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Massachusetts Institute of Technology
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The "Cantenna Radar" is a radar project that we (Tony Hyun Kim, Nevada Sanchez, Paresh Malalur) assembled from a kit provided by Lincoln Labs for an IAP 2011 course at MIT. The name "Cantenna" derives from the fact that the antenna actuators are actually recycled coffee cans! Photographs and basic schematic of the device are shown below:
In this page we document the various experiments that we were able to undertake with the project:
Some neat facts about the coffee-can antenna, before we get started:
Doppler radar:
The project was first configured to measure the Doppler shift in the reflected RF signal, in order to measure the speed of the reflecting object. We calibrated the system by measuring the free-fall of a massive object (the textbook "Signals and Systems" by Oppenheim and Willsky) and then calibrating the free-fall acceleration to 9.8m/s^2.
We then went out to the corner of Mass Ave and Memorial, and measured the speed of vehicles as they stopped at and started from a stoplight:
Cars coming to a stop at the stoplight.
Cars beginning to move after the light turns green.We also took some measurements of cars on the Memorial underpass:
Ranging:
The scheme for CW ranging is a bit trickier, so I'll spend a little more time discussing the technical aspects. The basic idea is to utilize a frequency chirp (which the VCO can do very easily) in order to give a unique temporal "marker" to the transmitted radiation. I start with a simple numerical example.
Numerical example:In the time domain, a frequency-chirped signal may look like the following blue curve:
In this example, the transmitted signal has a symmetric triangular chirp of period T=20, whose min and max frequencies are 0.5 and 5 respectively. The red signal shows a delayed version of the transmitted signal, as may be the case from an ideal reflector some distance away. The time delay of the reflected signal is directly proportional to the relative distance between the radar system and the reflector.
The mixer on the radar then takes the product of the transmitted (LO) and received (RF) signals and produces the following complicated curve (IF):
The two panels below the time-domain signal illustrate two alternative representation of the mixer output. In the second panel, the mixer output is represented as the product of two sinusoids with instantaneous frequencies as identified in the curves. In the third panel, the mixer output is the superposition of the instantaneous sum and difference frequencies.
Now, we are interested in the relative time delay between the transmitted (blue) and received (red) signals. For a known chirp slope (which we fix in hardware), it is clear that the relative delay can be computed by identifying the instantaneous difference frequency, which is ultimately proportional to the target range. We can use additional processing tricks to help us in the identification of the difference frequency; namely, we use a LPF to remove the sum frequency as shown below (read panels clockwise from top left):
Thus, aside from the expected glitches at the turning points of the chirp, the LPF output of the mixer (lower-left panel) shows a sinusoid whose frequency is proportional to the range of the target.
Real life:In actual practice, the radar signal turned out to be quite a bit more complicated. Presumably, this has to do with the various entities in the radar's environment that contribute to the reflection signal (shown below, blue curve). The red square wave marks the frame of the triangular chirp.
Where's the clean sinusoid?! In the case of the Doppler/velocity measurements, we immediately obtained beautiful raw radar data, since by the nature of the measurement, we were sensitive to only actively moving targets, which made identification of signals obvious. On the other hand, with range measurements, the system is now susceptible to static clutter in its environment, thereby necessitating further mathematical processing to reveal the relevant signal. The suggested technique by Lincoln Labs staff was to take differences between succesive chirp periods. Such a technique would preserve range data from moving targets (say, a running MIT student) but remove static fixtures of the environment.
Data analysis:One of the first range measurements (running down the second-floor hallway in Building 26) is shown below. The spectrogram is computed by taking the Fourier transform of successive differences.
While the motion signal is readily apparent, the above scan is marred by horizontal "noise striations", which is especially visible between t: 12~25s.
My suspicion was that the noise striation arose from timeframe errors in the successive differencing technique. Given the audio sampling rate (44.1kHz) used in this radar system, we will certainly fail to identify the exact chirp frame. Given the successive differencing scheme, such timeframe errors can give rise to spurious frequency content which will show up in the spectrogram as noise.
This hypothesis was investigated by taking differences of a single-frame radar signal respect to its time delay. This simulates a timeframe error in a perfectly-still environment. We then found the following "frequency signature" (bottom panel) of timeframe errors:
Comparing the spectrum of the frame-error signal to the range spectrogram, we found that the peaks line up with the locations of the striations, providing strong evidence that the striations are produced by timeframe errors in the differencing scheme.
A cheap way to counteract the timeframe error is to modify the differencing technique. Rather than taking difference of the successive samples in the time domain, for which good timeframe resolution is required, we opted for taking the differences of the Fourier transform magnitudes. (In theory, frame errors have no effect in the magnitude of the transform.) We then immediately obtained the improved range spectrogram (original shown again for comparison):
Tracking of two people in the same Building 26 hallway. The person nearer to the radar ocassionally blocks the line-of-sight to the further-away target. I also calibrated the frequency to a distance using a meter stick along the hallway.
SAR Imaging:
We then modified the radar assembly to lock onto a ~9 ft makeshift rail made of spare 80-20 parts. By taking multiple range measurements at various points along the rail, we can combine the information to produce an image of the environment. The information is stitched together using a SAR (Synthetic Aperture Radar) algorithm, provided by Lincoln Labs. We were able to take some neat photos of MIT!
Here we are, lugging the radar+rail assembly across campus:
This is what the SAR imaging setup and process looks like:
Now, various images of the MIT campus!
Green building:
