I just took a course on building a cheap coffee can antenna synthetic aperture radar organized by Lincoln Labs during MIT's Independent Activities Period. The was originally developed by Dr. Greg Charvat, formerly at Lincoln Labs, whosesite (and the tin can radar forum) has a lot more information on the project. Slides from the class, which contain a bill of materials and detailed step-by-step build instructions are available on MIT OpenCourseWare. The final product (assembled by groups of 3) looks as shown here:

The two metal coffee cans act as circular waveguides for the antennas (one is to transmit, the other to receive). These have a monopole wire probe that is attached to coaxial cables that carry the signal to and from the RF electronics. The distance between the wires and the back of the cans must be one quarter of the wavelength of the carrier frequency we use (2.4 Ghz - the ISM band, also the frequency used by wifi networks), since there is a π shift when the signal is reflected off the back wall and π/2 shifts involved in traveling back and forth from the back wall at this length, adding to a total 2π shift, maximizing signal power. Antenna design is complicated and there are a lot of DIY wifi antennas out there with different tradeoffs and all of them may be substituted for the coffee cans in this design (from my reading, the biquad design seems quite promising).

A description of the system layout (broked up into 3 distinct modules) is shown here (image taken from course slides):

The device is capable of measuring Doppler (velocity), range (distance), and being used as a synthetic aperture radar (multiple range measurements used to reconstruct a 2D projected image). Doppler mode is relatively simple - the transmit antenna puts out a constant sinusoidal wave at 2.4 GHz. The radar Doppler shift frequency is 2*velocity/wavelength (this is relatively easy to see - see the slides or Wikipedia for details). The velocity here refers to the radial velocity component of the object and the wavelength is given by c/2.4 GHz = 12.5 cm, where c is the speed of light. Therefore, a car moving at 35 mph would show a Doppler shift of roughly 250 Hz, which is in the range to be picked up by a soundcard (the data acquisition device on this system). Note however this is the Doppler shift, which means the actual signal being received is a sinusoid at a frequency of 2.4 GHz +/- 250 Hz - to convert this so that we only pick up the frequency shift, we just multiply the receive signal with the transmitted signal. Then because of the identity sin(A)sin(B) = 1/2(cos(A-B) - cos(A+B)),we will pick up the Doppler shift frequency as the sum or difference (depending on whether the imaged object is moving away from or towards the aperture) - either way we can filter out higher frequencies and only retain the Doppler shift frequency in our signal. Shown to the side is a Doppler plot of me waving my hand at varying speeds in the direction of the radar aperture.

Range measurements are a little more involved - the idea is to send out a pulsed waveform and see how long the signal takes to bounce back. The distance to the object is just 2*time delay/speed of light. In this implementation, the transmitter sends out little 20 ms long chirped pulses (with the instantaneous frequency linearly increasing from 2.4 Ghz to 2.48 GHz) with an IC that sends out linear voltage ramps to a voltage controlled oscillator. Theoretically, ranging is done by running a matched filter (with the impulse response being the transmitted chirp) and looking for a peak. Practically that is hard (impossible?) to do at RF frequencies. What is done instead is a trick called stretch processing. I have only seen this derived for linear chirp pulses, and I can see that it will not work for constant carrier frequency pulses, so my guess is that this is trick exclusive to linear chirps. The idea is that multiplying the return signal with the transmit will produce constant frequency sinusoids with the frequency proportional to the time delay (and therefore the range). This only works if the received signal is picked up while the transmit is still going, but with 20ms pulses that should be the case for any reasonable distances. For calibrating our range measurements we walked up and down a 20 m hallway and produced the image on the left below. We then pointed it out on the street and performed ranging on passing cars (image below on the right).

The final experiment we ran was synthetic aperture radar (SAR) imaging, which involves taking multiple range measurements of an object from a moving location (and we just moved it manually along a line) and processing these measurements together to resolve structure. Note that we still get 2D projections because we only moved along one dimension. We tried to image the "green building" at MIT from a breezeway connecting two other buildings looking on to it - the image of our view is on the left. The image from the data we gathered was overlaid on to a Google Earth satellite image of the same location after aligning the scale and orientation and is shown below on the right.

Wire probe |

The two metal coffee cans act as circular waveguides for the antennas (one is to transmit, the other to receive). These have a monopole wire probe that is attached to coaxial cables that carry the signal to and from the RF electronics. The distance between the wires and the back of the cans must be one quarter of the wavelength of the carrier frequency we use (2.4 Ghz - the ISM band, also the frequency used by wifi networks), since there is a π shift when the signal is reflected off the back wall and π/2 shifts involved in traveling back and forth from the back wall at this length, adding to a total 2π shift, maximizing signal power. Antenna design is complicated and there are a lot of DIY wifi antennas out there with different tradeoffs and all of them may be substituted for the coffee cans in this design (from my reading, the biquad design seems quite promising).

A description of the system layout (broked up into 3 distinct modules) is shown here (image taken from course slides):

The device is capable of measuring Doppler (velocity), range (distance), and being used as a synthetic aperture radar (multiple range measurements used to reconstruct a 2D projected image). Doppler mode is relatively simple - the transmit antenna puts out a constant sinusoidal wave at 2.4 GHz. The radar Doppler shift frequency is 2*velocity/wavelength (this is relatively easy to see - see the slides or Wikipedia for details). The velocity here refers to the radial velocity component of the object and the wavelength is given by c/2.4 GHz = 12.5 cm, where c is the speed of light. Therefore, a car moving at 35 mph would show a Doppler shift of roughly 250 Hz, which is in the range to be picked up by a soundcard (the data acquisition device on this system). Note however this is the Doppler shift, which means the actual signal being received is a sinusoid at a frequency of 2.4 GHz +/- 250 Hz - to convert this so that we only pick up the frequency shift, we just multiply the receive signal with the transmitted signal. Then because of the identity sin(A)sin(B) = 1/2(cos(A-B) - cos(A+B)),we will pick up the Doppler shift frequency as the sum or difference (depending on whether the imaged object is moving away from or towards the aperture) - either way we can filter out higher frequencies and only retain the Doppler shift frequency in our signal. Shown to the side is a Doppler plot of me waving my hand at varying speeds in the direction of the radar aperture.

Range measurements are a little more involved - the idea is to send out a pulsed waveform and see how long the signal takes to bounce back. The distance to the object is just 2*time delay/speed of light. In this implementation, the transmitter sends out little 20 ms long chirped pulses (with the instantaneous frequency linearly increasing from 2.4 Ghz to 2.48 GHz) with an IC that sends out linear voltage ramps to a voltage controlled oscillator. Theoretically, ranging is done by running a matched filter (with the impulse response being the transmitted chirp) and looking for a peak. Practically that is hard (impossible?) to do at RF frequencies. What is done instead is a trick called stretch processing. I have only seen this derived for linear chirp pulses, and I can see that it will not work for constant carrier frequency pulses, so my guess is that this is trick exclusive to linear chirps. The idea is that multiplying the return signal with the transmit will produce constant frequency sinusoids with the frequency proportional to the time delay (and therefore the range). This only works if the received signal is picked up while the transmit is still going, but with 20ms pulses that should be the case for any reasonable distances. For calibrating our range measurements we walked up and down a 20 m hallway and produced the image on the left below. We then pointed it out on the street and performed ranging on passing cars (image below on the right).

The final experiment we ran was synthetic aperture radar (SAR) imaging, which involves taking multiple range measurements of an object from a moving location (and we just moved it manually along a line) and processing these measurements together to resolve structure. Note that we still get 2D projections because we only moved along one dimension. We tried to image the "green building" at MIT from a breezeway connecting two other buildings looking on to it - the image of our view is on the left. The image from the data we gathered was overlaid on to a Google Earth satellite image of the same location after aligning the scale and orientation and is shown below on the right.

As we found out after looking at the images - SAR (and radar in general) works better at finding edges since the waves reflect off of walls and straight surfaces and don't reach the receive antenna, but diffract at edges and scatter in all directions. The radar seems to have picked up one corner of the building and possibly some trees in a row to the left (in the images). The other signal on the right is a processing artifact and is not within the field-of-view of the radar. Other teams did seem to have more success by imaging from a better vantage point and gathering more data (we gathered images every 2 inches for 10 feet, some people did 20 feet). Also, increasing the bandwidth of the pulse from the 80 Mhz recommended to us can improve resolution and signal-to-noise.

Overall, it was a fun experience and I learned a lot in 4 days (and whetted my appetite to learn more about radar, antennas and microwave electronics...I was already into the signal processing prior to this). Thanks to my team (Shana, Alex and me) and to Lincoln Labs for their time in putting this together (and the free radar, which I got to keep!).