Innovation: Null-steering antennas

February 11, 2016 - By GPS World Staff

Assessing the performance of multi-antenna interference-rejection techniques

Several factors affect the levels of signal rejection using antenna arrays. Our authors describe experiments to assess the bounds the factors impose on its signal rejection capability.

By James T. Curran, Michele Bavaro and Joaquim Fortuny-Guasch

INNOVATION INSIGHTS with Richard Langley

IT’S ALL PHYSICS. How things work, that is. Well, maybe a little chemistry too in some cases. But I might be a little biased in my opinion given that I’m an applied physicist by training. Radio? Satellite navigation? Yes, the principles of their operation are all governed by physics. Many physicists of my generation started out as radio tinkerers. I’ve recounted in this column before that I built my first radio (from a kit) when I was 14 (not counting the crystal radio that my father helped me to put together when I was 9). Built a few more during high school, got into radio astronomy as an undergraduate, and did a Ph.D. in the application of very long baseline (radio) interferometry to geodesy.

The great American physicist Richard Feynman was also a radio tinkerer in his youth. He recounts in one of his autobiographical books how he used to fix radios. And because he would approach the task of repairing each non-functioning set by first contemplating why it wasn’t working, he got the reputation of fixing radios by thinking!

One of Feynman’s special abilities was in explaining how things worked. In fact, he has been called “The Great Explainer.” He authored what is arguably the best physics textbooks ever produced: The Feynman Lectures on Physics. The three-volume set, developed from his Caltech lectures to undergraduates between 1961 and 1964, covers mechanics, radiation, electromagnetism, matter and quantum mechanics. Many students and practicing physicists have learned or re-learned aspects of physics from the famous “red books.” Many more will now thanks to Caltech, which recently put the Lectures on line for anyone to read (feynmanlectures.caltech.edu).

In this month’s column, we are going to learn about the development of a microprocessor-controlled multi-element GNSS antenna array for interference rejection. While there are many textbooks that describe how multi-element antennas work, Feynman explains their operation in his Lectures from first principles — from the principles of physics.

The phenomenon governing the behavior of antennas with multiple elements is called interference. If we combine two electromagnetic waves, they will interfere with each other with a result that depends on the phase difference of the waves. The waves might reinforce each other leading to a larger net amplitude, called constructive interference, or partially or fully null each other out, called destructive interference. When we apply this concept to the signals received by a pair of antennas making up an array, we find that the array has directionality and we can have a null in the reception pattern in the directions parallel to the antenna baseline and will be insensitive to signals arriving from those directions. And as Feynman describes in his Lectures, by adding more antennas to the array and “some cleverness in spacing and phasing our antennas,” we can have a fairly narrow pattern null in a chosen direction. In the case of a GNSS antenna array, that direction might be that of a jamming signal and so we can null out the jammer and maintain a positioning capability.

Several factors affect the levels of signal rejection using antenna arrays. In this article, our authors describe these factors and the experiments they conducted with their microprocessor-controlled array to assess the bounds the factors impose on its signal rejection capability.

Directional antennas offer a powerful means of achieving signal selectivity when various signal sources observed by a receiver are separated spatially. In the context of GNSS, which must accommodate a mobile receiver observing many moving transmitters, adaptive antennas — or controlled radiation pattern antennas—are an attractive option. The benefits of antenna arrays have been demonstrated both for signal rejection, such as interference and multipath mitigation or anti-spoofing; and for the purposes of gain enhancement, angle-of-arrival, or attitude estimation.

A number of different factors can influence the achievable levels of signal rejection using antenna arrays. These factors include: the gain and phase stability of the analog radio-frequency (RF) and intermediate-frequency (IF) stages, the linearity of the active analog stages, and the fidelity of the signal-combining stages. Seeking to identify the bound imposed by each of these limiting factors, we have carefully examined the signal rejection capability of an antenna array in our work. The study considers a circular antenna array, consisting of seven passive dual-polarized (right-hand circularly polarized [RHCP] and left-hand circularly polarized [LHCP]) L1-L2 elements. Although signal rejection can be performed both in the analog and in the digital domain, this article focuses only on the analog combination of signals at RF, using a bank of controllable phase shifters and attenuators. We conducted broadcast experiments in a large-diameter anechoic chamber, housing a rotatable central pillar upon which the array is mounted, and two broadcast antennas mounted on movable sleds.

The results presented here include a precise three-dimensional phase and gain calibration of the antenna array using a network analyzer to explore the properties of antenna elements when placed in close proximity on a common ground plane. Further results include an investigation of the nulling depth achievable by the array via the synchronous broadcast of two GNSS-like code-division multiple access (CDMA) signals from different broadcast antennas. We then extrapolated these results to infer the relative degradation in nulling capability when the receiver’s estimate of the amplitude and phase of the signal to be rejected is poor. Finally, a comparison of analog and digital element combining is explored, with emphasis on the rejection of strong jamming signals.

This experiment sought to illustrate and quantify the unique benefits and limitations of each technique. In particular, we note that analog combining enjoys high linearity and can accommodate high interference power, but is typically restricted to the use of coarse phase and gain coefficients when combining elements. In contrast, digital combining can offer notably higher gain and phase resolution, but is limited by the dynamic range of the digitizer.

Antenna Characterization

The work reported in this article has focused on the use of a seven-element circular antenna array, consisting of dual-polarized (RHCP and LHCP), dual-frequency (L1 and L2) elements. The antenna elements are mounted on a single circular aluminum ground plane 2 millimeters thick and 50 centimeters in diameter, and placed in a hexagonal arrangement at a spacing of 12.5 centimeters, as depicted in FIGURE 1. Because the antennas are passive, and can be used both for transmission and for reception, characterization tests were performed in broadcast mode while the typical receive-mode operation of the array is performed using an in-line low-noise amplifier (LNA) after the antenna.

The experiments described here were conducted in an anechoic chamber, hemispherical in shape with a diameter of 20 meters, as depicted in FIGURE 2. The array was mounted on a surveyor’s tripod and placed at a known position on a rotatable pillar at the center of the chamber. The chamber contains two sleds, Sled A and B, which can be precisely positioned along an arc through the zenith at positions between ±115° either side of the vertical. These antennas include 1.0 to 6.0 GHz vertically and horizontally polarized standard-gain horn antennas.

FIGURE 2. Antenna array and digitizing front end in the anechoic chamber during broadcast tests.

Because the characteristics of the antenna array itself are central to the ultimate performance of beamforming or null-steering techniques, a thorough characterization of the gain and phase properties of each of the seven antenna elements was conducted.

To do so, a network analyzer was used to observe the gain and phase response of the antenna under test from a range of observation angles. The array was operated in transmit mode, broadcasting a signal sourced from Port A of the network analyzer, which was received by an antenna mounted on one of the movable sleds, and fed to Port B of the network analyzer.

The network analyzer was configured to broadcast a series of 201 equally spaced tones spanning 20 MHz centered at 1575.42 MHz at a power of -7 dBm from the antenna array.

A mechanical RF multiplexer was used to implement a time-division multiplexing of this broadcast measurement signal across each of the seven elements, such that the series of tones were transmitted once per antenna element. By performing the scan for each antenna element, for a range of positions of Sled A, and repeating this for different rotations of the central pillar, a precise frequency response could be calculated for a large set of points across the entire upper hemisphere of the antenna. The scan was computed on signals received by both the horizontal and vertical elements on Sled A, such that both the RHCP and LHCP response could be computed. The vertical cuts of this gain pattern were measured with resolution of 2°, while the horizontal cuts were measured with a resolution of 5°.

The average gain response, calculated across the 20-MHz band, for each of the seven elements is depicted in FIGURE 3. The elevation cut of the peripheral element is taken such that the -90° direction of the cut aligns with a radial line pointing away from the center of the array. The azimuth cuts are oriented such that the 0° direction aligns with a radial line extending from the center of element number 1 to the center of element number 2.

FIGURE 3. The measured gain pattern of the central element, number 1, (blue lines) and one of the peripheral elements, number 2, (red lines). The gain of the peripheral element is deflected inwards toward the center of the array because of the asymmetry of its positioning on the ground plane. (a) Elevation angle cut at an azimuth of 0°; (b) Azimuth cut at an elevation angle of 40°.

It is interesting to note that the gain pattern exhibited by each element is sensitive to its position on the ground plane and its position relative to other elements. Because of the rotational symmetry of the array, the gain patterns of all of the peripheral elements are similar, differing only in orientation, each one exhibiting a deflection of the maximum gain towards the center of the array. The central element is circularly symmetric with a single lobe in the direction of the zenith, while gain of the peripheral elements is deflected inwards, having lower gain away from the center of the array and an increased gain for high elevation angles from the center of the array. The difference in gain pattern across elements is stark and should, perhaps, influence the choice of elements to be used when forming a beam or null in a given direction. One or other of the signals should be scaled to compensate for this gain difference.

Measuring Signal Rejection

Before exploring factors that influence signal rejection, this section details the figure of merit, which might quantify the achievable performance of the array. We examined the nulling performance of the system in terms of its rejection capability: assessed as the relative received power of the signal of interest, b(t), that is to be preserved, and an unwanted signal, a(t), which is to be rejected, before and after the nulling combination. If s_j(t) denotes some signal as received at antenna j, then the combination of signals received at antennas j and k can be denoted by:

(1)

where κ and ϕ, respectively, represent a unitless scaling gain and a phase rotation in radians applied in the combination. When intending to form a beam in the direction of the source of s(t), then this phase might be chosen to bring s_k(t) into alignment with s_j(t), and the gain may be determined as a function of the signal-to-noise ratio at each antenna, or simply set to unity. In contrast, when it is intended to reject s(t) then eⁱ^ϕmust be chosen to place s_k(t) in antiphase with s_j(t) and must be chosen to scale the amplitude of s_k(t) to be exactly equal to that of s_j(t).

In this case, we consider the problem of placing a null in the direction of signal a(t) while preserving signal b(t). If the relative received power of a(t) and b(t) at antenna j is taken as a reference, then the rejection of a(t) with respect to b(t), denoted R_a_,_b, can be assessed by examining the change in relative power after the null has been placed:

(2)

where denotes the expected value of x. Note also that this convention implies that a value of R_a_,_bgreater than unity corresponds to signal rejection.

Analog Null Steering at RF

This section explores some of the receiver-side factors that can limit nulling performance. The performance of an analog RF-combining circuit is examined, wherein the combining function was implemented using controllable analog attenuators and phase shifters.

The received signal from each of two antennas, j and k, was fed to a custom RF circuit board hosting a controllable phase shifter and attenuator chips. The output of two of these boards was then combined using a passive power combiner, filtered by an analog RF filter, limiting the band to the range 1530–1620 MHz, and finally fed to a power detector, which produced a signal voltage that was proportional to the total observed power. The experimental setup is depicted in FIGURE 4. The attenuators and phase shifters were controlled digitally via a microcontroller board, which also sampled the output of the power detector.

FIGURE 5. A simplified example of the steering constellation of an analog gain and phase shifter, having 3-bit phase and gain control and a gain step-size of ~1 dB.

The attenuators accept a 6-bit control, providing a dynamic range of 30 dB in steps of approximately 0.5 dB, while the phase shifters accept a 4-bit control traversing the unit circle in steps of 22.5°.

A simplified example of the finite resolution achievable using such a phase and gain shifter is shown by the steering constellation depicted in FIGURE 5, taking the case of 3-bit gain and phase control and assuming a gain step size of 1 dB. Note that the gain is displayed on a logarithmic scale. Each of the circular markers represents a possible gain and phase coefficient for a received signal, which would be used to steer one signal, a, to be approximately equal in amplitude and in anti-phase with the second signal, b.

FIGURE 4. A custom-built programmable analog phase shifter and attenuator pair used for the analog null-steering configuration.

The residual misalignment between the signals stems from the finite constellation of steering points and results in a reduced nulling performance, whereby a portion of the interference signal remains. The relative magnitude of the remaining interference signal is maximum when the true relative phase and amplitude of the signals a and b lies equidistant from the four nearest steering vectors. This is depicted in Figure 5, where the cross marker lies equidistant from the four vertices located at the corners of {0°,45°} and {7,8} dB. Note that as the gain is depicted on a logarithmic scale, the relative error is equal for points centered in any of the quadrants.

To investigate the performance of the system, we broadcast a continuous-wave interference toward the array, while the signal from one antenna was manipulated by all possible gain and phase combinations, keeping the signal from the second antenna at a fixed zero phase shift and –15 dB attenuation. For each of the 1,024 possible gain and phase combinations, the power detector was sampled and logged. A trace of the measured signal rejection as a function of the gain and phase is depicted in FIGURE 6, wherein a sharp peak is observable at approximately {–15 dB, 210°}, corresponding to the point at which the unwanted signal is most rejected — in this particular case, to a level of approximately 29 dB.

FIGURE 6. The measured interference rejection for a broadcast jamming scenario, where a brute-force search through all possible combinations of phase shift and attenuation was conducted. In this case, the maximum rejection happens to occur at an attenuation of 16.5 dB and a phase shift of 225°.

Estimating the Achievable Rejection Level. In this particular experiment, because all 1,024 possible gain and phase combinations were examined in a brute-force search, the signal rejection was not limited by inaccuracies in the estimation of the steering variables κ and ϕ. Rather, it was limited by how accurately the steering variables can be applied. A residual error exists between the phase and gain that would perfectly align and null the signal and the nearest values of phase and gain that the circuit can produce. This error is a function of the distribution of the true steering parameter and the resolution with which it is rendered. In this case, as the range and angle to the unwanted signal source is arbitrary and the distance between antenna elements is comparable to the carrier wavelength, then it is reasonable, perhaps, to assume that the residual error in the steering parameters is zero mean and uniform over the discrete control steps. To model this effect, similar to the previous section, the combining function, inclusive of these errors, can be expressed as:

(3)

where U denotes a uniform distribution, δϕ denotes the step size of the phase shifter control and δA denotes the attenuator step size. Note that as κ is in units of amplitude and δA represents the discrete steps in power gain, which corresponds to discrete steps of in amplitude, then the residual error will be distributed over a region extending in either direction. In this case, if a B-bit phase shifter is used, then:

. (4)

From this model, the minimum expected rejection level can be estimated as a function of the phase and attenuator resolution. Considering first the rejection expression given by Equation (2), we note that the variation of the power signal of interest, b(t), is a function only of the relative angles between each of a(t) and b(t) and the antenna array. When the signals are well separated, a gain of 3 dB is observed on b(t), and when a(t) and b(t) are located nearby or in exact opposite directions, then the rejection of a(t) will also reject b(t). As this power variation is a function of geometry and not of the particular nulling technique, for simplicity it is assumed that b(t) experiences no power variation. What remains is the relative power variation of a(t) with respect to and δϕ.

To find the minimum expected rejection level, we must examine the following metric:

(5)

(6)

where the two variables, eκ and eϕ, respectively represent the residual errors in amplitude and phase between the perfect steering vector, and that which can be attained by the combiner. Examining Equations (3) and (6), it is clear that the minimum rejection will be achieved when the residual phase error is equal to e_ϕ = 1/2δϕ and the amplitude mismatch is given by e_κ = . Substituting these values yields the minimum expected rejection, as given in Equation (7):

.(7)

Determination of the average expected rejection level requires the averaging of Equation (6) over the distributions of the two error variables, e_κand e_ϕ. As these errors are assumed to be uniform in this particular case, this reduces to the following:

(8)

which, after some manipulation, admits the closed form expression of Equation (9):

.
(9)

Inserting the specifications of the experimental setup used here, we find that the minimum rejection that can be expected is equal to approximately 14 dB with an average value equal to 18.8 dB. Further exploring this result, it is possible to predict the minimum performance that can be achieved given some arbitrary, but finite, resolution in gain and phase rotation. A portion of the surface defined by Equation (9) is presented in FIGURE 7. One useful application of this result is that it may be used by a designer to ensure that the resolution in gain and in phase are commensurate. This can be inferred by examining the gradient of the surface, noting that optimal choices of gain and phase step size will lie along the line of steepest gradient of this surface. A flattening of the surface in one dimension indicates that the performance is limited by the other dimension. For example, it can be seen that an increase in phase resolution beyond 6 bits yields no improvement in rejection when the gain step size is greater than 0.5 dB.

FIGURE 7. Minimum achievable rejection of analog nulling-combiner as a function of phase-shifter resolution (bits) and attenuator step size (dB).

Conclusion

Early results from this study suggest that the achievable signal rejection using a controlled radiation pattern GNSS antenna, under ideal conditions, is in excess of 70 dB, and is primarily limited by the accuracy with which the angle of incidence of the interference can be estimated. Accounting for typical estimation errors, the nominal rejection levels of the order of 20 to 40 dB can be expected. However, it is observed that other aspects limit the signal rejection performance. In a practical receiver, these factors stem from component selection for the signal-combining circuitry.

For analog combining schemes, this is the resolution of the controlled attenuators and phase shifters used. The results here attempt to characterize the relationship between the minimum expected performance and the component properties. Results suggest that the choice of analog combining components should be chosen such that the phase and gain resolution are commensurate and such that resolution in one parameter is not rendered useless by a lack of resolution in the other. These results may form useful guidelines when designing analog RF null-steering antennas.

Acknowledgments

This article is based, in part, on the paper “Analog and Digital Nulling Techniques for Multi-Element Antennas in GNSS Receivers” presented at ION GNSS+ 2015, the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation held in Tampa, Fla., Sept. 14–18, 2015.

Manufacturers

The equipment used in our study included an Agilent, now Keysight Technologies E8361A PNA network analyzer, Antcom Corporation 2DG1215A-MNS-4 GPS L1/L2 antennas, an Arduino LLC (www.arduino.cc) Arduino Uno microcontroller, a MACOM MAPS-010143 4-bit digital phase shifter, a Skyworks Solutions SKY12347-362LF 6-bit digital attenuator and a Tallysman Wireless TW127 in-line amplifier.

Innovation: Null-steering antennas