"Through-Wall Microwatt Radar"

Fall 2008: Senior Design NRL-sponsored Project

A project focusing on through-wall radar enhancements using feed-forward cancellation of the transmitter coupling is being conducted by five of the top Electrical and Computer Engineering seniors at Michigan State University. The project runs from Sept.-Dec. 2008.

Click to read Conference Paper on System

Through-wall 0dBsm scatterers at 500 Microwatts TX power

In about 10 weeks, I built a L-band linear FM (LFM/FMCW) through-wall microwatt radar transceiver for free from "junk" parts, using coffee cans for open-ended circular waveguide antennas. The system is used from the microwatt to milliwatt level as needed by imaging demands.

"Why FMCW?"

A primary driving reason for the use of FMCW is that high-resolution imagery at shorter distances can be economically achieved. This is useful for developing imaging algorithms, since target scenes can be created at much less expense than with a pulsed radar. It's easier to sweep an oscillator's frequency in a repeatable manner than to make it pulse at the very high rate needed to achieve equivalent resolution as FMCW.

A downside is that as the "CW" implies, the transmitter is continuously on, and so with a physically small front-end unit, it may be difficult to avoid saturating the receiver's front end if high power (say over 50 Watts) is used. For the type of systems a graduate student might implement, 50 Watts is often not necessary--in fact 1 Watt may be sufficient transmit power.

We have claimed that high resolution imagery is possible with a modest FMCW system (indeed, as has been shown by Dr. Gregory Charvat and others). The physics at work here is that instead of sending a pulse and measuring the time between incidence and reflection, range frequencies are measured. This process is viewed in greatly simplified form in the graphic below.

It may be intuitively seen that if the targets are too close together, the return waveforms will overlap, and they will appear as one "blob". This issue is also known in optics, as we would expect since visible light is just another part of the electromagnetic spectrum. Thus, for high resolution imaging, shorter pulses are needed since range resolution is proportional to pulse width (smaller is better!).

Since waves travel in free space at 3·10⁸ [m/s], a distance of 1 meter will experience a round-trip time t_R of 2·1/(3·10⁸) = 6.7 nanoseconds. For about US$10,000, one can buy a 10ns width pulse generator. However, that pulse length is too long to allow us to distinguish between two targets one meter apart. The return signals will overlap--in the diagram above, t₁+t_R1 < t₀+t_R2.

For the simple pulsed radar, the following relationships exist:

ΔR ∝ Δt_R → δR ∝ τ_r, and W_τ ∝ 1/τ_r, so δR ∝ 1/W_τ, where τ_r is radar pulse duration. Thus a short width pulse and concomitantly a wide bandwidth are needed for high resolution with simple pulse radar.

An overview of the physics underlying FMCW radar is in the image below.

The FMCW range frequencies f_R originate from the difference in the number of wavelengths as the radar sweeps in frequency. Usually, the radar sweeps in a linear fashion, although non-linear sweep waveforms have also been used.

Range resolution δR is determined in part from the minimum resolvable frequency difference: δR = (cδ(ΔN)) / (2W), where δ(ΔN) = unity, for a typical case [D. G. Luck]. To get 0.5m range resolution (helping to ensure we can see two targets separated by one meter), we use 300MHz of bandwidth W as follows: δR = (c·1) / (2·300·10⁶) = 0.5m.

It is easy to obtain relatively inexpensive VCOs from sources such as Minicircuits that can sweep 900MHz of bandwidth for under US$50. Compare this to the US$10,000 cost for the pulse generator alone for the pulse radar case!

The capital N with an overdot represents the time derivative of N, the number of standing waves over the complete roundtrip path. N₀ = (2R) / λ₀.
Then, f_R = ∂N_R/∂t which are the range frequencies for each target.
f_R = t_RW / t_m shows how bandwidth W and up or down ramp time (time it takes radar frequency to sweep from lowest to highest frequency linearly) are related. Thus we can derive the range frequencies expected for a given target range.

If the target is 5 meters away from the radar antenna that is using 300MHz bandwidth with a sweep rate of 250Hz, we expect:
f_R = (2R·W) / (c·t_m) = (2·5·300·10⁶) / (3·10⁸·2·10^-3) = 5.0kHz.
5kHz is readily digitized and analyzed. So if two targets are separated by one meter, the difference in range frequency would be 1kHz, which should also be very easy to detect with modest digitizing and signal processing.

Since finite transit time exists in all real radar system components and cabling, more round-trip time (and thus higher range frequenices) will be received than the physical separation between radar antenna and targets dictate. A practical method to account for this variance is to put a calibration target at a known distance within view of the radar. The signal processing algorithm can then calibrate the received data against that known distance to relate each range frequency to an equivalent physical range distance.

From this brief, simplified discussion the cost advantage of FMCW radar for short, low-power laboratory system has been made evident. To be sure, advanced modulation techniques can be employed with pulse radar, but fundamentally a wide bandwidth through very narrow pulses is needed for a successful pulsed high-resolution radar. The cost of a pulse radar that can give equal resolution at short range to an FMCW system will generally cost far more than the FMCW radar.

References

• D. K. Barton, Radar System Analysis and Modeling. Boston: Artech House, 2005.
• L. V. Blake, Radar Range-Performance Analysis. Silver Spring, MD: Munro Publishing Co., 1991.
• D. G. Luck, Frequency Modulated Radar. New York: McGraw-Hill, 1949.
• R. N. McDonough, A. D. Whalen, Detection of Signals in Noise. New York: Academic Press, 1995.
• M. I. Skolnik, Introduction to Radar Systems. New York: McGraw-Hill, 2001.

Affordable laboratory SAR rail

Simulated response of fourth-order Sallen-Key Butterworth low-pass filter. This filter also included a 40dB gain section. The low-pass filter was to help avoid aliasing of signals in excess of 1/2 sampling rate from reaching the digitizer.