1An antenna on a range is not the installed antenna

Every antenna arrives with a pattern measured over absorber, on a rotator. It describes the antenna, not the installation. On a tower that aperture acquires a radome, tower legs, neighboring antennas and a mount fabricated on site, and the pattern that governs coverage is the installed one.

Taking the antenna down for a range measurement costs a crane, an outage and a range booking, and it measures an antenna that is no longer installed. A ground receiver at a surveyed bearing returns a horizontal cut at the one elevation angle the terrain allows, and that cut is a valid measurement of the installation at that angle. A downtilted panel, a stacked array and a cosecant-squared radar face put their designed structure in elevation, which a ground receiver at a fixed elevation does not reach.

A rotary-wing platform reaches the elevation cuts in an afternoon, and it brings a constraint the range never had. The probe is never stationary, so every sample has to be acquired before the probe leaves the angular cell it belongs to. That constraint, as much as the geometry, decides whether the pattern is sampled or interpolated. Figure 1 sets out the two measurement topologies; which one applies decides what flies, and the rest of this paper follows from that choice.

2What an in-situ pattern measurement demands

Three requirements follow from the geometry before any instrument is chosen. The first is standoff: the far field begins where the path-length error across the aperture falls to a sixteenth of a wavelength:

Equation (1) is a convention rather than a boundary. A sixteenth of a wavelength is 22.5 degrees of residual phase error across the aperture, which costs about 0.1 dB on boresight and caps the measurable null depth near 20 dB. Null work is flown at three to five times the distance of equation (1).

The second is angular sampling. A pattern is the transform of an aperture of finite extent, so it is bandlimited in angle and can be sampled without aliasing at:

The beamwidth that spacing has to resolve follows from the same two quantities:

Equations (2) and (3) share their two variables, so their ratio is fixed: whatever the aperture and whatever the frequency, Nyquist sampling is a little over two samples per half-power beamwidth, and resolving a null takes four to eight. Once the platform moves, that sample count becomes a sample rate. A 5 m radar face at 1.3 GHz carries the arithmetic from here: far field from 216 m, a 3.2 degree beam, a sample every 1.32 degrees. Figure 2 draws the geometry, and Figure 3 plots equation (1) across the band.

3Why the platform's motion breaks a swept measurement

Standoff and sample spacing convert angle into distance; ground speed converts it into a budget. The probe spends this long in one angular cell:

At 250 m and 8 m/s that is 250 × 0.0231 / 8, or 0.72 seconds per sample, and a full arc is 273 samples in 196 seconds of flight. Slowing down buys cell time and costs endurance in the same proportion.

A swept-tuned receiver inside 0.72 seconds: it moves a resolution filter across the span, and the filter has to settle in every cell, giving a sweep time near k · S / RBW² with k around 2. A 100 MHz span at 10 kHz resolution takes 2.0 seconds, so the cell ends before the sweep does.

Fixing the tuning helps and does not cure it, because the emitter is duty-cycled. A pulse shorter than the reciprocal of the filter's impulse bandwidth reads low by roughly 20 log₁₀(τ · 1.5 RBW), which is 36.5 dB for 1 microsecond at 10 kHz, as Figure 4 plots. Widening the filter recovers 20 log₁₀ of the bandwidth ratio while raising the noise floor by 10 log₁₀ of it, a net gain, which is why a pulsed pattern is measured at the coarse end of the resolution list.

So the criterion applies to any instrument from any vendor: how many samples, each guaranteed correct in amplitude rather than only detected, does the receiver deliver inside one angular cell? Above one the pattern is sampled; below one it is interpolated. Figure 5 draws the cell budget against both architectures.

4Derived requirements

Table 1 is the hinge of this paper. Everything above it is physics; everything below it is instrumentation, and any receiver from any vendor can be scored against it.

5Meeting the requirements from a flying payload

A real-time analyzer transforms a continuous sample stream rather than tuning across it, so its amplitude guarantee is a boundary, not a probability. Berkeley Nucleonics publishes the relations for the ICX-FieldHawk 9.5, 20 and 40 GHz models, so the guarantee can be computed:

The factor of two is the arrival-phase penalty: a burst inside one window is seen but reads low, because only part of the window held energy. The published points are 0.512 microseconds at a 32-point transform with 3,906,250 frames per second, and 32.768 microseconds at 2048 points with 61,035, at M = 1. The 4.5, 6 and 9 GHz handhelds publish a 16 ns sample period (8 ns with option 50), so their guarantee at a given transform size is twice as long.

The same models publish real-time resolution bandwidths from 14.73 MHz down to 3.59 kHz in thirteen Flat-top grades, and the coarse end is what a 1 microsecond pulse needs (Figure 4). Power detection is published at 8 ns time resolution with six detectors, which turns each pulse into one number; Figure 6 shows that measurement and Figure 7 the per-pulse table it produces.

Figure 7 is a bench train rather than the worked case, and its use here is the population statistics. Before a flight is scored, the illuminator itself is measured this way, because a drifting pulse width appears in the pattern as a lobe that is not there, and the width deviation across a hundred pulses is the number that says whether the illuminator is stable enough to serve as a calibrated source. Table 2 lists the published payload figures, which decide the airframe.

Two published details matter more than their datasheet lines suggest. The host software runs on Linux on AArch64 as well as x64, with SCPI and Python standard, so the flight computer can be an ARM companion board on the airframe, with SpectraCore on the ground for reduction. And the transmit-side pass of Figure 1 needs an airborne source of known level and known pattern rather than a receiver, so the payload for that pass is a compact Signal Generator or a characterized beacon, with the receiver on the ground at the antenna port.

The constraint on this flight is at the top of the scale. At 14.73 MHz of real-time resolution the noise floor is near −88 dBm, from the published displayed average noise level of −159.9 dBm/Hz for the ICX-400U between 90 MHz and 3 GHz at a −50 dBm reference level in 1 kHz resolution bandwidth; the ICX-200U publishes −166.3 dBm/Hz under the same condition, 6.4 dB lower. A sidelobe 60 dB below the main beam is still 55 dB above the floor. Near a radar the first requirement on a flying receiver is therefore an attenuator sized to the main beam, not sensitivity. Figure 8 puts the five levels on one axis.

Limits of the amplitude figure. Amplitude accuracy is published at ±2.0 dB from 9 kHz to 9.5 GHz and ±3.0 dB from 9.5 to 40 GHz, at 25 °C after 10 minutes of warm-up with spur reject standard on, and a pattern is a ratio to boresight, so the fixed part of that figure cancels. The probe antenna's own pattern, airframe scattering and the ground-reflected path do not cancel, and in practice they set the error. A UAV pattern is an amplitude pattern of the installation under those conditions; it carries no phase, and it is not an anechoic chamber pattern.

6Measuring the aircraft's own radio

Turn the geometry around and the same payload characterizes the airborne radio. A command link, a video downlink or a 1090 MHz transponder all have patterns shaped by the airframe, and a belly blade that measured omnidirectional on the bench is shadowed by a battery tray and a motor arm. Those emissions are bursts, and a 120 microsecond squitter is the case a partial dwell mishandles.

Run that case through the same arithmetic and it comes out differently from the radar. At 120 microseconds the squitter is 3.7 times the 32.768 microsecond guarantee at N = 2048, so the amplitude of every message received is correct at the largest transform size. The constraint moves to the message rate. A transponder emits about four extended squitters a second, airborne position and velocity twice a second each and identification every five seconds (DO-260B), so the 0.72 second cell of section 3 holds about three of them, against the 720 pulses the radar put in the same cell. That meets the criterion of section 3 with three samples rather than hundreds, and three samples leave little to average: the difference between the radar and the transponder is not whether the pattern is sampled but how much scatter survives into it. For a transponder the pattern point is set by message rate, not by the receiver, and the options are to fly slower, widen the cell and accept the angular smear, or fly the orbit twice and interleave the samples. No instrument specification changes that number.

Here the fusion of two logs, not the precision of either, sets the accuracy. Any unmodeled offset between the receiver's time base and the flight log smears the pattern in angle:

Holding that smear to a tenth of the 3.23 degree beamwidth of equation (3), at 8 m/s and 250 m, allows 0.00564 × 250 / 8, or 176 milliseconds of skew, and Figure 9 plots the smear against the offset for three ground speeds. Published GNSS one-pulse-per-second timing is ±100 ns as standard, about 1.8 million times finer than the requirement. The instrument's clock is not the risk; the risk is an operating-system timestamp drifting against an autopilot log that is not disciplined to the same reference.

The installation is part of the measurement. Module, companion computer and battery all radiate and all scatter, so their positions relative to the probe are fixed and recorded before the first sortie, and every later correction is applied against that geometry.

7Measurement practice

None of the following depends on which analyzer is flown, and all of it decides whether the sortie produces a pattern.

1. Fit the pad before the first flight. Size it from EIRP and slant range, add 10 dB of margin for an unlisted beam, and store the attenuator's measured loss as an amplitude offset.
2. Choose the probe antenna for pattern flatness, not gain, because probe ripple multiplies into the error and does not average out. Apply its pattern as an antenna factor. An active directional antenna puts the main beam further above the input limit and adds its amplifier's compression to the budget, so it is not a probe for pattern work.
3. Fly constant slant range, not constant altitude, so amplitude change is pattern rather than geometry.
4. Discipline both logs to the same one-pulse-per-second edge, and fly one abrupt heading change at the start of each pass as a marker visible in both.
5. Warm up on the ground, since published specifications assume 10 minutes at 25 °C.

When not to do this: if the question is only whether an antenna points where it was aimed, and the emitter is a continuous carrier, a power meter and a surveyed position answer it for less.

Field evidence

Airborne measurement of installed antennas is offered commercially: a receive module flown on a multirotor with a companion computer, the pattern reduced on the ground, and the stated reason is that a flight replaces a climb. The arithmetic above is the cost of making that substitution: the standoff of section 2 decides whether a given face can be flown at all, the cell budget of section 3 decides whether the result is sampled or interpolated, and the input limit of section 5 decides whether the first sortie returns a pattern or a compressed one.

8Summary and selection

Table 3 lifts the governing relations and published values into an evaluation matrix, so a vendor's published data can be scored against them line by line.

Table 4 maps the job to the configuration. Frequency decides the module and the payload budget decides the mount, in that order, because a mount that will not fly makes the frequency question academic.

9Definitions, symbols and further reading

Antenna factor

The ratio of incident field strength to the voltage delivered to the receiver, in dB/m.

Far field

The region beyond 2D²/λ where the field's angular distribution no longer changes with distance.

Installed pattern

The pattern of an antenna in its mounting, with radome, structure and neighbors in place.

Probability of intercept

The minimum duration a signal has to be present for a correct amplitude measurement.

Further reading

• IEEE Std 149, Recommended Practice for Antenna Measurements, for far-field criteria and range error budgets; IEEE Std 1720 for near-field alternatives, which is the better answer for a large aperture that cannot be flown at three to five times its far-field distance.
• C. A. Balanis, Antenna Theory: Analysis and Design, Wiley, chapter 2 (fundamental parameters) and chapter 17 (antenna measurements).
• RTCA DO-260B for the 1090ES extended squitter message set and rates; RTCA DO-160, section 21, for airborne emission limits; ITU-R SM.378 for field strength.
• Berkeley Nucleonics BNC-AN-102, BNC-AN-103 and the ICX-FieldHawk datasheets at berkeleynucleonics.com.

If you are planning a flight program and want to work this arithmetic against your own antenna and airframe, our application engineers would be glad to help.