
May/June 2009
Aerial view of a transportererectorlauncher vehicle covered with camouflage netting, during ground launch cruise missile (GLCM) evaluation.
Synthetic Aperture GPS Signal ProcessingConcept and Feasibility DemonstrationIn addition to positioning, navigation and timing, GPS turns out to be a useful sensor for studies of the Earth’s atmosphere. Synthetically generated, phasedarray antennas can process GPS signals to create large antenna apertures. The resulting narrowbeam generation capabilities mitigate interference and jamming and produce highresolution radar images — which could lead to interesting civil and military applications.
Share via: Slashdot Technorati Twitter Facebook For the extended digital edition of this article, please download the pdf using the link above. Synthetic aperture techniques combine data obtained from multiple sensors — or one sensor moving among multiple locations, or both — to construct a single image. These techniques have been widely researched, developed, and applied in the area of radar systems. This article discusses efforts to extend synthetic aperture concepts to GPS signal processing, exploiting the beam steering capabilities of synthetically generated phased array antennas. In it, we will describe the fast Fourier transform (FFT)–based method used to simultaneously steer a synthetic array’s beams in multiple directions. We will also discuss the results of simulator and flight tests to demonstrate the efficacy of synthetic beam steering techniques for GPS antennas. Development of GPSbased SARs will enable highresolution imaging capabilities using passive receivers of GPS signals and allow 24hour global availability of imaging technology. It represents a dualuse technology that could support military applications such as imaging of military ground fleet hidden under foliage, as well as humanitarian applications such as detection of unexploded ordnance.
GPS SAR: The Concept As shown in Figure 1, an array beam can be steered in the direction of a GPS satellite to mitigate the effects of radio frequency interference and jamming signals that are originating from directions other than the satellite. Steering the array beam towards reflecting objects to record highresolution radar images provides the foundation for the development of GPSbased synthetic aperture radars (SARs). An important consideration in using GPSbased SAR is that large synthetic arrays are generated with small physical antennas utilizing platform motion and/or multiplatform integration. As a result, the physical size of the antenna does not act as a limiting factor. This, in turn, enables miniaturization of the technology for applications on small platforms such as miniautonomous aerial vehicles (UAVs) and microUAVs. Phased array antennas have been widely employed for antenna beam steering. In a phased array, phases of individual antennas are adjusted to maximize the array gain in a desired direction, while increasing the array size narrows the array beamwidth. Figure 2 illustrates beam steering in the case of a onedimensional (1D) array. In the GPS domain, beamsteering techniques — both analog beam steering and digital — have primarily been exploited to mitigate interference.
Hardware versus Software GPS A hardwarebased construction has several limitations. For instance, an increase in the physical size of the array is required to narrow its beamwidth. Moreover, adjusting the phases of individual antennas in hardware constrains the system’s capability to simultaneously generate multiple beams that can be used, for example, to track multiple satellites or to simultaneously track both direct and reflected (multipath) signals. To overcome these limitations, we propose a synthetic array generation scheme that uses a software GPS receiver architecture. Instead of adding new antennas to the array, the beam is narrowed by exploiting antenna motion — that is, the array is synthesized by observing an antenna at different locations over time. Figure 3 and Figure 4 illustrate this principle for 1D and twodimensional (2D) array cases, respectively. Generation of synthetic GPS antenna arrays is conceptually similar to synthetic aperture radar, where antenna motion is used to increase the antenna aperture in order to increase the azimuth resolution. The synthetic array generation needs to operate with signal samples. In particular, samples that are taken a certain distance apart (generally, a halfwavelength apart: d=λ/2) must be combined. Hence, we use a softwaredefined GPS receiver to generate a synthetic phased array antenna. The software receiver approach also allows the generation of multiple beams that are steered in different directions. Instead of hardware phase adjustments, a phase of a signal sample is adjusted to maximize the gain in a given direction (as seen in Figure 3). As a result, multiple beams can be generated simultaneously by applying different sequences of phase shifts to the same set of signal samples. This simultaneous steering in different directions can be used, for example, for simultaneous tracking of direct and reflected signals such as urban and ground multipath reflections. In the remainder of this article, we will first summarize previous efforts in the area of synthetic aperture GPS signal processing. Then we will discuss the principles of FFTbased multidirectional beam steering and how we applied them to develop signal processing techniques for synthetic phased array GPS antennas. Finally, we describe the simulation and live data test results used to verify the beam steering methods that we have developed. In particular, we apply actual flight data and ground data to demonstrate the operation of 1D and 2D synthetic phased GPS antenna arrays. Simulated data are exploited to demonstrate the use of 2D synthetic phased arrays for simultaneous tracking of direct and multipath signals. We also use simulated data to demonstrate GPSbased SAR imaging.
Earlier Work In the navigation domain, these earlier papers describe synthetic aperture GPS signal processing for a single antenna case as well as the exploitation of circular antenna motion to synthesize a circular phased array. In the work described by A. Broumandan et alia, a synthetic phased array is applied for interference mitigation while the paper by T. Pany et alia discusses the application of the circular synthetic array to suppress multipath. S. Draganov et alia discuss the use of the synthetic aperture technique by the ultratightly coupled GNSS/INS architecture to mitigate multipath. In their paper, Cherniakov et alia discuss the use of GLONASS signals from the Russian GNSS system as signals of opportunity for bistatic synthetic aperture imaging. There, antenna motion is utilized to achieve highresolution imaging capabilities in the direction of motion. The crosstrack resolution is achieved through use of the GLONASS precision (P)code, based on publicly available technical specifications, which provides a ranging resolution of about 30 meters. This article extends synthetic aperture GPS signal processing for those cases in which multiple GPS antennas are used. Antenna motion is used to synthesize onedimensional phased arrays. As indicated in Figure 4, the second dimension is added (synthesized) through the combining of signals received by multiple antennas mounted perpendicular to the direction of motion. We will introduce a computationally efficient 2D FFTbased signal processing algorithm to simultaneously steer the array beam in multiple directions. As suggested previously, the array beam can be steered towards reflecting objects to record highresolution SAR images with GPS signals. For GPSbased SAR, the rangebased resolution of the crosstrack image component is limited by the duration of the chip of the pseudorandom ranging sequence: 300 meters for the C/Acode and 30 meters for the GPS Pcode. Focusing the array beam using multiple antennas that are mounted perpendicular to the direction of motion to resolve the crosstrack component improves the crosstrack image resolution beyond the C/A or Pcode chip duration. The approach especially benefits cases where the multiplatform signal integration can be applied to construct large array apertures in the crosstrack direction.
FFTBased MultiDirectional Beam Steering The FFTbased beam steering technique processes synthetic phased array data to construct a GPS signal image in which each image pixel contains signal parameter information corresponding to a signal that is received from a particular steering angle. Figure 5 illustrates the FFTbased signal image construction for the 2D antenna array. Each cell of the 2D FFT frequency grid corresponds to a particular 2D steering angle, where the correspondence between frequency and angles is defined by the antenna size and FFT parameters. (We will present detailed equations later in this section.) Essentially, the FFTbased approach provides a signal image that is similar to the one constructed by a digital photographic camera: each “pixel” in the image is defined by the “intensity” of the signal that is received from the angular direction associated with this pixel. In the case of multidirectional beam steering, the “pixel intensity” is represented by a postcorrelation complex amplitude that contains the inphase (I) value (real part of the complex amplitude) and quadrature (Q) value (imaginary part of the complex amplitude). This signal image can be used to identify and process multiple signal sources that may include direct signals, interference signals, and multipath reflections. Hence, this image can be applied to simultaneously track multiple signal sources such as direct signal and multipath reflections. The following section describes the principles of FFTbased multidirectional beam steering for synthetic GPS antenna arrays.
FFT for MultiDirectional Beam Steering where R is the absolute value of the distance between the current antenna and the first antenna of the array. Beam steering is performed by multiplying samples S of the incoming signal by a complex exponential and then adding individual antenna outputs: In (2), S_{m} is the output of the m^{th} antenna, m is the antenna index number within the array (starting with index zero for the first antenna), and d is the distance between two adjacent antennas. Note that d=λ/2 is normally chosen to avoid grading lobes (i.e., a creation of multiple beams in the angular range from 0 to 180 degrees). For d=λ/2, equation (2) is modified as follows: The antenna beam can be steered simultaneously in multiple directions if we use the FFT mechanism to implement equation (3). FFT harmonic frequencies can be chosen to satisfy the desired steering angular range and angular resolution. For the case of a physical antenna array, the use of the FFT instead of summation transforms singledirection steering into multidirectional steering as follows: where {θ_{k}} are steering angles and k is the FFT frequency index. Note that k is changing from 0 to M/2 and not from 0 to M1. This is due to the fact that the FFT spectrum amplitudes with the index numbers M/2+1 to M are complex conjugates of the spectrum amplitudes with the index numbers 1 to M/21. Consequently, the former do not provide any new information and are not considered. From equations (3) and (4), the FFT spectrum amplitude for the k^{th} frequency harmonic is defined as follows: On the other hand, this spectrum amplitude can be related to the amplitude of the phased array that is steered in the direction of θ_{k}: From equations (5) and (6): Equation (7) defines mapping of the FFT frequencies into steering angles for multidirectional beam steering. Thus, the FFT that is applied to outputs of individual antennas generates multiple beams that are steered in different directions. These steering directions are defined by the initial steering angle θ_{0} and FFT harmonic frequencies as specified by equation (7). To cover the steering angular range from 0 to 180 degrees, a complete FFTbased procedure combines outputs of two FFTs that are performed for initial steering angles of 0 and 90 degrees:
FFTBased Synthetic Beam Steering for GPS Antennas First, batches of signal samples are formed in such a way that the spatial distance between first samples in the adjacent batches is d. Second, FFTs are applied to samples that have the same index number within different batches: for example, to first samples of each batch, second samples of each batch, and so on. The total number of FFTs required equals P; where P is the number of samples in the batch. Third, FFT results are added together to improve the signaltonoise ratio (SNR) for the received GPS signal. The FFT addition operation in the synthetic array case is equivalent to the incoming/replica signal correlation in the conventional GPS receiver architecture. Addition of FFT outputs forms the output of the synthetic phased array. To reduce the computational load, the number of signal samples in the batch can be reduced using averaging. In cases where P≥4 and d=λ/2, distortions associated with this averaging have negligible influence on the FFTbased multidirectional beam steering. We should note that GPS carrier phase tracking must be maintained for phased array antenna formation. Coherent signal accumulation over the entire synthetic aperture is required to maintain carrier phase tracking capabilities. To support coherent signal accumulation, downsampled GPS signals must be compensated for changes in the carrier phase due to intermediate frequency (IF) variations and satellite motion as well as for changes in the code phase of the pseudorandom code sequence (PRN). Navigation message data bits in the GPS signal must be wipedoff to avoid energy losses due to bit transitions for those cases where the time duration of synthetic aperture exceeds the duration of navigation data bits (20 milliseconds). The bit wipeoff can utilize bit estimates from GPS receiver tracking loops. Alternatively, an energybased bit estimation algorithm described in a forthcoming article by A. Soloviev et alia (see Additional Resources) or Kalman filter bit estimation routines (see the articles by N. I. Zeidan et alia and M. L. Psiaki et alia in Additional Resources) can be used for those cases where low carriertonoise ratio (C/N_{0}) signals are processed. To determine the spatial distance between signal samples we used the motion trajectory computed by an inertial navigation system (INS). We applied a quarterwavelength spatial separation between synthetic antennas to the methods reported in this article. This separation corresponds to approximately five centimeters for the GPS L1 carrier. Thus, the INS must provide centimeteraccurate trajectory estimates. This requirement is satisfied if INS error states are periodically estimated by a Kalman filter that uses GPS carrier phase measurements as filter observables. A pattern of the synthetic phased array that is constructed by adding outputs of individual FFTs (see Figure 6) can be approximated by a sinc function: where θ is the steering direction, θ^{*} is the direction of the incoming signal, and A is the total length of the array. In applying equation (9) we can see that the pattern of the synthetic array does not depend on the spatial distance between synthetically generated antenna locations. As a result, this spatial distance can be chosen to provide a desired angular range for the multidirectional beam steering. For our particular purposes, we chose a spatial distance equal to λ/4 so as to cover the angular range between 0 to 180 degrees. In this case, equation (10) provides the final expression for the FFTbased multidirectional beam steering for synthetic phased arrays:
TwoDimensional Beam Steering In (11), m and n are index numbers of the antenna in the physical and synthetic arrays, respectively, with corresponding steering angles ϕ and θ, as shown in Figure 7.
FFTBased MultiDirectional Signal Tracking Hence, the 2D FFT mechanism formulated by equation (11) simultaneously provides Is and Qs for multiple beam steering angles, which can be applied for multidirectional carrier phase tracking. I and Q values for each FFT frequency grid and its corresponding steering direction are treated independently from other frequency grids. Multidirectional carrier phase tracking is performed by processing I and Q values of each steering direction. Signal parameters for different steering directions can be estimated from I and Q values using an openloop receiver architecture described in the forthcoming article by F. van Graas et alia (Additional Reources). FFTbased multidirectional tracking will be illustrated later in the section describing simultaneous tracking of direct and multipath signals. So, with the foregoing theoretical background in mind, let’s turn to the feasibility demonstration and experimental verification phases of our discussion.
1D Synthetic Array: Flight Test Results We selected a straight segment of the flight to demonstrate the generation of synthetic arrays, with the aircraft traveling at approximately 63 meters per second. The synthetic array approach was verified using sampled GPS data recorded during the flight test by the AEC’s software instrumentation receiver described in the article by S. Gunawardena et alia (Additional Resources). To implement multidirectional beam steering in the range from 0 to 180 degrees using a single FFT — per equation (8), antennas in synthetically generated arrays are spatially separated by a quarterwavelength of the GPS L1 carrier wavelength (approximately five centimeters). As described earlier in this article, quarterwavelength batches of GPS signal samples are first formed and then processed. The motion trajectory reconstructed by the INS is applied to determine the spatial separation of GPS signal samples in order to combine samples that are quarterwavelengths apart. The INS motion trajectory is computed from measurements of a lowcost inertial measurement unit (IMU). This unit’s sensor errors are specified as 0.1 degree/second (one sigma) gyro drift and one milligal (one sigma) accelerometer bias. IMU measurements are periodically calibrated inflight using GPS carrier phase in order to maintain the centimeteraccurate reconstruction of motion trajectory needed to generate the synthetic phased arrays. Figure 9 shows synthetic array patterns computed by the FFTbased steering method for the case where the motion of the GPS satellite identified by its pseudorandom noise code — PRN 7 — is wiped off from the incoming signal. An estimated carriertonoise ratio (C/N_{0}) for PRN 7 is 47 dBHz. In the figure, the synthetic array pattern is represented as normalized signal energy (yaxis) versus steering angle, where the signal energy is normalized such that the maximum energy over the entire steering angular range is equal to one. This figure reveal patterns for cases in which the synthetic aperture corresponds to a 26element array that uses halfwavelength separation between their antennas. In the figure, the maximum energy is observed when the antenna beam is steered towards the satellite. An energy loss is introduced as the beam is steered away from the satellite. Essentially, an energy loss for the angle θ is equivalent to a suppression that would be applied to an interference signal (or any other unwanted signal) from a given angle while the beam is steered towards the satellite. The beamwidth is approximated as the distance between the points for which the energy is degraded by three decibels from its maximum (boresight) value. Hence, the beamwidths is approximately 5 degrees.
2D Synthetic Array: Ground Test Results Similar to the flight test, we implemented a straight motion trajectory with the van’s velocity at approximately four meters per second. An AEC twochannel software instrumentation receiver was used to record raw GPS signal samples. IMU data were applied to reconstruct the motion trajectory for the synthetic array formation. Two antennas mounted on the van rooftop formed the array beam in the direction perpendicular to motion. Array aperture in the direction of motion was synthesized by observing these antennas at different spatial locations. We calibrated the system’s interchannel and interantenna biases in advance of the ground test and removed their associated phase delays from raw signal samples prior to implementing the synthetic signal processing routines. Note that the beam steering capabilities in the crosstrack direction were limited by the number of frontend channels (two) currently available in the software receiver. This limitation can be mitigated by increasing the number of frontend channels and/or by implementing multiplatform signal integration techniques. Figures 11 and 12 show 2D synthetic array patterns generated for the ground experiment. In these figures, α is the steering angle in the direction of motion and β is the steering angle in the crosstrack direction. Figure 13 shows test results for a phased array constructed using two physical and six synthetic antennas. Similar to the 1D array case, the maximum signal energy is received when the array beam is steered in the direction of the satellite. As the beam is being steered away from the satellite, signal attenuation occurs. At a specific angular direction, this attenuation is equivalent to that which would be applied to a multipath or an interfering signal coming from this direction. As mentioned previously, beamsteering capabilities in the crosstrack direction are currently limited by the number of frontend channels in the receiver. With only two channels available, therefore, the array beam in the crosstrack direction is rather wide: approximately 30 degrees. Nevertheless, the experimental results demonstrate the feasibility of generating 2D arrays by using synthetic aperture GPS signal processing and combining signals from multiple antennas. Figure 12 shows the 2D synthetic array pattern for the case where the synthetic aperture is extended to 31 elements. This extension narrows the array beam significantly in the direction of motion. The beamwidth in the crosstrack direction remains unchanged.
FFTbased MultiDirectional Beam Steering: Simulation Results For the simulation, a multipath signal was added to the direct satellite signal. Multipath was simulated as a specular reflection from a horizontal planar surface collinear to the YZ plane. Figure 13 illustrates this multipath scenario. For the FFTbased synthetic array processing, the synthetic aperture corresponds to 20 physical antennas separated by a halfwavelength. A fourelement physical array with halfwavelength antenna separation was simulated to steer the beam in the direction perpendicular to motion. Array beams were steered in multiple directions using 2D FFTs (see Equation [23]). For the direct signal, a C/N_{0} of 40 dBHz was implemented. The multipath power was simulated to be three decibels below the direct signal power. Figure 14 shows a 2D signal image constructed using the 2D FFTbased beam steering method. The plot demonstrates simultaneous recovery of the direct and multipath signals. FFTbased multidirectional signal tracking was implemented and simulated for the case of simultaneous tracking of direct and multipath signals for the scenario illustrated in Figure 15. FFTbased Is and Qs are applied to track the carrier phase of direct and multipath signals. Real and imaginary parts of FFT complex amplitudes for beams steered in the direction of direct and multipath signals are exploited as I and Q values, respectively. Figure 15 illustrates the results of the simulated tracking. Carrier phase tracking errors are shown as differences between true carrier phase (known in the simulation) and measured carrier phase based on I and Q values provided by 2D FFT computations. Standard deviations of carrier phase errors are evaluated as 3.2 and 4.3 millimeters for the direct and multipath signals, respectively. Hence, the simulation results presented demonstrate the feasibility of simultaneous tracking of multiple signals using the FFTbased multidirectional beam steering.
GPSBased SAR Imaging A simulated receiver platform includes four GPS antennas mounted on an unmanned aerial vehicle (UAV) that is flying at 20 meters above the ground with a 2 meters per second ground velocity. The simulated scenario assumes a single point reflector located at ground level. The C/N_{0} of the reflected signal was simulated to represent an army tank hidden under a dense canopy. Analysis of RF GPS data collected in forestry areas shows that for highelevation satellites the signal is generally attenuated by 7 decibels as it propagates through the canopy. Therefore, the signal attenuation of 14 decibels was introduced for the twoway propagation path through the canopy, that is, from the satellite to the target and from the target to the receiver. The radar cross section (RCS) of the target is assumed to be five square meters. For the 14decibel signal attenuation due to the propagation through the canopy and a five square meter RCS value, the C/N_{0} of the signal that is received at the UAV platform is estimated at 17 dBHz. We simulated and processed the C/Acode component of the GPS signal. To process the GPS signal at a 17 dBHz level, a onesecond coherent integration interval was implemented. Construction of SAR images was based on the 2D FFTbased processing approach discussed in the previous section, augmented by beam focusing techniques discussed in the book by J. C. Curlander and R. N. McDonough (Additional Resources) to avoid image distortions that are due to the motion of the platform. Figure 17 shows an example of a simulated SAR image. To construct this image, steering angles were converted into X and Y Cartesian coordinates using the known height above the ground (20meters). The GPSbased SAR image shown in Figure 17 clearly identifies the presence of a target. Note that the image resolution in the direction of motion is achieved using the synthetic aperture. For the crosstrack direction, the image is resolved by focusing the array beam with multiple physical antennas mounted perpendicular to motion. This implementation differs from the classical SAR approach that uses a single antenna and the crosstrack image component is resolved using the carrier modulation by a ranging signal. For the GPS case, the chip duration of the C/Acode ranging modulation is 300 meters. Clearly, this resolution is insufficient for most imaging applications. Hence, multipleantenna beam focusing is applied to resolve the crosstrack image component. As shown in Figure 17, the multiantenna focusing approach allows for resolving the crosstrack image component within approximately three meters. In other words, the ranging resolution of the C/A code is improved by two orders of magnitude in the simulation scenario.
Conclusions This approach can be applied for improving GPS robustness to radiofrequency interference, simultaneous tracking of multiple signal sources such as direct signal and multipath reflections, and for recording highresolution images utilizing GPS signal reflections. Future research in the area of synthetic aperture GPS signal processing will focus on the demonstration of the GPS SAR concept with experimental data and multiplatform signal processing for generating large array apertures in the direction perpendicular to motion.
Acknowledgment
Additional Resources ManufacturersThe lowcost IMU used in the AEC flight test is a Coremicro manufactured by American GNC Corporation, Simi Valley, California, USA.Copyright © 2018 Gibbons Media & Research LLC, all rights reserved. 
