Summary
Antenna arrays and spatial processing techniques are among the most effective countermeasures against interference. Here, we demonstrate a new array concept consisting of spatially-distributed subarrays that are small enough to fit inside the non-metallic parts of an automobile. This will facilitate concealed installation of these devices in bumpers or side mirrors, which is a strict requirement of the industry and preferred by the customers. Using beamforming algorithms, this array was proven to be robust against jammers in the L1 band. The large distances between the individual antenna elements resulted in a non-negligible baseband delay that violated the narrowband assumption and increased with bandwidth. Hence, this paper demonstrates the influence of a jammer in the L5 band. Space-time adaptive processing that allows for compensation of the delays was introduced and analyzed. Improvements in interference mitigation capabilities were assessed and compared to those of pure spatial state-of-the-art implementation. Real-life measurement data was used to ensure realistic results.
1 INTRODUCTION
Antenna arrays and spatial signal processing techniques have proven to be the most effective countermeasures against radio frequency interference (RFI) (Pullen & Gao, 2012), spoofing attacks (Humphreys et al., 2008; Meurer et al., 2016), and multipath signals (Zorn et al., 2018). Using arrays, the direction of arrival (DOA) of incident signals can be determined by phase differences detected by individual antenna elements. Therefore, it is possible to amplify satellite signals or spatially mitigate RFI. Methods for developing compact arrays such as uniform rectangular arrays (URAs) shown in Figure 1(a) have been established. Likewise, two-stage beamforming algorithms are currently the state-of-the-art approach against sources of interference (Kurz et al., 2012). Compact arrays rely on the spatial proximity of the included antenna elements; the spacing between two adjacent antenna elements must typically be on the order of half of a carrier wavelength. Therefore, the size of the URAs needed for L-band signals in their minimum configuration (2×2 URA) with approximately 20–25 cm edge length precludes their use in applications that require conformal design or a hidden installation. This is particularly a problem for the design of (partly) automated or autonomous driving cars intended for the consumer mass market.
Comparison of the two array topologies under consideration (a) Conventional uniform rectangular array (b) Combination of two linear subarrays
Global navigation satellite systems (GNSSs) should act as the backbone of absolute positioning for vehicle navigation and should be complemented by various additional sensors such as inertial measurement units, cameras, lidar, radar, and odometers, among others. In the presence of a strong source of interference that blocks the reception of a GNSS signal in the direct vicinity of a moving car, absolute positioning capabilities will be virtually lost. The consequences of this problem depend on the level of automation involved and could extend from a simple loss of assistance functions in case of partly automated cars to a complete loss of functionality in cars operating autonomously. Multi-antenna array approaches have been considered and proven to serve as potentially powerful countermeasures against interference, jamming, and spoofing attacks. Unfortunately, the aforementioned URA cannot be incorporated in any of the current designs. The aesthetic design of passenger cars is a critical selling point for both the industry and customers. Hence, mounting these devices on the roof of the car is not an acceptable option. By contrast, installation below the metallic car body might be aesthetically acceptable, but the car itself would block the reception of the low-powered GNSS signals. The only remaining sites for hidden installation are the front and rear bumpers or the side mirrors which are typically manufactured from synthetic non-metallic materials. However, these components do not provide enough space for the large footprint of a conventional URA.
Aiming directly at the automotive sector, we present a new array design consisting of a set of at least two uniform linear arrays (ULAs) in a minimum configuration in which each includes two antenna elements (Brachvogel et al., 2018; Hasnain et al., 2018) as shown in Figure 1(b). In this configuration the distance δsub between the ULAs may exceed half of a carrier wavelength. Given this new degree of freedom, this array configuration solves the following problems with respect to automatically driving cars:
The array can mitigate incident jammers and spoofers via spatial processing;
Its manifold is free of rank-1 ambiguities (Tan et al., 1996), thus, a single dominant (jamming) signal can be mitigated without serious affecting other (satellite) signals; and
The footprints of the individual ULAs are reduced compared to the footprint of the URA.
Given their reduced footprint, the ULAs may be distributed in the bumpers and/or side mirrors as in the example shown in Figure 2. In this configuration, they can provide a robust defense against RFI, spoofers and multipath in a situation in which hidden installation is strictly required.
Examples of places in which the ULAs can be mounted in the synthetic parts of a passenger car
However, the new array design does come with some drawbacks. From the signal processing perspective, the increased size of the lever arm between the ULAs and the antenna elements may lead to differential effects on the antenna signals (Brachvogel et al., 2020b), including, for example, differential non-negligible delays in the received baseband signal, deviating Doppler frequencies with respect to the carrier signal, or unequal power levels due to hardware imperfections and shading from the metallic car body that blocks the signals to be received from the individual antenna elements. This implies that the correlation of an incident signal received at the spatially distributed antenna elements may be reduced in this array design compared to the conventional URA in which the spatial proximity guarantees a strong correlation. Consequently, a single incident signal evokes several (as opposed to a single) eigenvalues in the estimation of the covariance matrix between the antenna signals. The consequences of this reduced correlation will depend on the beamforming algorithm that has been incorporated. Moreover, with respect to interference mitigation, a single dominant source of interference may consume several degrees of freedom instead of just one; thus, the total amount of jammers that can be tolerated will be reduced. On the other hand, the effectiveness of beam-forming algorithms may be significantly reduced, such that residuals of jammers remain unfiltered or the achievable improvement in satellite signal-to-noise-ratio (SNR) will decrease compared to an application that utilizes signals of a conventional URA with the same number of antenna elements.
We have studied the impact of these effects in experimental simulations using a specific range of bandwidths and global positioning system (GPS) L1 C/A signals (Brachvogel et al., 2020b). For signals with higher bandwidths, for example, those used in GPS L5 or GALILEO E5a, decorrelation via differential delay is expected to be a dominant factor.
In this paper, we present experimental results from the array under consideration evaluated at a bandwidths above 10 MHz incorporated in the new signals for the GPS L5 or GALILEO E5a. Interference mitigation will be discussed in Section 3 that focuses on the spatial covariance matrix of incident signals using state-of-the-art implementation. Based on these results, a novel approach will be presented that calculates a spatiotemporal covariance matrix capable of compensating for the aforementioned differential delays. While similar approaches, better known as space-time adaptive processing (STAP) implementations for GNSS signal processing have been considered previously, these discussions were limited to the use of compact arrays. For example, in Fante & Vaccaro (2000) STAP was addressed as a countermeasure against multiple wideband sources in multipath scenarios and its performance was compared to that of a space-frequency processing approach. Similarly, Castañeda et al. (2013) demonstrated how the incorporation of the temporal correlation improved the characterization of the incident signal model and analyzed the behavior of the root mean square error on time estimation when omitting either the spatial or the temporal correlation. Konovaltsev et al. (2013) motivated the use of STAP against pulsed interference signals and compared the mitigation performance to pulse blanking techniques and in scenarios involving continuous interference, and Marcos et al. (2016) proposed a STAP implementation to counteract signal decorrelation resulting from hardware imperfections in the receiver front-end.
Our technique will be developed, analyzed, and the improvements in interference mitigation capability will be assessed using real-life data. The improvements in SNR will be presented in Section 5 using data captured in an anechoic measurement chamber in a controlled environment at Virtual Road - Simulation and Test Area (VISTA) (Hein et al., 2015) at TU Ilmenau. The effects on positioning accuracy will be considered in Section 6 based on data captured at an open-sky measurement at the Chair of Navigation in Aachen. Only code-based positioning was considered in this demonstration. While much effort was taken to improve the accuracy to decimeter level using carrier-based positioning, which will be especially important in the field of automated driving (Henkel & Sperl, 2016), the existing approaches are unable to perform spatial interference mitigation and are hence completely vulnerable to incident interference. While ongoing research aims to incorporate these techniques with array systems (Bamberg et al., 2022), this topic is currently beyond the scope of this paper.
2 SIGNAL MODEL
In the following scenario, we assume a planar array of N antenna elements at fixed positions as shown in Figure 3. The analytical signal of the i-th source impinging at a virtual ideal isotropic antenna element at the origin is denoted as indicated in Equation (1):
1
Coordinate system, direction of arrival (DOA) and relative delays compared to the origin for a signal incident from ϕi = 150° and θi = 40°
where 
denotes a complex parameter and 
is composed of an arbitrary baseband signal 
modulated onto a carrier signal defined through the received carrier frequency defined by Equation (2):
2
which consists of the transmit frequency ft and the additive received Doppler 
depending on the relative velocity vi of the source and speed of light c0. It is assumed that the array is located in the far field of the transmitting antenna, such that the incident wave will be approximately planar. The position of an arbitrary antenna element n in the xy-plane can be described as shown in Equation (3):
3
where ϕn (t) is the angle to the n-th antenna at time t in the xy-plane as shown in Figure 3. Note that a lowercase bold parameter such as rn (t) in Equation (3) denotes a vector and an uppercase bold parameter represents a matrix in the following equations. The signal received from this antenna element can be described by Equation (4) and by using Equation (1) as follows:
4
which differs from to the signal in the origin by a position-dependent delay 
, a velocity-dependent additive Doppler 
and 
describing the overall difference in received amplitude and phase via, among other things, components in the analog receiver chain. Using the wave vector shown in Equation (5):
5
which describes the wave propagation in Cartesian coordinates. The temporal offset of the signal of the n-th antenna element depending on the direction of arrival of the signal relative to the orientation of the receiver is calculated as shown in Equation (6):
6
The additional Doppler signals depending on the movement of the antenna array can be calculated using its instantaneous orientation and the constant direction of the carrier signal as indicated in Equation (7):
7
where 
denotes the velocity of the antenna element relative to the direction of the incident signal. Note that the received Doppler shift is composed of a common Doppler shift for all antenna elements 
associated with the Doppler frequency for the virtual reference antenna at the origin as denoted in Equation (1) and a differential Doppler shift due to the relative movement of the individual antenna elements 
with respect to the origin. The vector containing the signals of all antenna elements as defined in Equation (4) can be described as shown in Equation (8):
8
where ⊙ denotes the Hadamard product and 
the collection of hardware-dependent influences on the overall received amplitude and phase through antennas and analog front-end, which are dependent on the time-varying direction of arrival of signal i. The signals differ between the antenna elements by a time-varying phase offset defined by the product of instantaneous delay and received frequency, which is a delay between the baseband signals and different Doppler frequencies with respect to the carrier.
As we consider a GNSS receiver with N antenna elements in a possible interference scenario, the vector describing the received signals is denoted by Equation (9):
9
which is a superposition of L satellite signals, J interference signals, and additive noise 
. In the following scenario, it is assumed that 
is a vector with temporally zero mean white Gaussian noise. The contribution of the l-th satellite, 
, to the received signal 
described in Equation (9) is described by Equation (8), where 
collects the influences of the hardware 
and the time-dependent steering vector. The baseband signal is defined as 
and consists of the pseudo-random noise (PRN) sequence pl(t) for code division multiple access (CDMA) and the data or pilot signal dl(t), where Pl is the received signal power. Analogously, the j-th undesired interference signal is defined by 
, where 
denotes an arbitrary baseband signal inside the receiver bandwidth.
In the following scenario, the signals 
and 
with 
denote the demodulated and digitized signals using the sampling rate fs. A valid expression corresponding to Equation (8) for an arbitrary digitized signal received at the individual antenna elements can be determined using Equation (10):
10
In this case, 
includes the time- and frequency-dependent influences of attenuation, differential Doppler shift, and steering vector for antenna channel n, whereas 
is the sample delay between the digitized baseband signals. This delay is composed of the delay in seconds as described in Equation (6) and the incorporated sampling rate as indicated in Equation (11):
11
and is clearly fractional. As fractional values for 
do not lead to a meaningful expression using Equation (10), we express Equation (10) (Laakso et al., 1996) as shown in Equation (12):
12
where 
poses the ideal impulse response to express fractional sample delays. Because we have previously studied the impact of the parameters in 
(Brachvogel et al., 2020b), this publication focuses on the correlation loss through 
. Whereas all differential effects included in the two impulse responses 
and 
parameters that affect the correlation between signal i in the individual antenna channels, the latter has an increasing influence the larger receiver bandwidth or the sampling rate is chosen.
An example of this effect is illustrated in Figure 4 which shows 
for two different sampling rates, fs =5 MHz and fs = 25 MHz. These rates are frequently used to sample narrowband signals such as those from GPS L1 C/A and wideband signals from GPS L5 or GALILEO E5a. As the distance between individual antenna elements in the overall array shown in Figure 2 can be as large as the typical dimensions of a car, the path distance, which is the distance a signal travels between two antenna elements, is assumed to be 4 m. This leads from Equation (11) to a fractional delay of 
samples for fs =5 MHz as shown in Figure 4(a) and 
samples for fs = 25 MHz in Figure 4(b). One can clearly observe that most of the power is included in the central sample for the narrowband example, which has a height of approximately 1. By contrast, in case of the wideband signal, the height of the central sample is significantly reduced and the heights of the neighboring samples are comparatively increased. This means that the signal power of the current sample k at the first antenna element is spread to the neighboring samples at the second antenna, thereby leading to significant decreases in cross-correlation between the antenna signals received.
Absolute values of the impulse response for a distance of 4 m for two different sampling rates fs (a) fs = 5 MHz as used to sample narrowband signals, e.g., GPS L1 C/A (b) fs = 25 MHz as used to sample wideband signals, e.g., GPS L5 or GALILEO E5a
3 SIGNAL PROCESSING
As a countermeasure against interference and to amplify the weak GNSS signals received, we used a state-of-the-art blind two-stage beamforming technique (Kurz et al., 2012) as depicted in Figure 5. We analyzed the performance of this technique in several previous publications (Brachvogel et al., 2018, 2020a, 2020b) in the context of narrowband jamming scenarios using GPS L1 C/A signals. This technique detects incident signals without the need for further information by estimating their correlation before and after PRN despreading. In this paper, we introduce adaptations to the interference mitigation stage. The post-correlation beamforming algorithm combines the satellite signals using a similar approach, which is briefly explained in (Brachvogel et al., 2020b; Kurz et al., 2012). For the sake of clarity, this is not explained further in this paper.
Block diagram of the beamforming implementation
Potential interference is mitigated by decorrelating the raw antenna signals. The satellite signals are independently amplified after demodulation and despreading using the correlator outputs of the tracking channels.
The interference mitigation stage works on blocks of K samples of the digitized antenna signals defined as indicated in Equation (13):
13
where the window index κ points to an arbitrary sample in the digitized antenna signal 
.
3.1 State-of-the-Art Implementation: Space-Adaptive Processing
The spatial covariance matrix at an arbitrary time k of 
is defined by Equation (14):
14
with E{·} as the expected value and (·)H the Hermitian transpose. By assuming that the cross-correlation among satellites 
, interference 
, and noise signal 
are negligible (Brachvogel et al., 2020b), 
can be expressed as indicated in Equation (15):
15
where 
and 
denote the spatial covariance matrices of discrete satellite, interference, and noise signals. Additionally, since the power of GNSS signals is well below the thermal noise floor of the receiver, Equation (15) can be approximated to Equation (16):
16
where 
denotes the variance of the signals in the spatially white thermal noise vector 
and I is the identity matrix, such that 
has a diagonal shape.
The interference mitigation stage as shown in Figure 5 calculates an estimate 
of the covariance matrix by averaging 
over a block of K samples as in Equation (13) as indicated in Equation (17):
17
where SAP stands for Space Adaptive Processing and refers to the calculation of the covariance matrix using the state-of-the-art approach. It is therefore assumed that the block length K is chosen to be large enough so that 
can be modeled as wide-sense stationary over the interval defined in Equation (13). The state-of-the-art approach used to mitigate interference signals which is also known as a pre-whitening filter (Kurz et al., 2012) uses a scaled inverse of the covariance matrix defined in Equation (17) to derive the spatial precorrelation filter 
. The filtered signal block can then be expressed as shown in Equation (18):
18
where 
denotes the Frobenius norm.
Using Equations (16) and (18), one can distinguish between two possible scenarios:
In an interference-free scenario,
consists purely of . Thus has approximately the shape of I. In this scenario, the filter is transparent to all incident signals.Assuming active interference, the shape of
deviates from I, and the interference can be detected as spatial covariance between the antenna channels through the elements on the side-diagonal. Hence, using the inversion in Equation (18), this covariance is removed, thereby blindly mitigating the interference.
One drawback of this implementation is that Equation (17) uses only unshifted versions of the antenna signals to calculate the covariance matrix and thus to derive the weights of 
from Equation (18). Thus, this implementation poses a purely spatial approach that ignores delays between the antenna signals that increase with bandwidth and distance between individual antenna elements as shown in Figure 4. This becomes clear if we inspect the entries for one arbitrary row of 
as shown in Equation (17), which is an example for the first row and N = 2 antenna elements as indicated by Equation (19):
19
where (·)* denotes the complex conjugate operator. If large sample delays occur between antenna signals as shown in Figure 4(b), this approach is by design unable to estimate a temporal correlation between the signals. In this case, residuals of an interference signal (i.e., the non-central samples in Figure 4) will remain unfiltered in 
.
3.2 New Proposal: Space-Time Adaptive Processing for Delay Compensation
To solve this problem and eliminate the delay between antenna signals, a method known as Space-Time Adaptive Processing (STAP) (Castañeda et al., 2013; Fante & Vaccaro, 2000; Konovaltsev et al., 2013; Marcos et al., 2016) is proposed as a countermeasure. With this method, the vector of antenna signals used to calculate the covariance matrix is extended to include the time-shifted versions of 
, as indicated in Equation (20):
20
where M is an odd natural number and denoted as the number of taps corresponding to the time-shifts included in the STAP implementation. The estimation of the covariance matrix is similar to that shown in Equation (17), but now using 
instead becomes Equation (21):
21
This extended matrix with dimensions increased by the factor M is in inverse form similar to Equation (18) such that the vector of the filtered extended data block can be expressed as indicated in Equation (22):
22
The main difference between the two processing methods becomes clear when one inspects the entries for an arbitrary row of 
and comparing the results with the entries for 
after Equation (19). Using once again the example of N = 2 antennas and assuming a minimum of M = 3 taps, the coefficients for the first row of 
after Equation (21) become as shown in Equation (23):
23
One can clearly see that, in addition to the estimate of the pure spatial correlation coefficients, the coefficients for time-delayed and time-advanced combinations of antenna signals are now estimated and included in 
after inversion using Equation (22), in the filter coefficients of 
. Therefore, as an additional advantage, use of this method increases the degrees of freedom for filtering. The difference of the two processing methods can also be visualized in Figure 6 for the filtered first antenna channel, 
, using the example of N = 4 antennas and M = 3 taps. Note that the weights shown in Figure 6(b) correspond to the desired central un-shifted part 
and hence belong to the fifth row of 
. The example of 
from Equation (22) now becomes Equation (24):
24
Comparison between the state-of-the-art SAP and the proposed STAP implementation for 
(a) Conventional SAP block diagram (b) Proposed STAP block diagram for M = 3 taps
Shown is an example using N = 4 antennas.
4 ANALYSIS OF SYSTEM PERFORMANCE
The choice of M crucially affects the mitigation performance of the STAP implementation. However, this choice can drastically increase the computational demand to estimate the covariance matrix after Equation (21) and its inverse. Both parameters, which determine the maximum delay in samples 
according to Equation (11), depend on the system involved and can be controlled within certain boundaries. Hence, care must be taken to ensure that M is chosen optimally, such that incident interference signals can be mitigated sufficiently with a minimum demand on processing power. Therefore, this section provides a brief analysis of how the described leakage effect depends on the system parameters and how different choices of M affect the mitigation performance.
Recalling Equation (11), one can see that the sample delay depends linearly on both the sampling rate fs and the physical delay of the incoming wave to the origin of the coordinate system. The maximum sample delay between two digitized signals is therefore determined by the largest baseline between any pair of antennas in the overall array. To analyze how the effect shown in Figure 4 depends on these factors, we choose a fixed distance of 4 m for the baseline as a worst-case scenario in automotive applications. We will treat the sampling rate as the simulation parameter. However, the results shown depend on 
and can therefore also be observed for variations of the baseline.
To analyze how signals received by two antennas with a delay of 4 m are correlated, the absolute of the impulse response hFD [k] is shown for sampling rates up to 500 MHz in Figure 7(a), similar to Figure 4. One can see that the central tap of the impulse response is shifted away from the center with increasing fs. As a consequence, the signal power concentrated in the sample k is shifted to the neighboring samples, thereby decreasing the cross-correlation of the signal received at the different antennas as described in Section 2. This effect is illustrated in Figure 7(b), which shows the power of the central tap, hFD [0], compared to the accumulated power of all other taps, as indicated in Equation (25):
25
over fs for different delays. For low fs and delays, Pcb is approximately 1, such that most of the power received in sample k at the first antenna is located in the same sample when received at the second antenna. However, with increasing fs and delay, Pcb approximates −1, meaning that the power of the central sample is shifted almost completely to the other samples. The only way to recover this power loss is via STAP implementation.
Behavior of the impulse response hFD[k] over bandwidth fs (a) |hFD[k]| depending on fs for a delay of 4 m. The color denotes the magnitude of the channel tap (b) Power of the central channel tap of hFD[k] relative to the power in all other taps over fs for different baselines
The necessary M for STAP implementation can be determined by analyzing the correlation coefficient shown in Equation (23). The cross-correlation coefficient between the two antennas is shown over fs in Figure 8(a). As noted earlier, the pure spatial correlation 
drops with increasing fs. Since we know from Equation (23), that STAP implementation with M = 3 also calculates the spatiotemporal correlation up to a shift of two samples, in this case we could use Figure 8(a) to identify the upper boundary of fs. This is located approximately at fs =150 MHz, where 
reaches its maximum and drops thereafter. If a higher value of fs is chosen, M = 5 has to be chosen to be able to calculate 
. The results presented in Figure 8(b) document the effect of the interference signal after mitigation for different M on the residual normalized amplitude. From this diagram we can see that the pure spatial approach rapidly loses the ability to suppress an incident interference signal with increasing bandwidth; the residual amplitude remains low the higher M is chosen.
STAP performance over fs for a delay of 4 m (a) Correlation coefficients (b) Residual amplitude after mitigation for different STAP implementations
Note that, at this point, a temporal white Gaussian noise sequence was used for simulation in both figures of Figure 8 to evaluate the worst-case example in terms of temporal correlation of an interference signal. For other signals, for example, a continuous-wave jammer or any other signal correlated over time, the problem of decreasing 
and residual interference amplitude might be less severe. As mentioned in the beginning of this Section, the results shown are dependent on delay and sampling rate fs. By taking the application and GNSS parameters into account, one can find borders for both. The distance between antennas in the bumpers of a car will reach from approximately 2–5 m for width and length of a typical passenger car. The necessary minimal sampling rates in terms of the GNSS bandwidth range from 1 MHz to 40 MHz for signals in the GPS L1 C/A and GALILEO E5 band. To determine the effects of those signals, the results reveal that the sampling rate equals the aforementioned bandwidths. However, oversampling is associated with specific benefits, for example, better resolution; thus, this is often chosen during the design of the system. For that purpose, the shown decorrelation effects of the interference will increase up to the assumed level of a temporally-determined white noise signal occupying a receiver’s complete bandwidth.
5 EVALUATION WITHIN AN ANECHOIC CHAMBER
To evaluate the benefits of the proposed STAP implementation compared to the conventional SAP method, measurement data was recorded inside the an anechoic chamber in Virtual Road - Simulation and Test Area (VISTA) (Brachvogel et al., 2020b; Hein et al., 2015). This provides us with a substantial advantage compared to an outside measurement, as the signal conditions can be controlled and other effects, including multipath, will not affect the results.
The main purpose of this experiment was to demonstrate the benefit of STAP and obtain proof of its capacity to mitigate a jammer in a dynamic scenario. We also intended to show the differences in performance that depend on the signal bandwidth. The method described in this section evaluates the algorithms for various directions of arrival (DOAs) over an entire 360° rotation.
5.1 Measurement Setup
As shown in Figure 9, two subarrays (shown by red circles) were attached to the side mirrors of a car. Four antennas, each emitting two satellite signals (orange circles), and one jamming signal-emitting antenna (green circle) were placed around the car. Two sets of measurements were performed in which the emitted satellite signals were successively introduced as narrowband GPS L1 C/A signals and wideband GALILEO E5a signals with chip frequencies of 1.023 MHz and 10.23 MHz, respectively. In both measurements, the jamming signal was a white Gaussian noise sequence that occupied the entire receiver bandwidth (i.e. the sampling rates fs, were chosen to present the worst-case example of an interference signal in terms of temporal correlation as discussed in Section 4). The jamming to satellite signal power ratio (JSR) was set to approximately JSR ≈ 30 dB in the respective signal generators. The systems and PRNs corresponding to the emitting antennas are shown in Figure 9(b). An Ettus X310 Universal Software Radio Peripheral (USRP) with two Twin-RX daughterboards was used as capturing device and the data was stored on a PC; both devices were located inside the car. The chosen sampling rates for the two measurements were fs =5 MHz to sample L1 signals and fs = 12.5 MHz for E5a. During each measurement, the car was rotated clockwise by 360° such that the length of the path between the two subarrays traveled by each signal varied. The final processing steps using SAP and STAP were as described in Section 3 and were performed using MATLAB.
Image and parameters for the measurement setup in VISTA (a) Image of the measurement setup in VISTA. Orange, green, and red circles mark satellite, jamming signal emitting antennas, and subarrays, respectively (b) Sketch of the setup
As a metric to evaluate the differences between the two processing methods, the carrier-to-noise density ratio (CN0) was estimated (Pini et al., 2008) for each satellite from the beamformed correlator output 
after the two-stage beamforming implementation as shown in Figure 5. To determine the gains associated with the use of STAP rather than SAP, the differences ΔCN0 of the CN0 values achieved with each processing method were calculated. The process to calculate ΔCN0 is shown in Figure 10. The difference was calculated by subtracting the estimated CN0 for each measurement point through SAP from the CN0 achieved using STAP. The green highlighted areas mark the intervals where STAP alone had the capacity to process the signal and SAP had lost track of the satellite. By contrast, the yellow-highlighted areas show the intervals during which both methods failed to track the satellite.
Procedure to calculate ΔCN0 (a) Achieved CN0 with 3-tap STAP (b) Achieved CN0 with SAP (c) ΔCN0 between STAP and SAP
The CN0 achieved using STAP and SAP were subtracted for each satellite. The green- and yellow-highlighted areas mark the intervals where only SAP or both SAP and STAP lost the signal.
In the following section we will consider the results of three specific comparisons that lead to three important statements:
ΔCN0 was determined between a STAP implementation with M = 3 taps and a pure SAP approach for wideband GALILEO E5a signals. The results of this comparison will reveal whether a benefit for wideband signals can be achieved.
ΔCN0 was determined between a STAP implementation with M = 5 taps and a STAP implementation with M = 3 taps for the wideband GALILEO E5a signals. The results of this comparisons will reveal the impact of an increase of the number of taps on the system performance.
ΔCN0 was determined between a STAP implementation with M = 3 taps and a pure SAP approach for the narrowband GPS L1 C/A signals. The results of this comparison will reveal the effectiveness of this implementation with respect to narrowband signals.
5.2 Results
As shown in Figure 9, each antenna emitted two different PRNs during the experiments. For the sake of clarity, only the results of one PRN per emitting antenna and respective GNSS are shown (i.e., PRNs 4, 11, 19, and 21 for GALILEO E5a and PRNs 20, 22, 28, and 32 for GPS L1 C/A). The results for the other PRNs are similar and the statements derived from this data set hold for all.
Figure 11 shows the results of STAP with M = 3 compared to pure SAP for wideband GALILEO E5a signals. A clear improvement was seen in the ΔCN0 for all directions as the differences were almost always larger than 0 dB with approximately 5 dB as the average value. Furthermore, there were only a few intervals during which the signals could be tracked if STAP was used; these areas are marked in green. Hence, STAP with the minimum number of taps improves the signal quality for GALILEO E5a signals collected at a sampling rate of fs = 12.5 MHz.
Improvement observed with STAP with M = 3 compared to SAP for GALILEO E5a signals (a) ΔCN0 for DOA 1 (b) ΔCN0 for DOA 2 (c) ΔCN0 for DOA 3 (d) ΔCN0 for DOA 4
Next, we determined whether including more taps could improve the signal quality even further. Figure 12 shows the signals after processing with STAP with M = 5; these results can be compared to those shown previously that featured STAP with M = 3. Despite one interval for DOA 2 during which the signals could not be tracked with three taps, there were no significant additional improvements in the CN0. This may be because most of the correlation power is included in the taps in the direct vicinity of the central tap as shown in Figure 4(b). Hence, more taps can in some cases result in further improvements in the signal quality, albeit with drawbacks that include increased hardware requirements. This is because the complexity of the estimation of the covariance matrix and especially the calculation of its inverse increases dramatically with the number of taps M.
Improvement observed with STAP with M = 5 compared to STAP with M = 3 for GALILEO E5a signals (a) ΔCN0 for DOA 1 (b) ΔCN0 for DOA 2 (c) ΔCN0 for DOA 3 (d) ΔCN0 for DOA 4
Finally, Figure 13 documents the results of a comparison between STAP with M = 3 and SAP for the narrowband GPS L1 C/A signals collected with a sampling rate of fs =5 MHz. While one can see small improvements during some of the intervals, the overall improvement in performance is less than that achieved for the wideband GALILEO E5a signals as shown in Figure 11. Thus, we can conclude that STAP is especially beneficial if signals with larger bandwidth are considered.
Improvement observed with STAP with M = 3 compared to SAP for GPS L1 C/A signals (a) ΔCN0 for DOA 1 (b) ΔCN0 for DOA 2 (c) ΔCN0 for DOA 3 (d) ΔCN0 for DOA 4
6 EVALUATION OF POSITION ACCURACY
The experimental design described in Section 5 does not permit us to evaluate the influence of the proposed algorithm on improving the position accuracy of the overall system. This is because the satellite signals are emitted from four antennas distributed around the car and hence, the ephemeris data do not correspond to their true position. Therefore, the measurable pseudoranges include a systematic error and so do the position, velocity, and time (PVT) measurements derived from them.
6.1 Measurement Setup
A similar experiment was performed at the Chair of Navigation in Aachen as shown in Figure 14. Four patch antennas were mounted onto the front bumper of a car to generate a prototype of the new array concept (Figure 14(b)). The position solution of the processed signals of these four antennas was then compared with the signals received at a single antenna placed on top of the roof of the car (Figure 14(c)). The device on the roof is the reference antenna representing state-of-the-art GNSS antennas in cars. The position solution is compared under the influence of a jammer emitted via the antenna shown in Figure 14(a). The latter antenna is a Schwarzbeck CLSA 0110R, whereas the patch antennas on the car are Tallysman TW7875 antennas. The distance between the emitting antenna and the car is approximately 24 m. The signals from all five patch antennas are captured with two Ettus X300 devices each with two Twin-RX daughterboards and a sampling rate of 25 MHz: One X300 captures the signals of the four patch antennas of the array prototype shown in Figure 14(b), while the other captures the signal of the reference antenna on top of the car from Figure 14(c). Since the local oscillator (LO) inside an X300 with Twin-RX daughterboards is shared between all channels, this setup allows for phase-aligned operation required for the use of beamformers by the array prototype. The LO of the second X300 is not synchronized to the LO of the first; its signal is processed individually as a reference for a single antenna receiver that does not participate in spatial mitigation. A complete description of all parameters and devices used in this experiment are shown in Table 1.
Measurement setup at the Chair of Navigation in Aachen (a) Jamming antenna near the car (b) Array on the front bumper (c) Reference antenna on top of the roof
Parameters of the Jamming Experiment at the Chair of Navigation
The jamming signal is switched on after 60s as shown in Figure 15; thus, a complete ephemeris set from each satellite will be received before the experiment begins. Its power PTX is increased slowly from −80 dBm to 15 dBm in 95s. The MATLAB GNSS Array Receiver (MaGNAR) implementation of the Chair of Navigation was used to process the raw data up to the position solution. Three different position estimates were calculated:
The signal from the single roof antenna was processed. This represents the state-of-the-art but cannot perform spatial processing.
The signals from the four array antennas are processed with pure SAP. We can assess the influence of spatial processing on signals from distributed antenna elements in comparison to the roof antenna.
The signals from the four array antennas were processed with STAP with M = 3. These results can be used to assess the influence of STAP compared to SAP.
Properties of the jamming signal during the experiment (a) Jamming power over time (b) Eigenvalues of 
of the array antenna signals over time (c) Spatial distribution of received signals GAL/GPS, satellites; JAM, jammer
For all three position solutions, only the signals of those satellites (three GPS L5 and eight GALILEO E5a) as shown in Figure 15(c) were used. These signals were received at all antennas. Following this approach and using identical algorithms (despite the spatial algorithms) for data processing, a fair comparison between a state-of-the-art single-antenna GNSS receiver and our proposed array concept was derived.
6.2 Results
The results from Section 5 could be confirmed with outside measurements. Under the influence of the jammer, the SAP implementation was able to process satellite signals from the array antennas for approximately 20s longer than the reference antenna on the roof. This corresponds to 20 dB more tolerated jamming power as shown in Figure 15(a). The STAP implementation with three taps increased the reception time even further, tolerating up to an additional 5s or 5 dB more jamming power. At the same time, the signal quality in terms of the CN0 of the satellites was improved up to 15 dB.
Figure 16 shows the position accuracy determined for all three evaluations.The upper plots show the position deviation under the jammer influence from the mean estimated position in the jammer-free case in ECEF. The lower plots show the sum over the absolute values of the x, y and z components and hence the absolute deviation in meters. The data are plotted for all time points after 100 s of experiment time, which is the point at which the jamming signal begins to affect the reception at the receiving antennas as shown in Figure 15(b). The improvement in spatial processing is particularly emphasized when one evaluates how long the satellite signals can be received by the different implementations. For example, the roof antenna loses the first satellites after 117 s; all satellites are lost after 122 s.
Position accuracy in Earth-centered, Earth-fixed (ECEF) x,y and z and number of satellites (a) Roof Antenna (b) Array with SAP (c) Array with STAP with M = 3
The lower figures show the sum over the absolute values of all three coordinates in combination with the jamming power as shown in Figure 15(a).
By contrast, the array with the SAP implementation loses the first satellite approximately 11 s later (at 133 s). The transition to complete loss of all satellites takes another 10 s, and occurs at 142 s after the start of the measurement. The STAP implementation also stabilizes the reception of the satellites, such that the satellite signals can be received for a much longer period. Signals from all eleven satellites are still received 145 s after start of the experiment, which is 12 s longer than could be achieved using the SAP implementation and 25 s longer than the roof antenna and corresponds to 12 dB and 25 dB more jamming power. In terms of the absolute error, both spatial implementations show a similar behavior, With increasing jamming power, the deviation from the previously-determined position can be as high as 5 to 10 m for the SAP implementation. For the STAP implementation, the absolute error remains below 5 m, increasing only for the STAP3 implementation after 146 s, when the receiver rapidly loses track of the remaining satellites.
7 CONCLUSION
In this paper we proposed an algorithm that considers delays received from an incident signal between the individual antenna elements of an arbitrary array used in the estimation of the covariance matrix. This is particularly noteworthy because the antenna elements were not located in direct proximity to one another, as is the case for conventional compact arrays, for example, URAs. Aiming directly at the automotive industry, we previously proposed a new type of array in which a set of at least two ULAs can be mounted around a passenger car. In this configuration, there will be long baselines between the antenna elements of different ULAs. However, when using wideband signals such as for example those from GALILEO E5a or GPS L5, these baselines will generate non-negligible delays between the digitized baseband signals. This will lead to reductions in the performance of conventional algorithms for pure spatial interference mitigation. The algorithm was explained using an estimation of the covariance matrix using both the conventional spatial approach and the newly-proposed space-time adaptive (STAP) method. The performance of the STAP was dependent on the number of taps analyzed in a simulation that included different fractional delays. A GNSS jamming scenario was assembled in the VISTA anechoic chamber at TU Ilmenau to compare both methods using real-life measurements in a dynamic scenario. In this simulation, the car was rotated over 360° over the course of the complete measurement. The comparison between the received signal quality as determined by the means of the estimated CN0 demonstrated a clear improvement for wideband signals, sampled with a sampling rate of fs = 12.5 MHz using the proposed method. By contrast, the effect was less significant for narrowband signals, sampled with fs =5 MHz.
To assess the position deviation using the spatial processing methods with distributed antenna elements under influence of a jammer, a second experiment was performed at the Chair of Navigation in Aachen. In contrast to the previous experiment performed at VISTA, the car did not move over the course of the complete experiment. Instead, the jamming power was varied continuously. Both spatial processing methods exhibited superior behavior compared to a single reference antenna on top of the car (i.e., similar to state-of-the-art GNSS antennas found in passenger cars). Both methods provided position solutions in response to 20 − 25 dB increased jamming power; the position solutions were barely affected even when the reference antenna exhibited absolute position deviations of more than 10 m. Overall, our results suggest STAP could outperform state-of-the-art SAP implementation in applications requiring robust tracking, as it was able to process all satellites for an additional 12s.
HOW TO CITE THIS ARTICLE
Brachvogel, M., Niestroj, M., Meurer, M., Hasnain, S., Stephan, R., & Hein, M. (2023). Space-time adaptive processing as a solution for mitigating interference using spatially-distributed antenna arrays. NAVIGATION, 70(4). https://doi.org/10.33012/navi.592
CONFLICT OF INTEREST
The authors declare no potential conflicts of interest.
ACKNOWLEDGMENTS
Parts of the research leading to the results reported in this paper were funded within the project ROSANNA by the German Aerospace Center (DLR) on behalf of the German Federal Ministry for Economic Affairs and Energy under grant nos. 50 NA 1901 and 50 NA 1902. This support is acknowledged and greatly appreciated.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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