6.2 Results and Analysis
6.2.3 Interference Rate
The objective of this experiment is to test the expressions of the expected interference rate. Each experiment comes with three values, the experimental interference rate, the simulated interference
rate and the expected interference rate (expressions). The expression in evaluation is (see 4.3.3):
P(ti∈D) = ∆ TB
DB (6.2.6)
The setup for this experiment is the same as explained in the last chapter. Each plot point refers to an unique set of radars experiments. The interference trigger comes from a threshold detection (value obtained empirically) as the Figure 6.10 suggests. For every chirp transmitted is computed the FFT of the corresponding received signal, if the resultant signal is bellow the it is considered that there was no interference.
Interference detected
No interference detected
Figure 6.10: Two possible outcomes for the Fourier-Transform for a front-end RF output for the transmission of a chirp from the experiment. Thetopplot shows an example of a detected interference and thebottomplot no interference is detected.
6.2.3.1 Experiment 1: Equal chirps
For the first experiment is chosen equal parameters for each radar, present in the Table 6.3. Varying from run to run, the frequency slope, or consequently, the bandwidth of each chirp. The only differ-ence from the observer (the receiver radar A) and the interferer (the transmitting radar B) is the chirp period avoiding that way both signals to synchronize with each other. The results are presented in the Figure 6.11, where the experimental and simulated interference rate was calculated from100frames, each containing128chirps, resulting in a total of12800chirps.
Parameter Radar A(effective) Radar B
Freq. Slope (MHzµs−1) [0.25, 0.5, ..., 2.5] [0.25, 0.5, ..., 2.5]
Chirp Duration (µs) 40 (25.6) 40
Chirp Period (µs) 45 47
Initial Frequency (GHz) 77 (+[0.0015, 0.003, ..., 0.015]) 77
Idle time (µs) 5 (29.4) 7
Duty-Cycle - 0.859
Table 6.3: Radar parameters for the Experiment 1.
0 0.5 1 1.5 2 2.5 Slope (MHZ/us)
0 0.2 0.4 0.6 0.8 1
Interference Rate
Radar A chirp interference rate
Preal Psim Pexpected
Figure 6.11: Interference rate for identical chirps experiment.
The expected interference rate matches the simulated and theorical interference chirp probability, except for the first two points. Figure 6.12 is a frame retrieved from the Experiment 1. In the top plot, is seen the FFT of the radar RF output where the yellow refers to highest energy and blue to low energy. The second plot comes from applying the threshold to the first plot. Yellow is interference, while blue is below the interference threshold.
Figure 6.12: Interference pattern for the equal chirps experiment.
Because in the experience 1 the both radars chirps parameters have the same slopeS, then the instantaneous frequency of the interference pattern from equation 3.3.6:
f(t) = (Si−Sk)t−Skδi,k + (Fi−Fk)
= (Fi−Fk)−Skδi,k (6.2.7)
From the model it is expected that the interference frequency band is a simple frequency tone.
But, as it seen the Figure 6.12, each chirp house contains a frequency spread∆F that gets picked up in the interference threshold. This phenomenon could explain a slight increase in the interference rate, especially for lower values of slope. Where low slopes lead to low bandwidth and step outside of the optimal/linear radar working bandwidth.
6.2.3.2 Experiment 2: Similar chirps
For the second experiment it was chosen different parameters (see Table 6.4) for each radar configu-ration. Furthermore, for each run is varied the frequency slope of the interferer radar B, ranging from no slope to double the observer radar slope, containing one run with equal slope. The experimental and simulated interference rate was calculated from100frames, each containing128chirps, resulting in a total of12800chirps.
Parameter Radar A(effective) Radar B
Freq. Slope (MHzµs−1) 4 [0, 0.4, 0.8, ..., 7.6, 8.0]
Chirp Duration (µs) 40 (25.6) 100
Chirp Period (µs) 55 57
Initial Frequency (GHz) 77 (77.006) 77
Idle time (µs) 5 (29.4) 7
Duty-Cycle - 0.776
Table 6.4: Radar parameters for the Experiment 2.
0 1 2 3 4 5 6 7 8
Radar A (Slope = 4 MHz/us) chirp interference rate
Preal Psim Pexpected
Figure 6.13: Interference rate for similar chirp experiment.
In the Figure 6.13 are plotted the interference rate resulted from simulationPsim, the algebraic expressionsPexpected and from the practical results Preal. These three type results match for every combination of values of the experiment 2.
The results plot from the Figure 6.13 has some interesting points. Starting for radar B chirp slope equal0 MHzµs−1where the interference rate is0. As the radars chirps share bandwidth (for example the initial frequencyF0(A)−F0(B)= 0∈F), it is expected a non null interference rate. But because the observer radar has a delay between transmission and the first sample, the effective initial frequency isF00(A)= 77 GHz. Thus the minimum frequency from the RF front-end isF00(A)−F0(B)= 6 MHz which is outside of the in-band frequencyF. Concluding that for this point direct interference is impossible and the effective parameters are important to resolve the expected interference rate.
The second point of interest, is the run for same frequency slopes. For chirps with equal fre-quency slopes the mixing output it will be a sinusoidal signal with a constant frefre-quency tone. While chirps with different frequency slopes, the mixing output will have interference signal with a larger bandwidth footprint. For this reason, it is expected, and supported by this experiment, a minimum interference rate for equal slopes.
6.2.3.3 Experiment 3: Sweep effect on different slopes
As for the third experiment is looked upon the influence of chirp period has on the interference rate.
For that is chosen parameters that maintains the interference rate constant across runs (see Table 6.5).
The experimental and simulated interference rate was calculated from100frames, each containing 128chirps, resulting in a total of12800chirps.
Parameter Radar A(effective) Radar B
Freq. Slope (MHzµs−1) 4 2
Chirp Duration (µs) 50 (25.6) 50
Chirp Period (µs) 60 [51, 52, 53, ..., 69, 70]
Initial Frequency (GHz) 77 (77.006) 77
Idle time (µs) 10 (34.4) [1, 2, 3, ..., 19, 20]
Duty-Cycle - [0.6945, 0.7081, ..., 0.9532]
Table 6.5: Radar parameters for the Experiment 3.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
TA - TB 10-5
0.2 0.3 0.4 0.5 0.6
Interference Rate
SA/SB = 2
Preal Psim Pexpected
Figure 6.14: Interference rate in function of the chirp period experiment.
The interference rate results from the Figure 6.14 show the expected constant interference rate was achieved. Although it is noticeable that the variability changes for different values of chirp period.
The previous examples, were designed to a have a sporadic interference as the Figure 6.15. Therefore by lowering the number of interference per frame variability, allows to lower the number of runs per experiment to achieve a satisfactory precision.
Figure 6.15: Sporadic interference pattern forTA−TB=−4µs.
This experiment confirms, that sporadic nature of the interference rate is influenced by the chirp periodicity. By looking at the spike for the run withTA−TB = 0µs frame from the Figure 6.16, shows that by there is one interference, therefore the following chirps are interfered until one of the frames ends. Therefore it is common to see frames with a high numbers of chirps interfered, and frames such as the Figure 6.17 with no interference.
Figure 6.16: Frame with interfered chirps burst. Figure 6.17: Frame without interfered chirps.
Chapter 7
Conclusion
7.1 Conclusion
In this work the study of direct interference between FMCW radars is approached. In order to study the effects of the interference, it was created an algebraic expression that outputs the expected chirp interference rate. This study allows to understand the effect of each radar parameters on the radar system, it may be possible to reduce or eliminate the chirp interference rate within the radar system.
The expressions were inspired by set theory in order to better gather the numerous conditions that limit the interference rate, such as the frequency window and the chirps duration, to reduce the complexity of the FMCW radar signal, and lastly, to translate to a more efficient use of the simulation in regards to time and memory used.
The created simulators serves two purposes: first to allow to simulate interference between two radars with different configurations, supporting the expressions interference rate output. Second it gives an intuitive way to visualize and understand the interference behavior.
In every experiment, the practical work results matches the expected interference rate from the algebraic expressions and the simulations results. Although, there is a slight mismatch in the equal chirps experiment from the experimental to the simulator and expressions value.