A diversely polarized antenna array combines signal processing in the spatial and polarization domains for significant improvement in receiver robustness against interference. The C/N0 of line-of-sight components is improved since the receiver can use the power present in the left-hand circularly polarized channels, and also interference mitigation improves.
By Matteo Sgammini, Stefano Caizzone, Achim Hornbostel and Michael Meurer
POLARIZATION. We use the word in everyday speech to mean a division into two groups with sharply contrasting opinions or beliefs.
But the word has another use in physics and electrical engineering to describe a characteristic of electromagnetic waves. Electromagnetic waves, whether they be light waves or radio waves, have electric and magnetic fields vibrating perpendicularly to each other and to the direction of propagation. If the electric field (and, correspondingly, the magnetic field) vibrates in a specific non-changing plane, we say that the wave is linearly polarized.
In terrestrial radio communications, signals are typically transmitted as linearly polarized waves with the electrical field oscillating in the vertical plane or the horizontal plane. Receiving antennas are designed and oriented to preferentially respond to the particular polarization of the signals. Before the widespread use of cable and satellite distribution platforms, VHF and UHF TV signals were received using rooftop antennas consisting of multiple parallel metal rods (similar antennas are used now for terrestrial digital TV).
In North America, the rods were in the horizontal plane since the transmitted signals were horizontally polarized. In Europe, on the other hand, the rods were sometimes in the vertical direction since there, some TV signals were transmitted with vertical polarization.
If the plane of vibration of the electric and magnetic fields rotates uniformly as the signal propagates, we have the case of circular polarization. Since the sense of rotation can be clockwise or anti-clockwise, we have right-hand circularly polarized (RHCP) and left-hand circularly polarized (LHCP) signals following the direction of curl of the fingers of the right and left hands. Circular polarization is typically used for signals from satellites in low and medium Earth orbit, such as GNSS satellites, where the relative orientation of the transmitting and receiving antennas is not fixed. For maximum signal reception, the polarization of the receiving antenna should match the polarization of the signal. All GNSS satellites transmit RHCP signals and therefore most GNSS receiving antennas are designed for such signals.
However, a funny thing can happen to a satellite signal on the way to a receiving antenna. If the signal bounces off a nearby structure or the ground or the sea surface, its polarization is modified and it will become LHCP or a combination of the two polarizations. While this multipath phenomenon can be a pest, as discussed in last month’s column, it can be used to advantage in measuring sea-surface roughness, for example, by monitoring reflected GNSS signals from a low Earth orbiting satellite or an aircraft using a LHCP antenna.
But GNSS receiving antennas are not perfect—especially for direct line-of-sight low-elevation-angle signals. A primarily LHCP antenna can capture a significant portion of the energy in such a RHCP signal and could provide a strong response to a reflected signal when the line-of-sight signal is missing or very weak. So, there could be a benefit in having a dual-polarized antenna to improve positioning capability in marginal situations. Furthermore, jamming signals can be of arbitrary polarization and a dual-polarized antenna array with beamforming capability could better separate and mitigate such interference. In this month’s column, we examine the principles of operation of such an antenna array and how one performed in real-world jamming and non-jamming scenarios.
The rapid growth of the wireless telecommunication sector and, consequently, the high demand of spectrum assigned to the new services make the frequency spectrum very crowded and quite saturated. With the weak received signal power of GNSS signals, spurious harmonics from other systems can cause unintentional interference and, therefore, a serious problem to the reliable estimation of user position, velocity and time (PVT). Besides unintentional interference, more virulent intentionally radiated signals, called jammers, may knock out the GNSS receiver; this is especially the case when a jammer with high time-frequency dynamics (such as a chirp-like jammer) affects the GNSS signal spectrum.
Whether unintentional or intentional, interference represents a serious threat to GNSS in applications ranging from safety-of-life to critical sectors like law enforcement, transportation, communication and finance. In such critical applications, it is important that the GNSS receiver provides a minimum level of reliability and robustness, even at the cost of increased price and complexity.
To meet this need, some manufacturers and research institutions have been developing GNSS receivers equipped with anti-jamming capabilities.
In this article, we propose a novel approach to interference mitigation. We equipped a GNSS receiver with a diversely polarized antenna array to combine signal processing in the spatial and polarization domains in a novel way. By doing this, we demonstrated achievable improvement in interference mitigation. For this purpose, we extended an existing two-step blind adaptive beamforming algorithm to a new algorithm that includes the polarization domain. We evaluated the new algorithm through measurement data gathered during a campaign carried out at the Automotive Testing Center in Aldenhoven, near Jülich, Germany. We used different interference sources, including low-cost jammers, euphemistically called personal privacy devices (PPDs), in real-life situations such as in a moving car approaching a GNSS receiver.
The receiving antenna used in our work is a four-element rectangular dual-polarized (DP) array in a two-by-two configuration. Each element has two feeds available, one ideally receiving the right-hand circularly polarized (RHCP) field and the other the left-hand circularly polarized (LHCP) field of the polarized incoming signals. Due to antenna imperfections and coupling effects, part of the LHCP field impinging on the antenna will be received by the RHCP port and vice versa. Generally, the antenna axial ratio is fine-tuned at boresight so that the energy of a RHCP satellite signal impinging on the array at high-elevation angles will be mostly captured by the RHCP port, while the energy flowing through the LHCP channel can be ignored. This statement does not hold for satellite signals coming from lower elevation angles or in general for signals with polarization other than RHCP, this being generally the case for multipath and interference. In particular, the response of a planar antenna array for angles-of-arrival (AoAs) close to the horizon is almost linearly polarized. It follows that a significant portion of the RHCP energy in a signal is likely to be captured by the LHCP channels and can be used either to strengthen the line-of-sight (LOS) component, or to better separate and mitigate both multipath and interfering (jamming) signals.
Adding the polarization domain makes it possible to better discriminate spatially and temporally correlated signals. In some environments, such as urban canyons, the LOS signal might not be available or might be strongly attenuated. In this case, the reflected non-LOS signals can be used to perform positioning and would benefit from a DP antenna approach. As a matter of fact, the reflected signals will be no longer RHCP, thus the LHCP channel can be used to strengthen the echoes and improve positioning. Diversely polarized antenna arrays also have the advantage of increasing the total number of available degrees of freedom. The number of degrees of freedom of an antenna array corresponds to the number of nulls that can be placed in the direction of arrival of interfering signals. For a single-polarization (SP) array with M elements, M-1 nulls can be placed in the spatial domain. In the case of a DP array, 2M-2 nulls can be placed in the space and/or polarization domains. This is a key factor in counteracting high-power and highly-dynamic jammers, such as PPDs. Furthermore, the use of a diversely polarized array improves signal detection, as well as direction of arrival and polarization-estimation performance. This is particularly true for closely spaced signals with sufficiently separated polarizations. On the other hand, the introduction of the second polarization increases the computational complexity of signal processing, since the number of elements is doubled.
The results of our measurement campaign show a significant improvement in receiver robustness against interference when the DP approach is used compared to the general SP case.
In this section, we will briefly describe the theory of signal and antenna polarization with a minimal number of equations. A more complete discussion is included in the paper on which this article is based (see Further Reading).
Polarization of a Plane Wave. A received electromagnetic signal is assumed to be narrow band, and the source of radiation is assumed to be located in the far field. The plane wave propagating in free-space has the property that the direction of propagation is orthogonal to the electric and magnetic field vectors. This allows the electric field e of a polarized wave to be completely described in terms of the two unit vectors, and , orthogonal to the direction of propagation
where ∈x and ∈y are the real-valued, non-negative, amplitudes of the components of the electric field, Φx and Φy are the phase components of the field, ω is the angular frequency of the carrier and k is the wave number.
Only the real part of Equation (1) is physically relevant, with the complex exponential containing information about the phase of the oscillating field.
Switching from the linear to the circular basis vector set:
The polarization state of an electromagnetic signal is fully described by ∈R and ∈L.
More generally, the electric field of any plane wave impinging at the antenna can be expressed in the form
Dual-Polarized Antenna Array. A circular DP antenna features two orthogonal circular polarization output ports, meaning each element ideally receives the voltage induced by the RHCP and LHCP field components separately on the two different antenna ports. Due to antenna imperfections and the coupling effect, part of the received RHCP field is received by the LHCP port and vice versa. These undesired voltages are responsible for the emergence of the cross-polar components.
In view of this, we characterize the antenna in terms of its response to circularly polarized plane waves and express the electric field using the Jones vector notation in the circular basis as
where is the complex total electric field received by the RHCP port, is the complex electric field induced at the RHCP port by a purely RHCP electromagnetic wave, indicated as a co-polar component, is the complex cross-polar component of the electric field obtained by exciting the antenna with a purely LHCP electromagnetic wave, φ is the azimuth angle and θ is the elevation angle of the impinging signal assuming the antenna to be at the origin of the spherical coordinate system. Similar statements apply for the total electric field received by the LHCP port, and for the co-polar ( ) and cross-polar () components.
If vR and vL are the complex voltages induced at the RHCP and LHCP antenna outputs by the signal in Equation (4), respectively, the antenna outputs are given by
where ψ = [θ, φ] is the vector parameter carrying the information about the direction of arrival (DoA) of the incident signal and τ is the time delay of the incident signal.
With an M-element array of DP sensors, we can vR and vL to represent the complex array responses of the DP antenna array:
Problem Formulation. The analog signals collected by the antenna array are then passed through the receiver front end where they are amplified, filtered and shifted to baseband. The resulting complex baseband signal with bandwidth B that is received by an antenna array with M DP sensor elements at polarization port P is
where sp(t) defines the superimposed satellite signal replicas with l = 1 identifying the LOS signal and l = 2, …, L the non-LOS (multipath) signals and zp(t) denotes the superimposed radio frequency interference (RFI) signals with i ranging from 1 to I.
Additionally, we assume temporally and spatially uncorrelated complex white Gaussian noise np(t). can be expressed in terms of the steering vectors given the lth signal’s incident angle, the polarization vector and a complex scalar term involving the signal complex amplitude, Doppler frequency, carrier-phase offset and the particular pseudorandom noise sequence and associated
The baseband signals are then digitized at sampling frequency 1/Ts ≥ 2B. The observations are collected at K periods of the pseudorandom sequence at N time instances and the polarizations of the satellite signals and interferers as well as their DoAs are assumed to be constant over each single observation. We finally combine the two outputs of the DP antenna to benefit from both polarizations with a resulting unified signal output X. This increases the number of available degrees of freedom; furthermore, it allows us to carry out filtering in the polarization domain. On the other hand, the overall system complexity is increased; in particular, the computational complexity of the matrix inversion needed for pre-whitening (to be discussed next) is increased by a factor of about 23.
PRE-WHITENING AND EIGEN-BEAMFORMING
Interference mitigation and beamforming uses a two-step blind beamforming approach based on orthogonal projection. It is similar to an approach we developed for the single-polarization case, with the only difference here being the introduction of the orthogonal LHCP channel, which doubles the number of sensors. Doubling the number of sensors does not necessarily mean that the number of degrees of freedom is also doubled. It has been shown that when using diversely polarized antennas, to discriminate signals unambiguously it is required that the maximum number of signals D = L + I satisfies the relationship D ≥ 2M–2.
This means that one additional degree of freedom is required to discriminate in the polarization domain in comparison to the case of an antenna array of uniformly polarized sensors, where it is required that D ≥ M–1.
Pre-Whitening. We establish a sample spatial-polarimetric covariance matrix, where we assume that the satellite signals, the interfering signals and the noise are uncorrelated among each other. Furthermore, we ignore the influence of the signal replicas, because their power is usually much smaller than the power of the noise and interference. We then obtain the approximate pre-whitening matrix to be applied to X. The pre-whitening matrix is applied before signal despreading.
Eigen-Beamforming. In the next stage, the complex pre-whitened signal passes through the tracking loops for despreading and code and carrier wipe-off. We collect the post-correlation signal at K integration intervals to obtain the data matrix and the post-correlation spatial-polarimetric sample covariance matrix. The post-correlation eigen-beamformer is obtained following the same optimization problem that we solved for the single-polarization case. We apply the optimum weight vector, maximizing the ratio between the power of the desired signal and the power of the undesired signals plus noise, using the eigenvector with respect to the dominant non-zero eigenvalues of the post-correlation covariance matrix.
The receiving antenna used in our work is a planar four-element rectangular DP array in a two-by-two configuration, similar to one we have used previously, apart from the additional hybrid couplers needed to provide the LHCP channel outputs. Each element has a double feed, one ideally receiving the RHCP field and the other the LHCP field of the polarized incoming signals, resulting in a total of eight output channels. The single antenna elements are designed for the reception of the GPS L1 and L5 and Galileo E1 and E5 bands, but in this work we focus only on the reception of GPS L1 signals.
The eight signals are passed through a front end, where they are amplified, filtered and down-converted to the intermediate frequency of 2.5 MHz. The analog signals are then digitized with a sampling rate of 8 megasamples per second. The resulting 8-bit digital data are collected and stored on a solid-state drive for data analysis in post-processing. Data analysis is then performed by using a GNSS software-based receiver.
Description of Test Scenarios. The DP system has been tested using measurement data to assess its dual capability of improving the quality of LOS signal reception and robustness against both unintentional RFI and jamming. As mentioned previously, the measurement campaign was conducted at the Aldenhoven Automotive Testing Center. The location provides seven tracks of different lengths, inclinations and shapes. The test track used for this measurement campaign was the so-called autobahn, providing two lanes in each direction of travel and a total length of 1,000 meters (see FIGURE 1).
In this article, we report and analyze the results of three different test scenarios. In the first test, we collected GPS L1 data over 60 seconds in an interference-free environment. The aim of this baseline scenario was to verify if the additional LHCP channels improved signal reception in terms of carrier-to-noise-density ratio (C/N0) and PVT errors.
The second test scenario involved a horn antenna mounted on a mast, transmitting a continuous wave (CW) interference signal in the GPS L1 band and steered in the direction of the receiving antenna, as shown in FIGURE 2. Both the horn antenna and the receiving antenna were kept static during the measurement interval.
The objective of the third test scenario was to replicate a real-life situation involving jamming, similar to the so-called “Newark scenario,” where a GPS jammer in a truck driving past Newark Liberty International Airport caused ground-based and satellite-based augmentation systems receivers to malfunction. To carry out this test, we installed a type K-320 PPD jammer transmitting in the GPS L1 band (see FIGURE 3) in the 12-volt auxiliary power outlet (cigarette lighter receptacle) of a moving car approaching the receiver and driving by.
The car started its run at a distance of about 260 meters from the receiver. During the first 20 seconds, the car holds its position. After this time, it was driven in the direction of the receiver with a constant speed of 30 kilometers per hour, finishing its route on the other side of the autobahn track, as depicted in Figure 1.
Baseline Scenario. The benefits that come to light using a DP array are of a dual nature. First, the C/N0 of LOS signals is improved since the receiver can make use of the power present on the LHCP channels due to polarization mismatch, in particular for satellites with low AoA, resulting in better receiver-computed PVT solutions. This effect appears evident if we analyze the behavior of C/N0 values over time collected during the non-interference experimental test in the GPS L1 band.
With reference to the sky plot in FIGURE 4 indicating the positions of the satellites at the time of observation, we analyzed the subgroup composed of those satellites having an elevation AoA lower than 30°. There was a sensible improvement of C/N0 using both polarizations from the DP antenna compared to just using the RHCP output (see FIGURE 5(a)). On the contrary, satellites with an elevation AoA higher than 60° do not benefit from the DP antenna and experienced almost the same C/N0 whether the LHCP channel was used or not, as can be seen in FIGURE 5(b).
While the advantage of using the DP array is evident when observing the C/N0 behavior, this achievement does not translate with the same clear evidence when assessing the 2-D horizontal position error. Nevertheless, an improvement of about 6 centimeters in terms of the standard deviation of the 2-D position solution error in the horizontal plane has been obtained using the DP antenna (see TABLE 1). It is reasonable to expect that in a scenario where the availability of satellites is not as high as in our test case, the use of low-elevation angle satellites becomes more important for the accuracy of the PVT solution. In this case, the use of a DP antenna could play a key role in improving positioning accuracy.
CW Interference Scenario. The use of a DP array provides the ability to filter signals in the polarization domain, and at the same time we benefit from the additional degrees of freedom available. Thus, interference mitigation becomes more effective than using a SP array, increasing the receiver robustness and enabling tracking and successful PVT solutions in a severe interference scenario. This outcome appears evident analyzing the results of our test, where the linearly polarized CW interference described in TABLE 2 impinged on the array.
We show the 2-D horizontal position errors from this test in FIGURE 6. The figure highlights the improvement in position accuracy when both RHCP and LHCP channels are jointly used, limiting the root mean square (RMS) error to 2.65 meters, while it increases to 3.88 meters when only the RHCP channels have been used.
The advantages of using the DP array as assessed above are well summarized in FIGURE 7. The figure shows the history of the C/N0 split into two clusters. The upper cluster is from measurements during the interference-free period while the lower cluster is from measurements during the period the receiver is affected by the interference. In the figure, the improvement in terms of C/N0 is notable when using the DP array, in particular for low-elevation angle satellites, and for those satellites having a DoA close to the DoA of the interference. The latter case, when satellite signals and the interfering signal almost overlap in space, has been fully analyzed in a technical note (see Further Reading).
PPD Jammer Scenario. The goal of this test was to compare the overall performance of the DP array to the SP array, as well as to the case when only a single-element antenna was used and with no pre-whitening applied. The K-320 PPD employed in this test scenario poses a serious threat to any commercial receiver in obtaining a valid PVT solution. The spectrogram of the K-320 is shown in FIGURE 8(a), which illustrates that the chirp signal sweeps very rapidly (with a sweep interval of about 40 microseconds) across a frequency range of 15 MHz centered at the L1 carrier frequency, as can be seen in the plot of power spectral density in FIGURE 8(b). The frequency range is much larger than the receiver bandwidth of about 8 MHz (dual-sided). This means that the RFI is seen as pulsed RFI by the receiver.
An estimate of the jamming behavior during the test in terms of interference-to-signal ratio (ISR) is shown in FIGURE 9. The estimated ISR counts only for the portion of jamming power falling within the receiver bandwidth in baseband after down conversion; it is not an estimate of the ISR at the antenna array. The closer the jammer in the passing car is to the receiver, the higher the PPD power affecting it. The minimum distance between the jammer and the receiver is about 14 meters and is reached at 13:13:45 UTC as indicated in the figure.
In FIGURE 10, we can observe the impact of the RFI when the car drives past the receiver by means of the number of tracked satellites, or rather by the number of valid pseudoranges available for PVT computation. When the jammer is close to the receiver, the DP antenna is always better than the SP one. When the RFI is at the minimum distance (about 14 meters) from the receiver, the SP antenna is no longer able to deliver a valid position, while the DP antenna still can.
The higher number of valid pseudoranges when using the DP antenna is translated into a better position accuracy. This result can be seen in TABLE 3, which lists the RMS horizontal position error computed during the time the estimated ISR is greater than 25 dB. In the computations, only valid PVT solutions and 2-D positioning errors below 20 meters have been considered.
The results of the measurement campaign have shown a significant improvement in positioning accuracy and robustness against interference when the dual-polarization approach is used compared to the general single-polarization case. Position accuracy takes advantage of the better C/N0 for those satellites with an AoA below 30°, which experienced up to 2 dB C/N0 improvement. Although the benefit in PVT accuracy was not remarkable in our testing, this should become more notable in scenarios where a lower number of satellites are visible or when the LOS signals are obstructed, such as in urban environments. Receiver robustness takes advantage of the possibility of filtering in the polarization domain and the additional number of available degrees of freedom, enabling tracking and PVT solution availability in severe interference scenarios. In particular, a valid PVT solution was still available for an ISR of 53 dB using the dual-polarization array, while the single-polarization array was unable to deliver a valid position. While these improvements are noteworthy, they do come with added cost and complexity of the receiving system, since the number of channels to be processed is doubled.
This article is based on the paper “Interference Mitigation Using a Dual-Polarized Antenna in a Real Environment,” presented at ION GNSS+ 2016, the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation, held Sept. 12–16, 2016, in Portland, Oregon.
MATTEO SGAMMINI received an M.Eng. degree in electrical engineering in 2005 from the University of Perugia, Italy. He joined the Institute of Communications and Navigation of the German Aerospace Center (DLR), Wessling, Germany, in 2008. He is pursuing a Ph.D. in electrical engineering with research interests in interference mitigation techniques for GNSS.
STEFANO CAIZZONE received an M.Sc. degree in telecommunications engineering and a Ph.D. degree in geoinformation from the University of Rome “Tor Vergata,” Italy, in 2009 and 2015, respectively. Since 2010, he has been with the antenna group of DLR’s Institute of Communications and Navigation, where he is responsible for the development of innovative miniaturized antennas.
ACHIM HORNBOSTEL holds a diploma degree in electrical engineering and a Ph.D. degree from the University of Hannover, Germany. He joined DLR in 1989 and heads a working group on algorithms and user terminals at the Institute of Communications and Navigation.
MICHAEL MEURER received a diploma in electrical engineering and a Ph.D. degree from the University of Kaiserslautern, Germany. Since 2006, he has been with DLR’s Institute of Communications and Navigation, where he is the director of the Department of Navigation and of the Center of Excellence for Satellite Navigation. Since 2013, he has also been a professor of electrical engineering and director of the Institute of Navigation at Rheinisch-Westfälischen Technischen Hochschule (RWTH) Aachen.
• Authors’ Conference Paper
“Interference Mitigation using a Dual-Polarized Antenna in a Real Environment” by M. Sgammini, S. Caizzone, A. Iliopoulos, A. Hornbostel and M. Meurer in Proceedings of ION GNSS+ 2016, the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, Sept. 12–16, 2016, pp. 275–285.
• Technical Report on Overlapping Signals
Interference Mitigation using a Dual-Polarized Antenna:A Deep analysis in Space Domain and Polarimetric Domain by M. Sgammini. Internal Technical Report, Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR; German Aerospace Center), Dec. 2016.
• Authors’ Earlier Work
“Experimental Results of Interferer Suppression with a Compact Antenna Array” by A. Hornbostel, N. Basta, M. Sgammini, L. Kurz, S.I. Butt and A. Dreher in Proceedings of ENC-GNSS 2014, the European Navigation Conference, Rotterdam, The Netherlands, April 14–17, 2014.
“Detection and Suppression of PPD-Jammers and Spoofers with a GNSS Multi-Antenna Receiver: Experimental Analysis” by A. Hornbostel, M. Cuntz, A. Konovaltsev, G.C. Kappen, C. Hättich, C.A. Mendes da Costa and M. Meurer in Proceedings of ENC 2013, the European Navigation Conference, Vienna, Austria, April 23–25, 2013.
“Blind Adaptive Beamformer Based on Orthogonal Projections for GNSS” by M. Sgammini, F. Antreich, L. Kurz, M. Meurer and T.G. Nollin in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, Sept. 17–21, 2012, pp. 926–935.
“Field Test: Jamming the DLR Adaptive Antenna Receiver” by M. Cuntz, A. Konovaltsev, M. Sgammini, C. Hattich, G. Kappen, M. Meurer, A. Hornbostel and A. Dreher in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, Sept. 19–23, 2011, pp. 384–392.
“Suppression of Multipath and Jamming Signals by Digital Beamforming for GPS/Galileo Applications” by Z. Fu, A. Hornbostel, J. Hammesfahr and A. Konovaltsev in GPS Solutions, Vol. 6, No. 4, March 2003, pp. 257–264, doi: 10.1007/s10291-002-0042-2.
• Other Works on Antenna Beamforming
“GNSS Pest Control: Correlator Beamforming for Low-Cost Multipath Mitigation” by S. Gunawardena, J. Raquet and M. Carroll in GPS World, Vol. 28, No. 1, Jan. 2017, pp. 54–63.
“Null-Steering Antennas: Assessing the Performance of Multi-Antenna Interference-Rejection Techniques” by J.T. Curran, M. Bavaro and J. Fortuny-Guasch in GPS World, Vol. 27, No. 2, Feb. 2016, pp. 62–68.
• Diversely Polarized Antenna Arrays
“Subspace Fitting with Diversely Polarized Antenna Arrays” by A.L. Swindlehurst and M. Viberg in IEEE Transactions on Antennas and Propagation, Vol. 41, No.12, Dec. 1993, pp.1687–1694, doi: 10.1109/8.273313.
“Direction Finding with an Array of Antennas Having Diverse Polarizations” in IEEE Transactions on Antennas and Propagation, Vol. 31, No.2, March 1983, pp. 231–236, doi: 10.1109/TAP.1983.1143038.
• Antenna Array Signal Processing
“Two Decades of Array Signal Processing Research: The Parametric Approach” by H. Krim and M. Viberg in IEEE Signal Processing Magazine, Vol. 13, No. 4, July 1996, pp. 67–94, doi: 10.1109/79.526899.
“Multilinear Array Manifold Interpolation” by R.O. Schmidt in IEEE Transactions on Signal Processing, Vol.40, No.4, April 1992, pp. 857–866, doi: 10.1109/78.127958.
• Basic Antenna Concepts
“GNSS Antennas: An Introduction to Bandwidth, Gain Pattern, Polarization, and All That” by G.J.K. Moernaut and D. Orban in GPS World, Vol. 20, No. 2, Feb. 2009, pp. 42–48.
• GNSS Jamming
“Personal Privacy Jammers: Locating Jersey PPDs Jamming GBAS Safety-of-Life Signals” by J.C. Grabowski in GPS World, Vol. 23 No. 4, April 2012, pp. 28–37.
“GNSS Jamming in the Name of Privacy: Potential Threat to GPS Aviation” by S. Pullen and G.X. Gao in Inside GNSS, Vol. 7, No. 2, March/April, 2012, pp. 34–43.
“Know Your Enemy: Signal Characteristics of Civil GPS Jammers” by R.H. Mitch, R.C. Dougherty, M.L. Psiaki, S.P. Powell, B.W. O’Hanlon, J.A. Bhatti, and T.E. Humphreys in GPS World, Vol. 23, No. 1, Jan. 2012, pp. 64–72.