Estimation and Cancellation of In terferences in Automotiv e Radar Signals
Jonathan Bec h ter, Kushan Deb Bisw as, and Christian W aldsc hmidt
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DOI: -

Estimation and Cancellation of Interfer ences
in A utomoti ve Radar Signals
J onathan Bechter , K ushan Deb Biswas, Christian W aldschmidt
Institute of Micro wa ve Engineering
Ulm Uni versity , German y
email: [email protected]
Abstract: Radar sensors become typical components for automotive driver assistance
systems and autonomous driving . The widespr ead use of this sensor type leads to an
incr easing risk of unwanted interfer ences. Those interfer ences can se ver ely de grade the
detection performance and cause sensor blindness. T o over come this pr oblem, this paper
describes a method to estimate and r emove interfering signals in data of c hirp sequence
modulated radar s. The estimation is derived theor etically and applied on simulation and
measur ement data.
1. Intr oduction
Future generations of v ehicles in the ci vil sector get equipped with dri ver assistance systems for
safety and comfort functions. These systems rely on a v ariety of sensors, of which one typical
kind is the radar sensor . Thus, the amount of radar sensors which operate at the same time in
the same frequenc y range increases, leading to a high risk of unwanted interferences between
them.
In v estigations on the interference potential and ef fects between FMCW (frequency modulated
continuous wa ve) radars sho wed that such interferences can se v erely decrease the detection
capability of the sensors [1, 2]. The most common interference scenario is an intersection of the
frequenc y ramps transmitted by dif ferent sensors [3]. Such interference increases the recei ver’ s
noise floor and can lead to a sensor blindness. Especially tar gets with a lo w radar cross section,
like pedestrians, cannot be detected reliably an ymore due to this ef fect.
This paper addresses interferences between FMCW radars with short frequenc y ramps (chirp
sequence radars). The generation of such interferences is described in Section 2. As a counter -
measure we de veloped a method to remo ve the interference from the recei ve signal [4]. This
work w as carried on and an improv ed v ersion of this method is deri ved in Section 3. Its ef fec-
ti vity is demonstrated with data from a chirp sequence modulated radar in Section 4. The results
are compared to a common interference countermeasure, the notch approach.
The 18th International Radar Symposium IRS 2017, June 28-30, 2017, Prague, Czech Republic
978-3-7369-9343-3 c
 2017 DGON
1

2. A utomotiv e Radar Interference
A chirp sequence radar transmits a series of linear frequenc y ramps (chirps) of the form
s Tx ( t ) ∝ cos  2 π Z  f c + B
T c
t  dt  . (1)
A single chirp has the duration T c , the carrier frequency f c , and the bandwidth B . The ramps
are reflected from objects in the radar channel and return to the sensor after a time delay τ .
The transmit and recei ve signal are mix ed and afterwards filtered with a lo w-pass filter (LPF)
according to Fig. 1. The baseband signal of the k -th chirp is [5]
s BB ( t ) = A BB cos 2 π  2 f c R
c + 2 f c v
c k T r2r +  2 B R
cT c
+ 2 f c v
c  t  ! . (2)
v and R are v elocity and distance of a tar get, T r2r is the time between two chirps, and c is
the speed of light. The signal has the amplitude A BB . The baseband signal is digitized with an
analog to digital con v erter (ADC) and processed with a windo w function and a two-dimensional
F ourier T ransform to e xtract range and v elocity . In this work, a Kaiser windo w with β = 5 is
applied.
s Tx ( t )
LPF
Amp
Tx
Rx
ADC
Ramp Generator
s Tx ( t - τ )
s BB ( t )
B Rx
Figure 1 : Simplified block diagram of a chirp sequence radar .
In Fig. 2a two sensors operate at the same time and their frequenc y ramps intersect. Interference
occurs in the baseband signal of sensor 1 as long as the interfering signal falls into the recei ver
bandwidth B Rx limited by the lo w-pass filter in Fig. 1. The interference baseband signal is a
time-limited frequenc y ramp with a high amplitude le vel. Its duration is [2]
T Int = 2 B Rx
B Int
T c, Int − B
T c
(3)
B Int and T c, int thereby describe the bandwidth and ramp duration of the interfering radar sensor .
The time-frequenc y beha vior is determined by the slopes of the transmitted chirps [2, 4]. The
interference baseband signal is described generally as
s Int ( t ) = A Int cos ϕ Int ( t ) (4)
2

f
t
s Tx,2 ( t )
s Tx,1 ( t )
Interference
B Rx
(a) The frequency ramps of tw o sensors intersect.
This leads to unwanted interference.
0 200 400 600 800 1 , 000
− 20
− 10
0
10
20
Samples
Amplitude (a.u.)

(b) Simulated baseband signal of sensor 1 with an
ideal LPF in the recei ve path.
Figure 2 : T w o sensors transmit frequency ramps s Tx,1 ( t ) and s Tx,2 ( t ) and interference occurs. Its duration is limited
by the recei ver bandwidth B Rx . The baseband signal is affected by a short chirp with a high amplitude.
with
ϕ Int ( t ) = at 2 + bt + c, (5)
a = π  B Int
T c, Int
− B
T c  . (6)
The parameters b and c are determined by the point in time when the interference occurs and
the zero phases of the signals, b ut they are not further specified here. Equation (5) sho ws that
the phase of the interference signal follo ws the form of a parabola. For an interfering signal
which completely intersects B Rx as in Fig. 2a, the v erte x of the parabola is the center of the
interference duration. At this point, the frequenc y of the do wn con verted interference signal is
zero.
3. Interfer ence Signal Estimation
In this section, phase and amplitude of the interfering signal are estimated. It is assumed that
the amplitude of the interfering signal is much higher than the amplitudes of the desired sig-
nals (cp. [1]), so the signal part af fected by interference can be detected with a power detec-
3

tor [6]. It is assumed that the interfered recei ve signal s BB, Int ( t ) is comple x and of the form
s BB, Int ( t ) = s BB ( t ) + s Int ( t ) (7)
s BB ( t ) = X
n
A BB ,n (cos ϕ BB ,n ( t ) + j sin ϕ BB ,n ( t )) (8)
s Int ( t ) = A Int (cos ϕ Int ( t ) + j sin ϕ Int ( t )) (9)
s BB ( t ) is the complex, interference-free recei v e signal for n tar gets. The time deriv ati v e of the
comple x signal is
d
dt s BB,Int ( t ) = d
dt s BB ( t ) + A Int  j cos ϕ Int ( t ) − sin ϕ Int ( t )  d
dt ϕ Int ( t ) . (10)
(11)
The deri v ativ e of the mono-frequent baseband signals is
d
dt s BB ( t ) = X
n
A 0
BB ,n ( j cos ϕ BB ,n ( t ) − sin ϕ BB ,n ( t )) . (12)
The ratio of real to imaginary part in (10) is
Re ( d
dt s BB ( t ))
Im ( d
dt s BB ( t )) = − A Int sin ϕ Int ( t ) d
dt ϕ Int ( t ) − P n A 0
BB ,n sin ϕ BB ,n ( t )
A Int cos ϕ Int ( t ) d
dt ϕ Int ( t ) + P n A 0
BB ,n cos ϕ BB ,n ( t ) (13)
= − sin ϕ Int ( t ) − x P n A 0
BB ,n sin ϕ BB ,n ( t )
cos ϕ Int ( t ) + x P n A 0
BB ,n cos ϕ BB ,n ( t ) ≈ − sin ϕ Int ( t )
cos ϕ Int ( t ) , (14)
with
x = 1
A Int d
dt ϕ Int ( t ) . (15)
Equation (14) approximates that
x X
n
A 0
BB ,n sin ϕ BB ,n ( t ) ≈ x X
n
A 0
BB ,n cos ϕ BB ,n ( t ) ≈ 0 . (16)
It was sho wn in simulations that the deri v ati ve of the signal is dominated by the interference
component [4], so the abo v e approximation is v alid. The only exception is the time period when
dϕ Int ( t ) /dt ≈ 0 . This inaccuracy is visible at the v ertex of the parabola in the later sho wn Fig 6a.
It can be seen that (14) holds an estimation ˆ ϕ Int ( t ) of the phase of the interference component:
Re ( d
dt s BB ( t ))
Im ( d
dt s BB ( t )) = − tan ˆ ϕ Int ( t ) . (17)
In the ne xt step, the amplitude A Int is determined. Therefore, an initial real-v alued interference
signal is calculated as
ˆ s Int ( t ) = ˆ
A Int cos ˆ ϕ Int ( t ) , (18)
4

with an arbitrary v alue ˆ
A Int . W ith a scaling factor α , the real-v alued interference-free signal is
estimated as
ˆ s BB ( t ) = s BB,Int ( t ) − α ˆ s Int ( t ) (19)
or in a discrete notation as
ˆ s BB ( k T s ) = s BB,Int ( k T s ) − α ˆ s Int ( k T s ) , (20)
with the sampling time T s . The signal po wer is then
P 0 ( α ) = 1
M X
k
( s BB,Int ( k T s ) − α ˆ s Int ( k T s )) 2 . (21)
There, k accesses all interfered samples and M is their total number . The power of the
interference-free signal is called P . The dif ference of these po wers is described with a func-
tion
g ( α ) = P 0 ( α ) − P ≥ 0 . (22)
F or an optimum v alue of α , the interference is remov ed completely from the signal and the
function reaches a minimum. This leads to
dg ( α )
dα = d
dα P 0 ( α ) !
= 0 (23)
1
M X
k
2 · ( s BB,Int ( k T s ) − α ˆ s Int ( k T s )) · ( − ˆ s Int ( k T s )) = 0 (24)
and finally
α = P k ˆ s Int ( k T s ) s BB,Int ( k T s )
P k ˆ s Int ( k T s ) 2 . (25)
After α is determined with (25), the interference is remo v ed completely with (19).
Equations (7) to (17) assumed comple x recei ve signals, which can be achie ved with an IQ
recei ver . Ho we ver , an IQ recei ver is typically not required for chirp sequence modulated radars.
Thus, the imaginary signal part required in (9) is calculated with a Hilbert T ransform. The
simulation of an interfered signal in Fig. 3 compares the imaginary part generated with an IQ
recei ver and the imaginary part calculated with the Hilbert T ransform of the corresponding real
v alued signal. Half of the interfered signal part fits very well, b ut the other half is phase shifted
by π . The phase error occurs after the phase ϕ Int ( t ) reaches the verte x of the parabola described
in (5). At this point, the frequenc y of the interfering signal shifts from positi ve to ne gati ve v alues
or vice v ersa. The Hilbert T ransform cannot describe this behavior , as it does not provide the
additional information generated with an IQ recei ver .
It is also possible that the observed phase shift of π occurs before the v ertex is reached. An yway ,
the issue is solv ed by in verting the first half of the interfered si gnal. The imaginary part created
this way is then correct or multiplied by a f actor − 1 . In the second case, the negati ve sign is
carried on to (17). Due to the tangent in verse, it leads to a phase error of π in ϕ Int (t), which is
again a f actor − 1 . When α is calculated with (25), this error is corrected automatically . Thus,
the Hilbert T ransform can be used when an IQ recei v er is not a vailable.
5

26 26 . 5 27 27 . 5 28 28 . 5 29 29 . 5 30
− 1
− 0 . 5
0
0 . 5
1
T ime in µ s
Amplitude (a.u.)
Imaginary part
Hilbert T ransform

Figure 3 : Simulati ve comparison of the imaginary part generated by an IQ recei ver and the result of a Hilbert
T ransform applied on the data in Fig. 2b.
4. Evaluation of the Method
In this section, the described method is v erified with simulation and measurement data. In the
first part, the simulated signal in Fig. 2b is repaired. This is done with a comple x baseband
signal, so the a vailability of an IQ recei ver is assumed. The signal part af fected by interference is
sho wn in Fig. 4a after the algorithm is applied, compared to the same signal without interference
from another sensor . The corresponding spectra in Fig. 4b sho w , that the interference cannot be
remo v ed completely . The maximum gain in SNIR (signal to noise and interference ratio) that
could be achie ved in simulations is limited to around 26 dB. Further simulations sho wed that the
main limitation of this gain is the deri vati ve required for (17). This deri v ati ve is approximated
with the dif ference quotient, what leads to limited accuracy .
In the ne xt step, the method is applied on measurement data. Therefore, two radar sensors are
placed in a distance of 26 m. The sensors operate in the 77 GHz band and use chirp sequence
modulations. The interfered sensor is not equipped with an IQ mixer , so the Hilbert T ransform
has to be applied. The interference duration is adjusted according to (3).
Fig. 5 sho ws the measurement of an interfered frequency ramp af fected by a long interference
period. Ho we ver , the le vel of the interfering signal is not constant o ver time. The non-ideal
recei ve path (especially the lo w-pass filter) has a frequency-dependent amplification while the
interference baseband signal is a frequenc y ramp, thus A Int = A Int ( t ) . As (14) is independent
of this amplitude, the estimation of ϕ Int ( t ) is still correct. The phase estimation of the signal in
Fig. 5 is sho wn in Fig. 6a. From this phase, the frequency f ( t ) is determined, see Fig. 6b. Note
that the cut-of f frequency of the lo w-pass filter in the receiv e path is 4 MHz. The amplitude-
frequenc y dependenc y of the recei ve path is determined in a calibration measurement, so the
6

460 480 500 520 540 560
− 2
0
2
Samples
Amplitude (a.u.)
Repaired
Int.-free

(a) Repaired and interference-free time signals corre-
sponding to Fig. 2b.
0 0 . 1 0 . 2 0 . 3
− 60
− 40
− 20
0
f /f s
Norm. po wer in dB
Interfered
Repaired
Int.-free

(b) Comparison of the spectra of the repaired, inter -
fered, and interference-free signal.
Figure 4 : Reconstruction of the simulated signal in Fig. 2b.
0 5 10 15 20 25 30 35 40 45 50
− 400
− 200
0
200
400
T ime in µ s
Amplitude (a.u.)

Figure 5 : Measurement of an interfered time domain baseband signal with 235 of 512 samples af fected by inter-
ference.
amplitude-o v er -time behavior can be modeled. It is tak en into account for the interference re-
construction in (18).
The result of the interference reconstruction is depicted in Fig. 7a, the repaired time domain sig-
nal is sho wn in Fig. 7b. The frequency spectra of the original interfered signal and the repaired
7

25 30 35 40 45
0
50
100
T ime in µ s
Phase in rad

(a) The estimation of ϕ Int ( t ) is a parabola.
25 30 35 40 45
− 4
− 2
0
2
4
T ime in µ s
f in MHz

(b) Its deri vati ve holds the frequenc y of s Int ( t ) , opti-
mized with a least-squares fit.
Figure 6 : Estimation of phase and frequency of the long interference signal in Fig. 5.
0 10 20 30 40 50
− 400
− 200
0
200
400
T ime in µ s
Amplitude (a.u.)

(a) Reconstructed interference component.
0 10 20 30 40 50
− 400
− 200
0
200
400
T ime in µ s
Amplitude (a.u.)

(b) Repaired time domain signal.
Figure 7 : Estimation and cancellation of the interference signal in Fig. 5.
signal are compared in Fig. 8. Before the signal repair is applied, the interference-induced noise
floor is only 9 dB belo w the target le vel. After repairing the signal, the interference le vel drops
significantly and the tar get SNIR is 21.9 dB.
8

5 10 15 20 25 30 35 40 45 50 55 60
− 30
− 25
− 20
− 15
− 10
− 5
0
Range in m
Norm. po wer in dB
Interfered
Repaired
Notched

Figure 8 : Frequency spectra normalized to the tar get at 26 m.
The figure also sho ws what happens if the interfered samples of the time signal are simply
notched instead of using the presented approach. Notching interfered samples is described as
s BB,notched ( t ) = s BB ( t ) ·  rect  t
T c  − rect  t − τ
T Int  . (26)
The first rectangle represents the total measurement time. The v ariable τ shifts the second rect-
angle to the interference period, remo ving this signal part. In the spectrum, notching con v olves
an additional si-function with all tar gets. Thereby it reduces their power l e vels and introduces
additional artifacts. F or the long interference duration, this ef fect is clearly visible. In this case,
the sensor resolution is se verely reduced, see the corresponding wide peak in Fig. 8. Still, notch-
ing raises the SNR to 19 . 4 dB.
5. Discussion and Conclusion
The paper describes a method for the estimation of phase, frequenc y , and amplitude of inter-
fering signals for chirp sequence modulated automoti ve radars. The estimated interference is
remo v ed from the recei ve signal to achie ve interference-free operation. This method is espe-
cially ef fecti ve for long interference durations with high po wer , as these circumstances improv e
the estimation accurac y . Ho we ver , when applied on data with short interference durations, the
method will not be the best choice. In case of short interference durations, the disadv antages of
a simple notching approach are ne glectable with much lo wer computation ef fort.
F or longer interference durations the proposed method of fers the adv antage that the full signal
information can be preserv ed compared to the notching of interfered samples. There is no loss
in resolution and no additional artifacts are created in the spectrum (cp. Fig. 8). Simulations
9

sho wed that a gain in SNR of up to 26 dB can be achie ved. In measurements, an SNR impro v e-
ment of 12.9 dB was possible, clearly outperforming the notching of interfered samples.
Refer ences
[1] G. M. Brooker , “Mutual Interference of Millimeter-W a ve Radar Systems, ” IEEE T ransactions on
Electr omagnetic Compatibility , v ol. 49, no. 1, pp. 170–181, Feb . 2007.
[2] T . Schipper , M. Harter , T . Mahler , O. K ern, and T . Zwick, “Discussion of the operating range of
frequency modulated radars in the presence of interference, ” International J ournal of Micr owave
and W ir eless T echnolo gies , vol. 6, pp. 371–378, June 2014.
[3] D. Oprisan and H. Rohling, “ Analysis of Mutual Interference between Automoti ve Radar Systems, ”
in International Radar Symposium (IRS) , 2005, Berlin.
[4] J. Bechter and C. W aldschmidt, “Automoti ve Radar Interference Mitigation by Reconstruction and
Cancellation of Interference Component, ” in IEEE MTT -S International Confer ence on Micr owaves
for Intelligent Mobility (ICMIM) , April 2015, pp. 1–4.
[5] V . W inkler , “Range Doppler Detection for automoti ve FMCW Radars, ” in Eur opean Micr owave
Confer ence , Oct. 2007, pp. 1445–1448.
[6] C. Fischer , M. Barjenbruch, H.-L. Bl ¨
ocher , and W . Menzel, “Detection of Pedestrians in Road En-
vironments with Mutual Interference, ” in 14th International Radar Symposium (IRS) , vol. 2, June
2013, pp. 746–751.
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