Direction finding using a linear three-element interferometer approach



[1] Results are presented from the operation of a system employing a linear three-element antenna array to determine the angle of arrival of a radio signal in a low-angle terrestrial situation. Based on a system successfully employed in determining the direction in space of meteor echoes at elevated angles, accurate direction determination was obtained in three widely varied terrestrial environments. While such a system would be susceptible to strong multipath signals, and therefore unsuitable for congested cellular environments, there are applications, for example emergency beacon location, in which this does not present a significant problem.

1. Introduction

[2] The need to locate a radio transmitter in a terrestrial environment arises from time to time and direction-finding techniques are often applied to determine the angle of arrival (AOA) at the monitoring site. These techniques are many and varied, and of differing complexity depending on the circumstances. Often, measurements of amplitude and/or phase of the incoming signal are involved and a problem that often arises is the generation of multipath signals from surrounding buildings and terrain. In such cases, fairly complicated systems have been used involving, for example, uniform circular arrays [Rossi et al., 1997; De Yong et al., 1998] and other phase measuring variants. Signal processing of array data is often applied using algorithms based on, for example, Maximum Likelihood [Kennedy and Sullivan, 1995], MUSIC [DeGroat et al., 1993] and ESPRIT [Roy and Kailath, 1989].

[3] All of this is aimed at the difficult situation where the transmitter and monitoring site are relatively close and surrounded by potential reflecting and blocking surfaces. In less demanding circumstances, a simpler approach was felt to be appropriate and experimental measurements have been made using a three-element linear array with spacing of a few wavelengths but (crucially) with the difference between the spacing of adjacent elements set at one half wavelength (λ/2).

[4] Such a configuration has been applied with considerable success to the spatial location of meteor echoes using a backscatter radar [Jones et al., 1998]. In this application, two such arrays, arranged at right angles in the horizontal plane, provide two angular estimates leading to a measure of the elevation and azimuth of the meteor echoes to better than 1 degree. While the system is capable of great accuracy under these conditions of a signal arriving from a single direction, it was acknowledged that under severe multipath conditions, often insufficient information would be available to allow any estimate to be made.

[5] Nevertheless, it was thought that the approach might be useful under single or mild multipath conditions that might be found in a maritime or rural environment and possibly some urban locations. Further, a two-axis version similar to that employed in the meteor work may have application in an aeronautical scenario. With this in mind, experimental measurement of the performance of such an array in a terrestrial (i.e., low elevation angle) situation was felt to be helpful and this is the focus of this current work.

2. Three-Element Array Principle

[6] The basic idea behind the array is to take advantage of two properties of arrays as they relate to the determination of the angle of arrival of an incoming radio signal. The first is that the wider the aperture (in wavelengths, λ) of the array, the more accurate the estimate. And second, individual element spacing should be ≤λ/2 if an unambiguous answer over the whole 180° of potential angular coverage is desired. For a filled aperture, this would mean many closely spaced (∼λ/2) elements with attendant problems arising from mutual coupling effects. While not insurmountable by any means, these problems make for a system more complicated than it needs to be, at least for a well-defined single angle-of-arrival situation.

[7] The three-element array circumvents all of this by employing widely spaced elements in a linear fashion with the difference between the two spacings equal to λ/2, as illustrated in Figure 1. The price paid for this simplification is that the system is capable strictly of handling only one incoming signal at a time, so that multipath generated, for example, by reflections from structures, etc., off-line from the transmitter to receiver must not be comparable in strength with the direct path.

Figure 1.

The linear three-element array. The center element is used as the phase reference and the spacings differ by λ/2.

[8] Measurement of the phase at each of the outer elements relative to the center reference element, ϕ10 and ϕ20 respectively, allows two estimates of the angle of arrival (ξ):

equation image

[9] The first, involving the full aperture, gives an accurate but many-valued estimate of ξ since the phase meter cannot resolve the potential ±2 nπ in the measured phases. The second (with d1d2 = λ/2) removes this uncertainty since the phases ϕ10 and ϕ20 are opposite in sense so that (ϕ10 + ϕ20) lies in the range ±π. The value of the overall aperture, d1 + d2, is not critical provided that the difference is λ/2 and the wider the better from the point of view of the accuracy in the final estimate. However, too wide an aperture can result in uncertainty in the choice of adjacent estimates depending on the signal:noise ratio (see Jones et al. [1998] in the place cited). Values of d1 = 2.0λ and d2 = 2.5λ are used in the measurements described here and all bearing angles, or angles of arrival, presented are the angle, ξ, relative to the normal to the array.

[10] From the above, for a total error (Δϕ) in the estimate for (ϕ10 − ϕ20), the error (Δξ) in ξ is given by

equation image

A typical total phase error Δϕ ≈ ±15°, corresponding to a 10 dB signal:noise ratio, results in an uncertainty in ξ of Δξ ≈ ±0.5° for ξ ≤ 45°.

3. Equipment

[11] The antennas used were commercially available “discone” antennas designed to cover a wide frequency range (25 MHz to 1.3 GHz). Most of the measurements were made at a frequency of 157.05 MHz (with a few at 48.7 MHz) and at this frequency, the antennas were very closely matched as assembled “out of the box” (see Table 1).

Table 1. Antenna Characteristics at F = 157.05 MHz
166 + j13Ω1.4
071 + j15Ω1.5
269 + j15Ω1.5

[12] The receivers were originally built for a related experiment designed to use 2 three-element arrays arranged at right angles, for a total of 5 antennas, to determine the angle of arrival from meteor forward scatter echoes [Webster and Jones, 1991]. The original operating frequency was 48.7 MHz and a preamplifier/converter was fabricated to mix down from 150.05 MHz to this input frequency. The receiver operates on the “phase-swept interferometer” principle illustrated in Figure 2.

Figure 2.

The phase-swept interferometer used to measure the phase angle ϕ. The output signal, fo is compared with the reference fo/0.

[13] The phase of the signals from the two outer antennas relative to the center (reference) antenna is measured at frequency f0 = 1.6 kHz, the phase difference (ϕ) being maintained through the receiver. This has several advantages including the relatively narrow final filter bandwidth for reduced noise levels and insensitivity to any modulation on the received signal. An average of 50 consecutive phase measurements, one per cycle, was used in determining the phase. The phases were stored as a single byte so that the range of 2π was represented by 256 “digital” degrees (d.deg.); the error introduced in the final answer by this is <±0.1°.

4. Measurements and Results

[14] Measurements were made at three sites, the UWO Elginfield Observatory (rural), the Lake Huron Pumping Station (maritime) and the roof of the Physics and Astronomy building on the UWO campus (urban). All measurements were conducted with the antenna separations set at d1 = 2.0λ and d2 = 2.5λ. Transmissions were made from a number of sites in each case, up to a few kms away from the receiving system and vertical omni-directional antennas used throughout. The coordinates of all locations were established using GPS.

4.1. Elginfield (Rural) Site

[15] Measurements were made at two frequencies, at the receiving system's primary frequency of 48.7 MHz and at 157.05 MHz; the maximum available transmitter power was 20 mW and 2 W respectively. Transmissions were made from various locations as outlined in Figure 3 from a car-roof mounted multiband vertical antenna. The accuracy of these locations, as derived from GPS, is well illustrated by the excellent fit with the roadway from which the transmissions were made. All of the transmissions at 48.7 MHz were masked by stands of trees, as were many of the ones at 157 MHz; the wooded areas are indicated by the shaded areas. A few of the latter were line of sight with the transmitter clearly visible from the receiver. Moderate traffic, including heavy trucks, was encountered on highway 23 though it appeared not to have too much effect on the measured phases.

Figure 3.

The locations of the transmitting sites at 48.7 MHz and 157.05 MHz in relation to the receiving arrays (RX) located at the Elginfield Observatory. The shaded areas represent thick woods. The orientation of the arrays for the two frequencies differed by 43.5°.

[16] After removing the 2π phase ambiguities and the offset due to the receiver, the bearing, ξ, of each location was derived using equation 1 and these are compared with those derived from GPS measurement of each location in Figure 4. It will be noted that typically, the GPS location is within ±4.0 m, so that the GPS bearings are typically accurate to better than ±0.25°. The results for the two different frequencies are shown together for the sake of compactness; it should be noted that the orientation of the arrays at the two frequencies differed by 43.5° and the bearings quoted are entirely consistent with this.

Figure 4.

The phase-derived bearing of each of the transmitting locations at Elginfield compared with that from GPS measurements; f = 157.05 MHz and 48.7 MHz with array orientations differing by 43.5°.

[17] For the data taken at 157.05 MHz, a fitted regression line shown results in a slope of 0.9947 and a coefficient of determination, r2, of 0.9951. The r.m.s. value of the difference between measured and calculated values is 0.89°, with a worst case value of 1.85°.

[18] A similar result is found for the observations made at 48.7 MHz. Although the measurements taken are fewer, the basic result is very similar. The slope of the regression line is 1.0462 with an r2 value of 0.9983. The r.m.s. value of the difference between measured and calculated values is slightly higher at 1.14°, partly due to the fewer number of measurements. The maximum deviation between measured and calculated values is 2.32°.

4.2. Lake Huron (Maritime) Measurements

[19] The equipment was set up at the Lake Huron Water Pumping Station (LHWPS) just north of Grand Bend, Ontario. The line of the array was roughly parallel to the general trend of the coastline and set back from the lake by about 30 m. The height above the lake surface was about 15 m, and a clear line-of-sight view of the transmitter was had for all of the measurements. The wind was light and the lake surface relatively smooth with small waves that caused no difficulty for the 21′ boat used for the transmissions, though moderate rolling and pitching movement of the boat was experienced. The frequency used here was 157.05 MHz as at Elginfield. A total of 20 transmission locations were used and the coordinates established using GPS once again. The locations and movement of the boat is illustrated in Figure 5.

Figure 5.

The track of the boat on Lake Huron from which the transmissions were made at f = 157.05 MHz.

[20] The values of the bearing angle as measured by the system and as calculated from GPS were determined. The result of this is shown in Figure 6 in which the slope is 1.0058 with r2 = 0.9986. The maximum difference between measured and GPS calculated values is 0.98° with an r.m.s. value of 0.41°.

Figure 6.

The phase-derived bearing of each of the Lake Huron transmitting locations compared with that from GPS measurements; f = 157.05 MHz.

4.3. U.W.O. (Urban) Site

[21] The receiving antennas were installed on the roof of the Physics and Astronomy building (PA) at the University of Western Ontario at a height of about 12 m above the local terrain. All measurements were made at a frequency of 157.05 MHz.

[22] Following some preliminary measurements on campus, the transmitter was driven to the 9 sites indicated in Figure 7; the sites are numbered in the order in which they were visited. As before, the transmitting antenna was multiband and mounted on the roof of a car. At all sites, with the single exception of site 9, the line of sight to the receiver was blocked by a mixture of low buildings and trees. A clear line-of-sight was available to site 9, the tallest building in downtown London, Ontario. The choice of transmitting locations was somewhat restricted by the river Thames, which flows more-or-less North-South through the UWO campus.

Figure 7.

The location of the transmitting sites used in the urban measurements. The UWO is located north of and slightly higher than the London downtown area. Low residential buildings and many large trees characterize the entire area outside of the campus. The normal to the array is shown dotted.

[23] The resultant derived bearing angles are shown in Figure 8 and several points are to be noted. First, the extreme value of ξ for site 1 (∼73°) coupled with the error in the measured phases due to many local campus buildings resulted in an indefinite value for the measured direction (the value of sin(ξ) > 1). Second, the measured bearing of site 3, also close by on campus, appears to have been affected adversely by the proximity of some of the buildings close to the receiver resulting in an error of about 7.4°. The rest of the estimates of the site bearings are much better with an r.m.s. error of ±2.5° with site 3 included and ±1.3° without.

Figure 8.

The urban measurements from UWO showing the derived bearing angles versus the calculated values from the site coordinates. The regression line excludes point 3.

5. Discussion and Conclusions

[24] As previously mentioned, this approach to direction finding is not able to cope with situations where many strong paths exist from transmitter to receiver, such as would be found in a downtown cellular environment with many local reflecting surfaces, and is not intended to do so. The technique also requires that measurements be made at a well defined frequency, and as such would be applicable to single frequency beacon applications or narrowband systems, such as marine VHF radios, where the carrier can be isolated using modern signal-processing techniques.

[25] Given that, the results presented here indicate that the relatively simple three-element antenna array is indeed capable of reasonably accurate estimates of the bearing angle of radio transmissions in a low-angle terrestrial environment in less demanding circumstances.

[26] It was expected that the maritime measurements would provide the best environment from the multipath point of view, and indeed this turned out to be the case. Since line-of sight was maintained throughout, the system had little difficulty providing bearing angles with an average accuracy of better than 0.5°. This would represent a lateral distance of better than 100 m at 10 km. Surface reflections were not expected to present a problem since those in direct line to the receiver would affect all 3 antennas almost equally. Reflection from off axis in “rough seas” with long swells might result in some multipath but it is expected that with appropriate averaging, this would not be a problem due to the ever-changing nature of the wave structure.

[27] In the rural measurements, the landscape is fixed so that a reflection from some off-axis topographical feature might result in a secondary path. The results suggest that some mild multipath was generated but the final results indicate that this was not a serious problem in spite of the fact that many sites did not have line of sight. In the 17 measurements at 157 MHz, there were a few potential minor reflections from a few farm buildings close to the transmitter as the transmitter progressed along the road, but these, if any, had little effect on the final answers. Any such multipath could have a much more profound effect were it to originate from buildings close to the receiver.

[28] Such buildings were present for the urban measurements made at UWO and appear to have affected 2 out of the 9 measurements made. The rest resulted in remarkably accurate estimates in spite of the fact that the transmitter was “buried” in the urban milieu for all but one site. This resulted in a much worse signal:noise ratio than would otherwise have been experienced and would be expected to raise the probability of multiple reflections. In spite of this, quite reasonable results were obtained for this phase of the experiment.

[29] In any deployment of a system such as this, the objective would be presumably to measure the bearing angles to at least the accuracy presented here. To do this, allowance has to be made for several points. First, the alignment of the array itself must be at least as good as, or better than, the required precision, not always an easy matter; in these measurements careful alignment of the array to better than 0.1° was achieved. Second, it is important that the receiving antennas are closely matched to allow accurate phase measurements, though system calibration using a source at a known location should also be made. Third, it must be recognized that the practical range in ξ will be less than the theoretical ±90°, depending on the expected signal:noise, and hence the uncertainty in the measured phase, which results in greater errors, and possible indeterminate answers, near the extreme ends. Some care needs to be exercised in selecting the receiving site to minimize reflections from buildings close to the receiver and to provide line of sight where possible. An elevated receiving site is to be recommended.

[30] If the idea were to measure angles of arrival over a fairly restricted range of frequencies, say 10% of the nominal frequency, then the above points should be checked over the entire band. Further, the nominal difference in separations of λ/2 would not be met over the entire band, although this is not too serious and allowance can be made relatively easily in the software; the main effect would be some restriction in the angular range. Significantly different frequency bands would require relocation, and maybe replacement, of the receiving antennas.

[31] Some modifications to the system specifications might be contemplated to tailor it to this specific task. The requirements for noise bandwidth and dynamic range (500 Hz and 50 dB for the equipment used here) might be examined in the light of the different character of the source. If the angular range in ξ were restricted to, say, ±75° in the forward direction, then more directive antennas might be used rather than the all-round looking ones employed here.

[32] In these measurements, a single (carrier) frequency was used, although the receiving equipment was rather specialized and insensitive to modulation of the received signal. In other applications, provided a strong carrier component is present it can be isolated using modern signal processing techniques. Finally, as mentioned previously, there is every reason to believe that a two-axis version of this system would perform well in an aeronautical situation where the source would be elevated and multipath minimal.


[33] Much of this work was supported by the Communications Research Centre, Ottawa, Canada. The authors would like to thank the Lake Huron Pumping Station for their help in allowing the use of their facilities for the Lake Huron measurements. The assistance of Mr. H. Chen and two summer students, Ian Brooks and Greg VanLeeuwen. is also acknowledged.