostatic and bistatic signals and the subsequent SAR processing. The approach is verified via simulations and measurements, in which conventional SAR is compared to the proposed BR-SAR system. Hardware effects leading to a deteriorated system performance of the bistatic system are analyzed and countermeasures are discussed and implemented. Finally, the benefits of the bistatic system are demonstrated based on a realistic measurement scenario.

coherently performed in the monostatic receiver and both mono-and bistatic signals are processed within the same system.
Repeaters have been used before in radar networks to achieve coherency between nodes without requiring complex synchronization. Applications range from direction-of-arrival and velocity estimation [18], [19], [20] to locating repeater nodes within a radar network [21]. Bistatic SAR experiments were performed by moving either the radar [22] or the repeater [23]. In these works, the repeater solely amplifies the signal before sending it back.
Recently, the use of unmanned aerial vehicles (UAVs) as a platform for radar imaging has increased due to technological advances and higher availability of these systems [24], [25], [26], [27]. Compared to airborne systems on larger aircrafts or spaceborne systems, unmanned aerial vehicle (UAV)-based radar offers a higher flexibility in operation. Monostatic SAR imaging with UAVs already showed promising results in detecting buried objects [28], [29], determining snow depths [30], and in archaelogical surveys [31]. Time-domain methods in particular have proven to be suitable for UAVbased SAR imaging due to the absence of simplifying assumptions compared to frequency-domain methods [25], [32]. Considering different viewing angles, imaging can be further improved as different angles complement each other [12]. This can be achieved by using a bistatic acquisition geometry.
Using a repeater, mono-and bistatic paths are measured simultaneously. If their ranges are similar, they can not be distinguished at the receiver. A separation can be achieved by strictly constraining the measurement geometry to guarantee different ranges. To take advantage of the flexibility of UAV flight paths, another means of separation is therefore required. An additional frequency modulation at the repeater represents a solution to this challenge. Using this modulation, the mono-and bistatic paths are separable and both signals can be received and processed at the same time [18].
In this article, a UAV-borne SAR system based on a frequency-modulated continuous-wave (FMCW) radar [33] is extended by a repeater to allow both monostatic and bistatic measurements of a scene. This approach circumvents the high demands on synchronization when using two radar systems for bistatic data acquisition. In contrast to [22], [23], the signal is not only amplified at the repeater but also frequency modulated. Due to the proportionality of frequency and range in FMCW processing, the bistatic signal becomes separable from the monostatic one. However, modulating the signal at the repeater places demands on digital signal processing. The required adaptations are presented in this work, enabling both bistatic and monostatic SAR images.
A detailed description of the radar signals and the required signal processing is given in Section II. Section III shows simulation results of the proposed implementation, which are validated by measurements in Section IV.

II. THEORY
In the following, first, detailed definitions of all signals involved in basic FMCW radar and SAR processing are given.
Afterwards, the definitions are extended for bistatic imaging using a repeater.

A. FMCW RADAR EVALUATION
The frequency ramp sent out by an FMCW radar is described by [34] f where f 0 is the start frequency of the ramp, B is the bandwidth, T is the ramp time and k r is the slope of the ramp. Its phase can be described by Assuming a single target, the signal is reflected at the target back to the radar. The received signal is equal to the transmitted one, but delayed by t due to the distance to the target. The signal phase is By mixing the transmit and receive signals, the relevant target information is extracted as the phase difference (4) If the target is located at a radar range R and moves with a relative velocity of v away from the sensor, the time delay can be described by which leads to This corresponds to a beat-frequency of If f 0 = 1 GHz, k r = 3 × 10 12 s −2 , this leads to if v and R are in the same order of magnitude. The influence of the velocity of a target is negligible. In that case, the beatfrequency can be estimated to The beat signal is digitized using an analog-to-digital converter (ADC) before further processing. The radar does not use an Inphase/Quadrature (IQ) mixer, the signal is therefore real-valued. For clarity, continuous-time signals are noted by s(t ) and their discrete-time counterparts are noted by This step of extracting the range information is referred to as range compression. It is commonly implemented using a fast Fourier transform (FFT). After range compression, the single target that was assumed at the beginning of this section results in a peak in

B. PHASE OF A POINT TARGET
Employing synthetic aperture processing, high-resolution images of a static scene can be obtained. The radar system is moved along a trajectory, periodically recording measurements. As long as the position of the radar sensor is known with sufficiently high precision, an estimate of the radar crosssection (RCS) of points in the scene can be calculated. For the following derivation, a single ideal point target at a static position is assumed. Due to the moving radar sensor, the distance R m between radar and target is dependent on the measurement index m. The true beat-frequency is also dependent on m and is therefore explicitly written as f B (R m ).
First, the range information from each radar measurement m is obtained via range compression, as stated above. For the given single point target, the range-compressed signal is [32] with A continuously evaluable function is given by which includes interpolation for the right expression. Relying on sufficient zeropadding in the range compression, linear interpolation between the neighboring samples in S B,m [ f r ] is used.
The maximum amplitude of the sinc is reached at the true beat-frequency of the point target for every measurement. With (13) and (9), the expected phase of the point target can be derived: Synthetic aperture processing can be achieved using a variety of approaches. These can mostly be divided into timedomain and spatial frequency-domain methods [35], [36]. Frequency-domain methods offer the advantage of lower computational complexity due to their relation to the FFT, but they impose strict requirements on the measurement, such as linear trajectories or equidistant measurements. Although more computationally expensive, time-domain methods such as backprojection (BP) iteratively process all measurement data and therefore rely on very few assumptions regarding the measurement geometry [33]. This work relies on BP because of the highly-nonlinear flight trajectories of multicopters and the additional degree of freedom regarding the measurement setup. BP processes radar measurements and populates a grid of pixels, usually on a plane or in a volume. Due to its iterative nature, it can be mathematically described in terms of its operation on a single pixel at a position x 0 = [x 0 , y 0 , z 0 ]. After processing all measurements m, the resulting pixel value A(x 0 ) is given by [32] A( where is the range from antenna to pixel and x a,m is the position of the radar antenna for measurement m. The theoretically expected phase φ e (R m ) of a point target is used to compensate the phase extracted from the range information. If x 0 contains a target, A(x 0 ) becomes a coherent sum over complex values resulting in a value with large amplitude. If there is no target, the summation is not coherent and the result is of much lower amplitude. Therefore, the SAR image is a representation of the RCS of the investigated area sampled at the pixel coordinates.

D. FMCW WITH REPEATER
This work extends the FMCW radar by a repeater element, enabling the evaluation of a bistatic path. The repeater consists of a transmit and receive antenna as well as an amplifier and mixer. The mixer is used to shift the incoming signal in frequency by f mod . This requires a single-sideband mixer, otherwise shifting by ± f mod would occur. The signal applied to the mixer in the repeater is given as whereŝ mod is the amplitude of the modulation signal, f mod the modulation frequency, and ϕ mod,0 (γ ) the modulation phase at the starting time of radar transmission. Since the repeater is independent of the radar sensor, the start phase ϕ mod,0 (γ ) depends on the global start time γ of the FMCW chirp. Due to the modulation within the repeater, the mathematical description for an FMCW radar from Section II-A needs to be extended, see [18] for more details. The frequency of the receive ramp is changed via the repeater to As a consequence, the beat frequency in the linear region of each ramp is given as A target at a bistatic range R bi is therefore additionally shifted by The virtual received range for a bistatically received signal is then given asR The ramp frequency shift via the bistatic path is advantageous, because it enables the separation of monostatic and bistatic signals with similar physical ranges by virtually shifting the bistatic target response in range. Without the shift, monostatic and bistatic signal components at similar ranges interfere and lead to poor imaging quality after BP processing. This is especially relevant for complex trajectory geometries now possible using UAVs, since the separation of mono-and bistatic receive signals in range would place significant restrictions on the geometries. An example setup of the bistatic radar system including both signal paths is depicted in Fig. 1.
The bistatic path length R bi consists of the total distance between radar, repeater and target, as depicted in Fig. 1. The transmission delay caused by the signal run time within the repeater further increases R bi and needs to be included.

E. EXTENDED BACKPROJECTION
The FMCW model for bistatic measurements necessitates an extension of the BP algorithm. As described in the previous section, the bistatic range of the target measured by the FMCW radar is shifted via the repeater. The extended processing must take into account this range shift.
While the discrete-time monostatic signal can be described by the bistatic signal includes an additional phase term due to the modulation: Contrary to the start phase of the transmitted radar chirp, ϕ mod,0 (γ ) is not compensated in the receiver. For coherent processing, it must therefore be calculated based on the global time for every chirp. Due to tolerances in manufacturing and measurement inaccuracies, the repeater phase cannot be calculated directly. It needs to be estimated from f mod , γ , as well as measurement data of a stationary point target to account for drifts.
To allow bistatic targets to be processed using classic BP, the signal is digitally demodulated: where ξ [t] represents modulation products irrelevant to the following BP. At the top of Fig. 2, the periodic spectrum S B ( f ) of the sampled base band signal including both mono-and bistatic components is displayed. Using the demodulation, the spectrum is shifted towards negative frequencies, such that the bistatic response is now positioned where the monostatic response was previously located. The resulting spectrum is displayed at the bottom of Fig. 2. In the demodulated spectrum S B,dem ( f ), aliasing introduces a copy of the bistatic signal in the base band, which is of no concern, since its location corresponds to distances not evaluated during BP. Thus,s B,bi,demod [t] can be processed with standard BP if R bi is known.

III. SIMULATIONS
In this section, the proposed extensions to FMCW and BP are verified using simulations. The radar parameters assumed for simulation and measurements are equal to allow for a reliable prediction of results. All parameters are listed in Table 1. The modulation frequency in the repeater is assumed to be f mod = 1.2 MHz. First, the interference effects that occur

TABLE 1. FMCW Radar Technical Parameters for Simulations and Measurements
without a frequency modulation in the repeater elements are investigated. This is followed by the simulation of the extended backprojection algorithm from Section II-E.

A. BENEFIT OF SIGNAL MODULATION VIA REPEATER
To demonstrate the degrading effect of interference, a repeater without modulation is assumed. A grid of 7 × 7 point targets with 50 cm separation in x and y direction is simulated. The radar system moves in a straight line from (x, y) = (−5 m, −5 m) to (−5 m, 10 m), while the repeater is stationary at (0 m, 4 m).
Both mono-and bistatic target responses are received by the radar. As the area is populated with many targets, there is a large variety in target ranges. Mono-and bistatic target responses occur at similar ranges which are superimposed at the receiving radar. Without modulation, no separation of the received signals is possible, leading to interference.
For bistatic signals, the expected receive power is reduced compared to monostatic signals. This is due to a larger bistatic range (R bi > R) and losses introduced by the repeater element itself. In this simulation, a power difference of 13 dB is assumed.
Monostatic processing using classic BP still gives a focused SAR image, because the monostatic signal power is significantly above the bistatic one. All point targets can be focused, as is visible on the top of Fig. 3. In contrast, bistatic processing with f mod = 0 yields a degraded SAR image, as can be seen on the bottom left of the same Figure. The monostatic signal masks the bistatic signal of interest, significantly reducing the coherency of the summation in BP for bistatic target responses.
A modulation in the repeater as described in Section II-D avoids this masking, by separating mono-and bistatic responses in virtual range as described in (24). Bistatic BP after demodulation then gives a significantly improved result which is visible in the bottom right of Fig. 3.

B. BISTATIC SIMULATION -SINGLE-TARGET CASE
Introducing a modulation in the repeater element leads to a shift in the range-compressed signal, which is later removed by digital demodulation. For a single-target scenario, simulated range-compressed data before and after demodulation can be seen in Fig. 4   signal is assumed. The curvature of the target response is due to the measurement geometry with changing distances between radar sensor, repeater, and target. Aliasing leads to a second curve at higher ranges, as shown in Fig. 2.
Using the precisely known trajectory and stationary repeater antenna positions from the simulation, BP is applied. In this idealized example, the resulting image (Fig. 5) is free of clutter and interference. The single simulated target is clearly visible at the expected position. This confirms that bistatic SAR including modulation is possible under ideal conditions.

IV. MEASUREMENT RESULTS
The preceding theory and simulations are validated via outdoor measurements using an UAV equipped with an FMCW radar and a static repeater placed in the scene, see Fig. 6. The target area contains a large metal cylinder [A] and, optionally, various other metal objects [B-E]. A close-up image of the target area with all objects is included in Fig. 6(a). The main radar parameters are listed in Table 1. The positions of the repeater antennas as well as the ground truth position of all targets were measured using a total station. For the position of the radar antennas, information from a realtime kinematic global navigation satellite system (GNSS) was fused with data from an inertial measurement unit aboard the UAV [37].

A. SINGLE-TARGET EVALUATION
For the evaluation of the data, various measurement errors, inaccuracies and disturbances must be taken into account while performing data acquisition and evaluation. Avoiding or mitigating system-related disturbances to the received signal phase is a critical concern. Therefore, the scene is first populated only with the large cylinder [A].

1) STATIONARY RADAR MEASUREMENT
To visualize the effect of disturbances on the radar range evaluation, a stationary measurement was performed. During the measurement, the repeater was switched on and f mod was varied, see Fig. 7. The modulation frequency of the repeater directly influences the virtual range of the bistatic targets. Although a single target was placed in the scene, two distinct closely spaced lines can be observed in region 1. This can be explained with the repeater as a target object in the scene. The modulated radar signal is not only transmitted to the target, but directly received by the radar. This line-of-sight component leads to an additional target, which is stronger than true bistatic targets observed via the repeater.
Beside the desired signal in region 1, region 2 shows a strong interfering signal, which could potentially mask the bistatic signal. Using a suitable f mod , regions with strong interference signals can be avoided for the bistatic range evaluation. For the following measurements, the modulation frequency was set to f mod = 1.2 MHz corresponding to a bistatic range shift of R shift = 60 m, as described in (23).
Beyond 60 m no strong interferers were present during the measurements. The mixing process in the repeater results in the desired signals, but also includes other unwanted signal terms, such as the carrier signal, harmonics, and intermodulation products. The terms present after the mixing process are given by where f in is the frequency of a signal received by the repeater and f out is a set containing all theoretical frequency components resulting from f in after the mixing process. In case of the used IQ-mixer, the undesired sideband ( f in + f mod ) is dampened, but still visible. Due to its shift in range, no disturbance of the bistatic signal is to be expected.

2) BISTATIC SAR
For this section, the UAV system is periodically moved back and forth on a linear trajectory, see Fig. 6. All occuring signal components are again visible in the range evaluation plot (left side of Fig. 8).  The varying distance of the UAV to the target is visible as a periodic shape in the radar range. The 60 m shift via the repeater leads to a bistatic received target range as observed in region 1. Region 2 contains the dampened sideband. The corresponding monostatic target range progression over time can be seen in region 4. The signal in region 3 is an artifact generated by the radar itself. Both regions 2 and 3 do not interfere with the measurements and can be disregarded, because there is no overlap with mono-or bistatic target responses for relevant radar ranges.
On the right side of Fig. 8 the range-compression after the demodulation is shown. Region 4 containing the monostatic signal is no longer visible, because it is moved to negative frequencies. The signals in regions 1* and 2* are mirrored copies of 1 and 2, respectively and occur due to aliasing, see Fig. 2.
Using these demodulated range-compressed data and recorded localization information, the SAR image is processed and displayed in Fig. 9. The cylinder target [A] can be detected bistatically with high precision. Due to the implicit target generated by the repeater itself, a second peak is observed in the computed SAR image close to the location of the transmitting repeater antenna.
This result demonstrates the viability of repeater-based bistatic SAR processing. The benefit of the multiperspectivity on any given target via the repeater is further discussed in the next subsection.

B. MULTI-TARGET EVALUATION
Measurements are again performed monostatically and bistatically with additional metal objects [B-E] placed in the scene, as displayed in Fig. 6. An excerpt of the results of rangecompression before and after demodulation is displayed in Fig. 11. Between mono-and bistatic measurements, there is a large difference in received power. In both cases, the varying range of multiple targets can be seen in the images.
The SAR evaluations of all target types is given in Fig. 10. To enable an accurate comparison between the monostatic and bistatic cases, the SAR images are further analyzed.
A statistical analysis of pixels in the target area is performed. Pixels containing higher power levels due to a target or because of imaging artifacts close to strong targets caused by the short linear aperture are excluded. For the remaining pixels, the amplitude in dB is extracted. From these amplitudes, a probability density estimate (PDE) is calculated using kernel density estimation.
This distribution is bell-shaped and its maximum value occurs at a certain amplitude value which will be referred to as the background level. Due to the difference in received power between mono-and bistatic images, the background level differs for the two cases. By normalizing the amplitude values to their respective background level, the distributions can be superimposed in a single plot (see Fig. 12).
Dividing the maximum amplitude of a target by the background level results in a signal-to-background ratio (SBR) for each target, which is additionally displayed in Fig. 12. Since the shape and width of the PDEs of the images is very similar, this measure enables a direct comparison between the monostatic and bistatic setup, regardless of the difference in overall received power.
In contrast, the SAR images allow for a comparison of the target within its surrounding area. Also, the shape of the target responses can be compared. Both representations have certain advantages. The following analysis therefore relies on both representations. A comparison of estimated target RCS is performed using the SBR, while heightened clutter level in an area is deduced directly from the SAR images.
Target A is again the large metal cylinder and serves as the reference target, since it yields the highest amplitude in monoand bistatic evaluations. As expected, the cylinder has a large mono-and bistatic RCS. Target D is a large sphere covered in aluminum foil. This also results in a large mono-and bistatic RCS.
Target B is a small corner reflector. Its monostatic RCS is large in comparison to the bistatic one. Nevertheless, the reflector is not visible in the monostatic SAR image. This is mainly due to the measurement geometry, that resulted in target B overlapping target A at very similar ranges throughout the aperture. This leads to the same problem illustrated in Section III-A for repeaters without frequency modulation. Therefore the target is not visible, but a heightened clutter level is observed around the target location, which is again similar to the situation described above. In the bistatic case, the geometry is different and the overlap between targets A and B is reduced, resulting in a very weak target peak at the expected location, leading to an increased SBR.
Target C consists of a small ball of crumpled aluminum foil. Its monostatic RCS is small in comparison to the previous targets, but the target is still visible in the SAR image. In the bistatic image, this target cannot be detected, because the bistatic RCS is small due to strong scattering at the rough ball surface. This is confirmed by its low bistatic SBR.
Target E is a horizontally placed smaller metal cylinder. Due to is positioning, its RCS is larger in a bistatic scenario, which can be observed in the corresponding SAR images. In contrast to the previous targets, this leads to a bistatic SBR larger than the monostatic SBR.

V. CONCLUSION
This work demonstrates the BR-SAR concept using an active repeater element to enable simultaneous monostatic and bistatic SAR imaging with only a single radar sensor. The repeater receives the radar signal and modulates it using a mixer, which allows for a clean separation between monostatic and bistatic radar responses in signal processing.
Therefore, both mono-and bistatic SAR images can be generated from the same measurement data. The practical implementation of BR-SAR could be demonstrated in realistic measurements, leading to both monostatic and bistatic high-resolution SAR images. Additionally, it could be demonstrated that objects with larger bistatic RCS result in a higher amplitude in BR-SAR and are therefore easier to detect than using monostatic SAR. This improves detection performance and supplies additional target information.