Effect of Phase Noise in Doppler Radar Systems

As with many radar systems, Doppler radar systems include a transmitter that sends out a signal over an area that it is under surveillance. Moving objects in this area will reflect a signal, whose fundamental frequency has shifted as a function of the object’s velocity, back to the radar receiver. Slow moving objects, which produce small Doppler shifts in the reflected signal’s frequency, can only be detected if the radar system’s phase noise at the reflected frequency is less than the power of the reflected signal. Similarly, fast moving objects will reflect a signal with a larger Doppler shift that can only be detected if the radar system’s phase noise at the reflected frequency is less than the power of the reflected signal.

The phase noise of low phase noise oscillators is higher at frequency offsets closer to the carrier. Therefore, it can be more difficult to detect slow moving objects, like jeeps, than it is to detect fast moving objects, like aircraft.  In order to build a radar system that can track both slow and fast moving objects, the phase noise of a radar system over a wide span of offset frequencies is essential.

For example, let’s examine a Doppler radar, with a transmission frequency, f, that is used to detect a fast supersonic aircraft as well as a relatively slowly moving vehicle, such as a jeep. The signal reflected by the aircraft will be at a frequency that is shifted approximately 10 kHz from the originally transmitted signal and will be at a much lower power. Figure 1 below shows the signal being transmitted by the Doppler radar system while Figure 2 shows the signal reflected back toward the radar. Figures 3 and 4 show the frequency content of the transmitted and reflected signal, respectively.

Figure 1_3 Figure 2_3
Figure 3_3 Figure 4_3

In order to positively identify the aircraft, the phase noise at 10 kHz from the transmitted signal, f + 10 kHz, must be less than the power of the reflected signal at f + 10 kHz. Figure 5 shows the overlay of the transmitted signal and the reflected signal. Since the noise of the reference oscillator at f + 10 kHz is significantly less than the noise of the reflected signal, there is a high probability of the radar detecting the aircraft.

Figure 5_3

As a second example, let’s look at the ability of a radar system to detect a slow moving jeep, which would reflect a signal that is approximately 70 Hz offset from the transmitted signal. Figures 6 and 7 show the signal transmitted by the radar followed by the reflected signal. Assume the same signal is transmitted as shown in Figure 3 above. Figure 8 shows the frequency content of the signal reflected back by the jeep at f + 70 Hz, 70 Hz from the originally transmitted frequency. By examining the overlay of the transmitted frequency on the reflected frequency in Figure 9, we see that, when received, the jeep’s reflected signal has about the same amount of power as the signal transmitted by the radar. Therefore, the probability of detection by the radar system is minimal. Improving the probability of detection of these jeeps would require the phase noise of the radar transmission system at f + 70 Hz to be reduced.

Figure 5_3

As a second example, let’s look at the ability of a radar system to detect a slow moving jeep, which would reflect a signal that is approximately 70 Hz offset from the transmitted signal. Figures 6 and 7 show the signal transmitted by the radar followed by the reflected signal. Assume the same signal is transmitted as shown in Figure 3 above. Figure 8 shows the frequency content of the signal reflected back by the jeep at f + 70 Hz, 70 Hz from the originally transmitted frequency. By examining the overlay of the transmitted frequency on the reflected frequency in Figure 9, we see that, when received, the jeep’s reflected signal has about the same amount of power as the signal transmitted by the radar. Therefore, the probability of detection by the radar system is minimal. Improving the probability of detection of these jeeps would require the phase noise of the radar transmission system at f + 70 Hz to be reduced.

Figure 6_3 Figure 7_3
Figure 8_3 Figure 9_3

In Radar systems the phase noise from the LO normally dominates over other sources. The phase noise for a typical LO has two
components:

• Device noise or white noise – uncorrelated sample-to-sample;

• Flicker noise which caused a random walk – strongly correlated between adjacent samples.

This is where it can be useful to utilize the Allan Deviation measurement to characterize the phase noise of the LO and determine the effect of averaging. A graph of Allan deviation is shown below. It shows the stability of the device improving as the averaging period (Tau symbol ) gets longer, since some noise types can be removed by averaging. At some point, however, more averaging no longer improves the results. This point is called the noise floor, or the point where the remaining noise consists of non-stationary processes such as aging or random walk. The device in the graph has a noise floor of about 5 x 10-11 at Tau symbol = 100 s.

adevgraph

The Allan deviation is also used to identify types of oscillator and measurement system noise. The slope of the Allan deviation line can identify the amount of averaging needed to remove these noise types, as shown in the graph below. Note that the Allan deviation does not distinguish between white phase noise and flicker phase noise.

adevnoise

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