Radartutorial .euFrequency-Modulated Continuous-Wave Radar
echo signal
Figure 1: Ranging with an FMCW system
echo signal
Figure 1: Ranging with an FMCW system
CW radars have the disadvantage that they cannot measure distance, because it lacks the timing mark necessary to allow the system to time accurately the transmit and receive cycle and convert the measured round-trip-time into range. In order to correct for this problem, phase or frequency shifting methods can be used. In the frequency shifting method, a signal that constantly changes in frequency around a fixed reference is used to detect stationary objects and to measure the rage. In such a Frequency-Modulated Continuous Wave radars (FMCW), the frequency is generally changed in a linear fashion, so that there is an up-and-down or a sawtooth-like alternation in frequency. If the frequency is continually changed with time, the frequency of the echo signal will differ from that transmitted and the difference Δf will be proportional to round trip time Δt and so the range R of the target too. When a reflection is received, the frequencies can be examined, and by comparing the received echo with the actual step of transmitted frequency, you can do a range calculation similar to using pulses:
| R = | c0 · |Δt | | = | c0 · |Δf | | where: | c0 = speed of light = 3·108 m/s Δt = measured time-difference [s] R = distance altimeter to terrain [m] df/dt = transmitters frequency shift per unit time |
(1) |
| 2 | 2 · (df/dt) |
Accordingly, measuring the difference between the transmitted and received frequencies gives the range to the stationary target. It is generally not easy to make a broadcaster that can send out random frequencies cleanly, so instead these frequency-modulated continuous-wave radar, use a smoothly varying “ramp” of frequencies up and down. If the frequency modification is linearly over a wide area, so within this region by a frequency comparison Δf, the distance can be determined on a simple way. Since that only the absolute value of the difference can be measured, the results with increasing frequency modification equal to a decreasing frequency change at a static scenario. Sawtooth modulation forms are preferred for imaging radar; triangular shaped modulation is used more for non-imaging radars.
Characteristic feature of an FMCW radar is:
- the distance measurement is done by comparing the actual frequency of the received signal to a given reference (usually direct the transmitted signal);
- the duration of the transmitted signal is much larger than the time required for measuring the installed maximum range of the radar.
By suitable choice of frequency deviation per time unit can be varied the radar resolution, and by choice of the duration of the time of the frequency shift the maximum range can be varied. For example, a radar with a linear frequency increase over 1 ms duration can measure a time-limited maximum range of nearly 150 km. If the maximum frequency deviation is 250 MHz, then stay about 6.6 kHz per meter for the filter for analysis. Of course, the amount of frequency modulation must be significantly greater than the expected Doppler shift or the results will be affected. The simplest way to modulate the wave is to linearly increase the frequency. In other words, the transmitted frequency will change at a constant rate.
Figure 2: Strip-line patch antenna of maritime FMCW- navigation radar operating in X-Band
As a result of the proceedings (simultaneous transmission and receiving), a ferrite circulator shall make the separation of transmit and receive path, when using a single antenna. But using of separate transmitting and receiving antennas is much cheaper in today's common used patch antennas in strip-line technology. On a common substrate transmitting and receiving antenna are mounted directly above each other as an antenna array. The direction of the linear polarization is rotated against each other by 180 degrees. An additional shielding plate reduced a direct "cross talk" (i.e. a direct coupling of both antennae) often. Since the measurement is performed to as a frequency difference between transmit and receive signal, the signal that arises from this direct coupling is suppressed due to the same frequency.
Imaging FMCW Radar
This radar method is used in so-called Broadband Radar™ as a navigation radar for maritime applications. Here, the frequency sweep after reaching the maximum measuring distance is, however, stopped. The transmitted signal looks more like the signal from a pulse radar using intra pulse modulation therefore. This break, however, has no direct effect on the maximum measuring distance, in contrast to the pulse radar. However, it is necessary to read the very many measured data from a memory buffer, and to transmit this data without loss through a narrow-band line to the radar scope. Because of its principle of operation – frequency comparison of the received echo signal with the transmitted signal, which is available over the whole range sweep – it remains an FMCW radar. The transmitter is switched off for a few milliseconds only, as more data are simply not needed.
An imaging radar carries out a distance measurement for each point or pixel on the monitor. The radars range resolution depends more on the size of a pixel on this screen therefore, and depends on the capacity of signal processing to provide the data in the required speed.
With the above as example given frequency deviation of 65 MHz per millisecond we can get good values.
- For an unambiguous runtime measurement hereby only a maximum of 500 microseconds can be measured, (see Figure 1) corresponding to a possible measurement range within 75 km.
- The frequency deviation of 65 MHz per millisecond corresponds to a change in frequency of 65 hertz per nanosecond. If the subsequent filters are technically capable of dissolving frequency differences of 1 kilohertz, then herewith a measurement of runtime differences of 15 nanoseconds is possible, corresponding to a range resolution of about 2 meters.
- If the maximum processable difference frequency by evaluating circuit is two megahertz (which already can manage simplest single-chip microcomputer), then distances up to 4000 meters can be measured. (Without a microcontroller would have to be operated 4000 different individual filters in parallel.)
- Caused by the measurement procedure here is the precision of the measurement is approximately equal to the range resolution, and is further limited by the resolution of the screen scale.
This FMCW radar can achieve with relatively little technical effort, a high spatial resolution. To achieve the same spatial resolution with a pulsed radar, this one must be able to measure the runtime in steps of 15 nanoseconds. This means, that this one pulse radar must have a transmitter's bandwidth of at least 80 MHz, and it must use a sampling rate of 166 MHz for digitization of the echo signals.
Non-Imaging FMCW Radar
Figure 3: Analog indicator of a radar altimeter
The measurement result of this FMCW radar is shown as a numerical value on a moving coil meter or digitized as alpha-numeric symbols on a screen. It can only be a single dominant object to be measured, but of this with a much high degree of accuracy down to the centimeter range. The most common form of FMCW radar is the radar altimeter used on aircraft to determine height above the ground, especially during the landing procedure of aircraft.
A possible Doppler frequency fD is displayed on the moving coil meter as a measuring error. The gradient of the slope can be chosen that the influence of the Doppler frequency is very small in contrast to the measured frequency difference. An analysis of the Doppler frequency is possible by using a triangular shaped modulation and a separate frequency comparison during the rising and falling side of the triangle shaped modulation. For a reflective object with a positive (moving towards the radar) radial velocity the entire received signal will be moved by the Doppler frequency to higher frequencies. Compared to a fixed reflector, the frequency difference between transmit and receive signals on the rising edge of the triangle is reduced by the Doppler frequency and increased on the falling edge by the Doppler frequency. The difference between the two difference frequencies is therefore twice the Doppler frequency. Since both of difference frequencies are not available simultaneously, therefore this comparison, however, requires a digital signal processing.