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The Problem with Police Speed Detection Equipment - Part 1

Here's how radar works - and how it can makes mistakes.

By Dennis Jensen

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So, you got a speeding ticket. Either you were pulled over, or you got a ticket through the mail. Since they got you using "high technology" equipment, there really can be no mistake, can there?

Well yes, actually, there can. Every type of currently used equipment that is used to detect speeding offences has fundamental issues that can lead to the incorrect driver being fined, or to incorrect speed readings. First, we will get into the theory of the equipment that is used and then deal with issues relating to each technology.

It is important to realise at this point that although speed cameras send you a picture, speed is in fact determined using radar.




Basic Radar Theory

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Before getting into the issues that affect the reliability of radar speed detection, it is necessary to understand the fundamentals associated with radar propagation.

Radar is an electromagnetic wave, usually broadcast at microwave frequencies. This electromagnetic radiation propagates at the speed of light. Despite what many people believe, the speed is not measured by timing the differences between the time of broadcast and the time that the pulse is returned. In fact, speed detection radar is not pulsed in its operation at all (pulsing is the equivalent to rapidly turning a torch on and off), but is, in fact, a continuous wave (similar to leaving the torch on all the time).

Doppler Effect

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The basic principle of speed measuring radar (remember that speed measuring radar is used in speed cameras as well) is that of the Doppler Principle. We have all heard approaching sirens, horns, engine noise or whatever that appear to have a higher pitch approaching us than when they are leaving us. The reason for this is that the source (making the noise) is "chasing" the signal that it sends out, "bunching up" the soundwaves when approaching. When departing, the source is moving away from the waves, tending to stretch the waves out.

Now that we understand that the broadcast waves and the returned waves will have different frequencies, it should be realised that the difference in these frequencies will result in interference between the return and broadcast frequencies; the resultant waveform will have a frequency known as the Beat Frequency. It is this frequency that is in fact measured by the radar in order to determine the speed of the vehicle that is approaching or departing.

So far, this all makes complete sense, and there is no doubt that, if the radar unit is correctly calibrated and the correct value is given for the speed of the waveform, the speed of an object can be quite easily determined from this beat frequency if the beam is pointing straight at the object. There are, however, issues that may lead to either incorrect target identification or an incorrect speed being detected.

Beamwidth

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Next we come to the concept of beamwidth. The police and the road safety authorities would have you believe that the radar beam is very clearly defined, where radar is projected as a beam, and you have the situation where inside the beam you have the electromagnetic signal, and outside the beam you have no signal at all.

In fact, nothing could be further from the truth.

The radar beam beamwidth is, in scientific terms, described as either the -3dB beamwidth or the full width half maximum (FWHM) - these two terms describe exactly the same thing. The latter term actually describes the situation quite well; it is the width of the peak from the point at which the energy is half the signal strength in the centre of the beam. This is all very well, but here we come to a problem. You will note from the diagram below that there is still quite a bit of signal outside the defined main beamwidth.

In fact, the so called null-to-null beamwidth (the width of the beam where the energy at the edge is truly zero) is about double the -3dB beamwidth (in fact, in the case of the devices the police generally use, it is slightly more than double). So, when a radar beam is described in the manual as having a 12-degree beamwidth, it should be realised that there is actually energy present out to 24 degrees!

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The red vertical lines in this graph represent the -3dB beamwidth. Note the radar energy outside the defined beamwidth and out to the null-null beamwidth.

There is even more complexity than this! Signal is not only present in the main beam; it is in fact present in many directions. This energy is present in what are called sidelobes. Sidelobes are an issue with all radar systems, even the most expensive and sophisticated military types such as active electronically scanned array (AESA) type radars that are beginning to get fielded by the military in aircraft such as the F-22 that is currently in development. These sidelobes are an issue, even with techniques such as array shading, taper and other techniques to reduce the sidelobe size. The simple presence of sidelobes is used to the benefit of electronic jamming systems.

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So for police spokespeople to make statements - such as that by a Queensland police spokesperson - that their radars are not affected by interference is simply ludicrous at best, or demonstrating a complete lack of knowledge by a person who should know better. I can assure everyone, the military would be very interested in a radar system that was immune to jamming, and the radar manufacturer would make an absolute fortune from such technology, even if just from royalties.

The issue with these sidelobes is that if there is a vehicle in a sidelobe, it is possible for this vehicle's speed to be detected. Problematically, if the vehicle in the sidelobe has a radar cross section that is much larger than the vehicle in the main beam, it is entirely possible for the radar device to display the speed of the vehicle in the sidelobe, while the operator is of the belief that the vehicle in the mainlobe is the vehicle that has its speed displayed.

Attenuation

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The energy that is returned to the radar unit from a reflecting object is affected by a few factors:

  • The returning energy will be dependent on the amount of energy (or power) that the radar unit projects.
  • The antenna design will have a great effect on the energy returned in that it is the antenna that "aims" the radar power.

Clearly it is better to put the power into a focussed beam than it is to simply project power in all directions. This is known as array gain or directivity index, and can be simply thought of as the ratio of the total surface area of a sphere divided by the surface area of the beam front at the same distance as the sphere.

The ability of the object to actually reflect radar back to the receiver is a very important consideration. This reflectivity is known as the radar cross section. This is a critical factor, for example, stealth fighters and bombers reflect very, very little energy back to the radar unit, although they have quite a large physical size.

Distance from the radar unit to the target is another critical factor, and is an area where the police that use the devices, and the training authorities and training manuals have it all wrong - surprising given that this is very fundamental radar theory. The police manuals state that the signal returned obeys an inverse square relationship; this is a result of the one way radar equation. The problem is that they are using the incorrect formula; the radar beam is projected and is then returned. The result is known as the two-way radar equation, and the dependence of the signal returned with distance is what is known as an inverse fourth power relationship.

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As an example, consider objects with the same radar cross-section, but one is twice as far away from the radar unit as the other. Using the one-way radar equation, you have the closer object having a signal that is received by the radar unit four times as large as the object that is twice as far away. In fact, using the correct two-way radar equation, you actually have the closer object having sixteen times the signal! Why the police and radar training manuals have this all wrong is unknown, but it is very possible that they are attempting to make out that the issue of sidelobes is relatively unimportant - certainly less important than it is in reality.

Let's have a look at the sidelobe issue. Without what is known as array shading or other signal processing schemes to reduce the sidelobe size, the first sidelobes will have a signal output that is -13dB compared to the central beam (or about 1/20th of the intensity of the centre of the main beam). So, how does this make any difference to the issue of sidelobes?

Consider two vehicles, both having the same RCS, one in the first sidelobe, and the other in the mainlobe. If we say that the vehicle in the sidelobe is at a distance of 1, how far away must the other vehicle in the mainlobe be to have the same signal strength as the vehicle in the sidelobe? Using the (wrong) one-way radar equation, the object in the main beam would have to be about 4.5 times further away. In reality, that vehicle only has to be 2.11 times further away. Think about that the next time you get pulled over!

Now, given these issues, and particularly the incorrect radar equation and sidelobe effect, it would seem that that alone is enough to question the issue of radar speed detection and target identification. Bad as that is, it is not the end of the problem, as there are a whole host of other issues that relate to incorrect target identification, as well as some issues that will result in an incorrectly displayed speed.

Next week: factors that affect radar results

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