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Basic phased array radar questions

  1. Jan 29, 2017 #1
    So, I already understand that the maximum resolution of a radar system is λ R / L, where lambda is the wavelength, R is the range to the target, and L is the diameter of the antenna, and that for a phased array, L would be the maximum distance between antennas (correct me if I'm wrong :) ). But there are two things I don't know:

    1) How would one go about calculating the maximum bandwidth of a phased-array system? I know that they can be retargetted "in milliseconds" and different portions of the array can be used to track different targets at the same time. But when sweeping across terrain, what determines how many return datapoints you can read per second?

    2) How does one calculate / estimate range accuracy when measuring distances to the target? Again the multiple antennas throws me off a bit because I know that in a single antenna system you generally have the antenna switch between pulses and waiting for returns, but I imagine that on a phased array when you have many antennas that it might be different.

    This is all concerning terrain mapping from a lighter-than-air vehicle. Just trying to calculate what sort of data quality could be gathered, and it seems that most radar questions on stack exchange are in this section. :)

    On that front...

    3) Am I wrong that phased array is the ideal radar choice for this application? I know aerial terrain mapping is usually done with SAR, but a) a lighter than air vehicle moves much slower than an airplane or spacecraft (bad for SAR), and 2b) spreads out over a large physical area (good for phased array). Correct me if I'm wrong and SAR or some other type of radar else would be superior from a mass perspective for a given resolution
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  3. Jan 29, 2017 #2


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    is air speed really an issue ? I would have thought not ... do you have technical papers that suggest it is ?

    that's the huge advantage of SAR, is it's high resolution and the ability to produce 2D or 3D terrain data
    I am not sure if a phased array has that same ability ?

  4. Jan 29, 2017 #3
    Perhaps then I misunderstand how SAR works. My understanding of SAR is that it's based around the motion of the antenna between transmission and reception of the return in order to create a larger effective aperture - which would imply that the further the vehicle moves during that timeperiod, the larger the effective aperture. By all means, please correct me if my understanding is erroneous!

    Is not the maximum resolution of any radar system inversely proportional to the aperture (real or virtual)? And isn't 3D data (distance) simply the timing difference between broadcast of a pulse and reception of its return? Certainly phased array can measure distances, it'd be worthless for its main application (military) if it couldn't.
  5. Jan 30, 2017 #4


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    This is my take on it. First, to scan across the direction of travel, we do not have SAR action, so there is a finite time for the transmitted beam to be scanned laterally across the path. The switching of antenna elements is restricted by the desired bandwidth of the system (as narrow as possible for noise but as wide as possible for speed) and by the bandwidth of each element. We would like a whole TX pulse for each beamwidth, so this sets the time.
    The spacing of TX pulses must allow the go-return time of the pulse.
    Last edited by a moderator: Jan 31, 2017
  6. Jan 30, 2017 #5
    That doesn't pan out when I run the numbers. For example, consider the Space Shuttle's SAR mapping of Earth - perhaps 250km up, so 500km round trip. Speed of light is 300000 kilometers per second, which would mean that they could only get 600 readings per second. Which is impossibly low, because they mapped nearly the whole Earth at high resolution.

    Ed: Here, for example, is a proposal to use InSAR to map Venus:


    Two antennas separated by 3.1m, scanning at 30 degrees from normal, from 240km up, yielding at max resolution backscatter with 15m pixels, 20 million per second, with altimetry resolution 250m pixels with a height resolution of 5m.

    Clearly they're not just sitting around waiting for single pulses to be returned.

    Ed2: I calculate the orbital velocity for a circular orbit at 240km on Venus to be 7185m/s, for whatever that's worth.

    Ed3: Reading up more, altimetry isn't about timing at all, it's about measurement of phase offsets on returns. Still trying to understand how one could calculate something like "...a bandwidth of 20 MHz that results in a range resolution of 7.5 m, which projects to a ground resolution of 15 m ... resulting in a 14.5 km swath width and an azimuth resolution of 2 m ... with a posting of 250 m and a height accuracy of 5 m."

    Altitude: I'm thinking that it's about how accurately you can measure phase differences? If I run the numbers on VERITAS I get 0,5% of a phase, which sounds like a plausible figure.

    Bandwidth: Still working on this one....
    Last edited: Jan 30, 2017
  7. Jan 31, 2017 #6


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    First illuminate a large regional area with a transmitted signal from a smaller array. Then synchronously down-convert and digitise the reflected signals received at each antenna element. You can then use software to synthesis spot beams by combining the digital signals with different time delays.

    If the array is moving quickly then it only needs to lie across the vehicle as front – rear mapping can be resolved by doppler shift.

    There are several pulses in transit from the satellite to the ground. The pulse rate is arranged so reflections from the swath being mapped will arrive between two later transmit pulses.
  8. Jan 31, 2017 #7


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    I remembered later that for the lateral scan, if it is looking to one side, it can rely on simple time of arrival to obtain the picture, without the need for a phased array scanner.
  9. Jan 31, 2017 #8


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    You are not restricted to pulse radar for terrain mapping from a low speed vehicle. You could use a linear frequency sweep or chirp. Multiplying the received signals by the transmitted sweep produces a difference frequency determined by sweep rate and transit time.

    Direction comes from the phasing of your synthetic spot beams, while the received difference frequency gives you range to target.

    Because the frequency sweep can last for some time, an FFT of the digitised received signal will give the difference frequency with a processing gain equal to the square root of the number of samples in the FFT. It will also give you an idea of the variations in range within the spot beam.
  10. Jan 31, 2017 #9
    Thanks for all of your knowledge, Baluncore. However, I don't need to know how to actually implement it, just how to calculate the rough capabilities of a system based on its parameters. :) So

    1) Am I right in that for a very large but low-speed vehicle, phased array is the best option for getting high resolution imagery? (relative to system mass)

    2) Am I correct that maximum resolution is λ R / L, where R is the distance to the target and L is the maximum distance between antennas (perpendicular to the path to the target)?

    3) Am I correct that the maximum altitude resolution is a function of a) the altitude of ambiguity / the height difference that causes one phase difference in the received data, and b) the degree of precision that phase offsets can be calculated from the output (and would 0,5% of a phase be a realistic figure? Because that's what I calculate for VERITAS using that method).

    4) How would one calculate the maximum bandwidth, meaning the amount of datapoints that can be calculated per second of scanning? For VERITAS in the link above, they have a figure of 20 MHz. Where does that sort of figure come from?
  11. Jan 31, 2017 #10


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    Yes. But with digital processing today, the best pattern of antenna elements will probably not be a rectangular or cross shaped array. For best performance for minimum weight and aerodynamic drag you can do better by having many variations of spacings and orientation to reduce the side-lobes of the 2D synthetic spot pattern. For example, consider using an array of elements spaced equally around the circumference of a circle.

    As a rule of thumb, the -3dB points of the spot beam will be separated by λ / L radians. You can discriminate between two targets if they are separated by >= that angle. So your equation R · λ / L will be acceptable so long as you remember to correct L with a cosine off-axis term.

    The principle of aperture illumination is as applicable to reception using phased arrays as it is to parabolic reflectors used for transmission. There are situations where resolution can be worse than predicted by the equation. The ring of elements mentioned in the point 1) paragraph above is an example of an unusual aperture illumination that may be a good compromise in some vehicles.

    If the target is illuminated with the same spot beam that is used for reception it will take much longer to scan and build an image of an area. But you will get a narrower beam because squaring the array pattern will move the beamwidth in from the -3dB points to the -1.5dB points. With the smaller spot beams it will take even longer to scan the image. In that situation, resolution can be improved beyond the equation but at a great cost in acquisition time.

    I think you are talking here about range resolution. It will come down fundamentally to SNR and the bandwidths of the signal transmitted and the receiver used. The time resolution of the correlator of the received signal with the transmitted signal will then determine range resolution. For time delay measurements, a short chirp or a PRBS burst is better than a rectangular pulse. You are restricting your consideration to a pulse type radar rather than considering a frequency swept signal with process gain, where you can extract range and phase from the processed data.

    The data would be processed on board at a very much higher rate. The processed result appears as spot heights at a rate of 20 million data points per second. That would still take a long time to beam back to Earth.
    There are RF processing chips available for mobile phone receivers that down-convert and digitise signals at 1G samples / sec. One of those could be applied to each element of an array. The processed data points would appear at a rate dependent on the cost of your dedicated parallel post processors.

    How high above the ground will your proposed vehicle be floating ?

    What “look” angle, from the nadir towards the horizon will you be imaging ?
  12. Feb 1, 2017 #11
    Indeed, in my research I came across a spherical equivalent (the "Crow's Nest" antenna); they mentioned the same side lobe avoidance issue as the motivating factor. That design is of course intended for omnidirectional usage.

    Understood. Basically, for a given array, you can trade off your maximum resolution for an improved acquisition time as needed - you can scan at near R · λ / L, or you can scan quickly, but not both simultaneously.

    When I look up stats for a system like on VERITAS, there's generally the following:

    * Maximum resolvable feature size - in the case of VERITAS, 15m
    * Maximum altitude resolution - in the case of VERITAS, 5m
    * Bandwidth / acquisition rate - in the case of VERITAS, 20m

    We already covered maximum resolvable feature size; I'm trying to get hang on the other two. I know that at least for InSAR, scan imagery forms a sort of "sawtooth" pattern that has to be reconstructed in software, because you can't tell the difference between X phases plus some fraction N, and X + 1 phases plus the same fraction N. The height representing one phase being the altitude of ambiguity, which is Ha = λ R sin θ / (2 B) where Ha is the altitude of ambiguity, λ the wavelength, R the distance to the target, θ the look angle, and Bn the perpendicular baseline. When I run the numbers for Veritas, I get an altitude of ambiguity that is nearly 200 times greater than the maximum altitude resolution. Is the maximum altitude resolution just a signal to noise issue? If so, are there any rough guidelines on estimating how bad SNR will be for one system in comparison to another?

    So the maximum rate in which datapoints can be acquired is not a radar limitation, but a processing / transmission limitation? There's no physical limitation?

    55km, 30°.

    (It's a followup to Landis 2003; I'm trying to determine how effective the proposed habitat would be as a radar platform in comparison to the sort of orbital radar systems that are likely to conduct mapping in the interim).
  13. Feb 1, 2017 #12


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    Now I understand the dimensions of the Venus problem.

    There is no point duplicating the results of earlier surveys, and there are physical limitations. From a fixed height, best resolution will require a large sparse array and a short wavelength. I think there will be plenty of time and power for processing.

    Speed over ground due to the wind at 55km will be about 210 km/hr. That will probably not be a nice laminar flow. The problem with a large sparse array will be platform stability and rigidity. I do not know how much buffeting turbulence there will be. To some extent it will be possible to physically orient and stabilise the array, maybe by using solar powered propellers. But the short wavelength will require very high element position accuracy. For that reason some form of continuous element position measurement will be needed with software to correct for element position errors in the beam forming module. That will be needed to eliminate blurred images due to structural flexing of the array. Meanwhile, drops of sulphuric acid will contaminate the surfaces of the radomes that protect the elements.
  14. Feb 1, 2017 #13
    Okay, this is somewhere that I can add a lot of input, as this is more my field :)

    Re, laminar flow: At high latitudes (for example, ~70°), 55km-altitude groundspeed is somewhere in the ballpark of 40-70 m/s, whether you trust the VIRTIS (cloud tracking) or VeRa (radio sounding). 144-252 km/h. That is however at altitude. Since you don't specify whether your concerns are the surface flow, the flow at altitude, or in-between:

    1) Venus's surface winds are not a laminar flow, but they're much closer to laminar than winds measured at equivalent heights over Earth's surface. In terms of flow behavior, Venus's surface is sort of halfway between that of an atmosphere and an ocean
    2) At flight altitude (middle cloud layer) it's convective conditions roughly similar to Earth's troposphere. The motion over the surface is fast, but the surface is 55km below, with only a relatively weak coupling at cloud height (although there is some degree of coupling, as can be seen in gravity waves).
    3) Between there there's a series of dynamically stable and convective layers - mostly dynamically stable, like Earth's stratosphere.

    Yes, orientation and stabilization is not only possible, but required. Also, in turbulence, airships don't shake or plunge like heavier-than-air aircraft, but instead tend to roll in a manner similar to ships at sea.

    Yes, the habitat can be expected to flex, and precise antenna position monitoring would be absolutely required.

    No, sulfuric acid would not be in contact with the array. The array would be located inside the habitat, with the habitat itself effectively functioning as the radome. The envelope is multilayer - fluoropolymer outer layer, followed by one or more biaxially oriented structural/barrier layers, followed by an optional fluoropolymer inner coating for antifog/antifouling, with fibre reinforcement. The exact combination requires environmental testing which has not yet been conducted. Of particular interest is PCTFE for outer coatings, as it's relatively low fluorine but still has good chemical resistance and weathering properties, and is one of the best water vapor barrier polymers out there (though ECTFE is more workable). As for biaxial structural layers, mylar (PET) always comes up in the context of Venus aerobots, but EVOH and PVDC are also very interesting because of their superb barrier properties (and greater potential for ISRU).

    (Also, just to point out - the middle cloud layer is not like an acid bath, it's more like a bad smog. Or more precisely, vog. Visibility is several kilometers; acid particulate densities are a few to a few dozen milligrams per cubic meter. On Earth, OSHA lets you breathe up to 1mg/m³ ;) )

    There are some issues concerning radar, mind you - for example, IR rejection to control temperatures means low-E coatings / additives like ITO and ATO, which are radio blocking, so you have to pattern them so that they don't form continuous conductive paths. But this is territory that's already been well tread.

    Concerning wavelength, it depends on what sort of parameters you select, but I come up with Ka-band being optimal, in the rough ballpark of 1cm / 30GHz. Absorption goes up with the square of the frequency, so there's a limit to how short of a wavelength you can utilize. But the mass and power budgets are significantly higher vs. orbital mapping.

    Back to the previous issues:

    How does one calculate or estimate those physical limitations? And likewise, maximum altitude resolution?

    I'm not sure what you mean by "no point in duplicating the results of earlier surveys". The point of repeated radar surveys is higher resolution. The first radar maps we had of Venus were kilometers per pixel. The best we have now is a bit over 100 meters per pixel, from Magellan. VERITAS would have been 15 meters per pixel (something like it will surely be done in the next decade or so). The formula discussed earlier for a first-generation Landis-style habitat yields about 1-2 meters per pixel. There's a dramatic difference in the sort of science you can do between different resolutions.

    Of particular interest - and the reason I'm focusing on wanting to be able to include an estimate of altitude resolution - is the utility of radar for monitoring for volcanic and tectonic activity (uplift, etc). While there's little doubt that Venus is still volcanically and tectonically active, understanding the nature of the geological processes that shape it today are crucial for understanding how it ended up the way it is, and what implications that has for Earth. Venus is somewhat of a cautionary tale, in that it's locked into a vicious cycle. It's hot because it cannot sequester carbon dioxide as carbonates. It cannot form carbonates because it's too hot (and has driven off most of its water). Its climate also seems highly unstable. About 500mya it underwent a global resurfacing event - the entire planetary surface (with only a few possible exceptions) looks to have been molten. Why? At this point, we don't know. But we certainly want to know why. And what happened before that. At one point, Venus was once like Earth. It had oceans like Earth (the deuterium ratio indicates massive water loss). It really was our sister planet.
    Last edited: Feb 1, 2017
  15. Feb 2, 2017 #14


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    I was only concerned with the local atmosphere at 55km altitude. The wind speed is fast enough to cause turbulence and platform stability problems. The wind speed is too low to make doppler SAR accurate with such a steep look angle from an aerostat. For that reason a 2D radar array is needed.

    If the vertical component of the wind is significant, it might be better to make a spherical aerostat rather than a flat flying saucer. That might limit the size of the radar array. To carry extensions of the array for higher resolution I would consider an external open space-frame that the wind could blow through, with a significantly lower windage.

    Hot air balloons navigate by rising or falling to select air travelling in the direction they want to go. A submarine maintains depth by moving slowly forwards with control planes correcting for minor buoyancy variations. The same is true of dirigibles. The typical surface vessel has no directional control without “steerage way”. Likewise I would expect an aerostat to keep moving slowly so as to remain stable and enable a hopefully controlled migration over different parts of the planet without expensive changes in altitude.

    There needs to be a reference grid. On Earth we have GPS, referenced to ground stations. GPS transmitters or base stations on Venus are not really possible for many reasons. I expect it would be worth “seeding” the surface with many (wavelength tuned?) three cornered radar reflectors to act as random cardinal “trig” points. They can be used for very accurate range, velocity and position measurements of vessels relative to the surface. They will also show up on the radar terrain mapping as tie points, but we don't want them to be so good that they blind the array. Any tectonic movement will slowly move the relative position of the trig points in 3D. That should show up clearly as automated navigation using the network of reflectors could involve many simultaneous accurate range measurements, the reciprocal of what is done now with GPS.
  16. Feb 3, 2017 #15


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    The reason why littering and better-than-needed broad-band reflectors on the surface should be avoided is that it could blind high resolution imaging. What follows is an early example of a good reflector obliterating parts of the nearby image.
    J. Patrick Fitch in “Synthetic Aperture Radar”, 1988, writes on page 75:
    “The final scene is a 1024 by 1024 pixel image with each pixel representing an area on the surface of the Earth about 25m on a side. The bright star-shaped reflection in the left side of the image is a 26m antenna installed at the Goldstone Deep Space Network tracking station in southern California. The tails of the star shape, which are caused by ringing in the point response, can be reduced using windowing techniques applied in the frequency domain. The results of using a cosine–squared window are shown in Figure 2.40. The faint cross pattern of bright spots, visible to the right of the antenna, corresponds to a set of nine reflectors, ranging in size from 2 to 3m and spaced about 300m apart.”

  17. Feb 3, 2017 #16


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    I presume the antenna was not pointing at the radar, but still gives a strong reflection.
    It is interesting that a reflector antenna should re-radiate if terminated with a matched load. But we normally assume that half the incident power is re-radiated from an antenna. I have seen the reflection from a 3m diameter microwave link antenna in the form of echoes on the pulse response at a distance of about 20 miles.
  18. Feb 3, 2017 #17


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    You can expect it to re-radiate if the radar is outside the bandwidth of the front-end. It just happens that the 26 metre dish was originally designed to track fast satellites, but I think what shows is the glints from the huge metal support structure rather than the dish surface. Tracking a radar satellite with a 26m dish would be over-kill for the cooled receivers at the focus.
  19. Feb 3, 2017 #18
    Wind speeds relative to the surface are not a relevant factor. Venus superrotates; the winds circle the planet much faster than the planet itself rotates. Many of these layers, despite their speed relative to the ground, are dynamically stable; there is no turbulence at all. The middle cloud layer is not dynamically stable - but it's not abnormally unstable by Earth standards. Think "Earth's troposphere" and you're in the right ballpark.

    Indeed, this is exactly what my logic was when looking at a phased array instead of SAR. However, as a note, the look angle is something that can be changed as needed for optimal mapping capability (the altitude and airspeed cannot be significantly altered).

    Size is one thing that is not a limitation. The biggest challenge with the proposal laid out by Landis is the ascent stage. Rockets are very, very heavy when fuelled; Venus, being so similar to Earth, is similarly difficult to get off of; an envelope lofted by O2+N2 has less lift on Venus per cubic meter vs. helium on Earth; and for temperature reasons you have to float fairly high, ~0,5 bar or less. All of this together means large sizes, dozens to hundreds of meters on each axis. As a baseline, we're using the largest US hangars, such as Hangar No. 1 at Moffett Federal Airfield, with 10-15 meters clearance on each axis, to define the dimensions, which yields ~50x80x330m, with the ~50m being the vertical axis. We're also giving some analysis to smaller and larger airships (the latter requiring a new ~$200-400m hangar, or acquisition of the former CargoLift hangar in Germany).

    A caveat with the dimensions: there are ballonets inside which *greatly* change in size over time (slowly). So while there are locations within which are relatively static (anywhere bordering the external envelope, plus in the top 5-10% where the ballonets don't extend to, the central channel, the empennage, and the ISRU / propulsion section underneath), everwhere else, you could have antennas, but they'd have to move with the ballonets.

    There's little changing of altitude. It descends about 1-2km at night due to loss of lift and, again, a different temperature profile. There's a lingering latitude of around 70N° and 70S° which yields the highest air pressure / lift with low drift and little risk from the polar vortices. For moving between them across the equator the habitat has to ascend 1-2 km over the baseline. The poles allow for lower altitudes / even higher pressures, but are generally a no-go zone because of the polar vortices. (To be fair, we've never flown anything into them, so we can't say for sure that they're turbulent, but the resemblance to terrestrial hurricanes is enough to give one pause)

    Latitude shifts are purely propulsive, not by changing altitude. There is a meridional drift that must be overcome, but it's not nearly as strong as the superrotating zonal winds (which are essentially impossible to overcome regardless).

    That's actually an interesting idea. Mind you, there are already a dozen or so manmade items on the surface of Venus already - the Venera landers, the Pioneer multiprobes, and by now the wreckage of the Vega balloons too ;) But they're not designed specifically as reflectors, and they're not available at all latitudes. The Veneras would have the brightest radar signature - they're basically heavy steel spheres with an aerobraking disc and spiral antenna on top. They don't show up on the Magellan data, but the resolution on that was ~100-250m/pixel, so not exactly great...

    There's also topographic features, but I'm not sure whether those would do the trick. But so far, the radar maps have been built up by aligning the new data with the old data, without the use of surface markers. Concerning natural topographic features, Venus has some curious highly radar-reflective areas in the highlands, believed to be one or more kinds of metallic or semiconductive frosts or snows. How static they are, that's still unknown - we don't even know what they are.

    The existing mapping spacecraft have had at their disposal star trackers for orientation, as well as signals from the DSN on Earth. Star tracking cannot be done inside Venus's middle cloud layer; you can't even see the disk of the sun from there. However, signals from the DSN still reach it. Also in the baseline proposal there's a "relatively" geostationary satellite (tracking the speed of the zonal winds, not the surface) to act as a communications relay (without it, the habitat would only have communications with Earth for roughly half the time). So there's two external points of reference by radio.
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