Wireless Sensor Network, 2009, 1, 293-299
doi:10.4236/wsn.2009.14036 Published Online November 2009 (http://www.scirp.org/journal/wsn).
A New Method for Anti-Noise FM Interference
Changyong JIANG, Meiguo GAO, Defeng CHEN
Department of Electronics Engineering, Beijing Institute of Technology, Beijing, China
Received May 30, 2009; revised June 20, 2009; accepted June 21, 2009
Abstract
Noise Frequency Modulated (NFM) interference causes a disaster to almost all types of Radar systems. The
echo signal and the interference are overlapped and because of strong energy of the NFM interference noth-
ing could be detected except the interference in the Radar receiver system. Up to now no good method
against NFM has been declared, conventional methods are based on the passive Radar to track the interfer-
ence source which are not applicable under most conditions. Here a novel anti-noise FM method is proposed
to suppress the NFM interference, the method multiply the mixed signal two times by different reference
signals. The principle and some key factors of the new method are analyzed in detail and some rules for pa-
rameters designing are given. What’s more, results show that the method can eradicate NFM effectively.
Keywords: ECM, ECCM, NFM Interference, Anti-NFM
1. Introduction
FM jamming is a common jamming forms in oppressive
jamming on radar systems [1–2]. Noise FM is a mostly
used ECM method, and can cause disasters to nearly all
types of Radar systems. So, analysis of the performance
of NFM in ECM and solutions against NFM in ECCM
has developed for years. [3] Proposed the noise FM
jamming method. The effect of noise FM jamming
against ISAR one or two-dimensional imaging is de-
scribed in detail, and the power requirement of noise FM
jamming is compared with that of RF noise jamming.
Song [4] uses growth factor analyzed the capability of
radar MTI in noise FM jamming. Liu [5] uses signal to
jamming ratio (SJR) gains discussed the performance of
anti-noise FM jamming of PRC-BPM fuze. [6] uses the
effect of Doppler f requency, pseudo-random co de width,
the effect of period pseudo-random code serial and aim-
ing frequency deviation analyzed the performance of the
pseudo-random code binary phase modulated (PRC-
BPM) fuze. Xu [7] gave methods of multipath jammer
tracking with a passive radar seeker. Chen [8] studied the
formula of composite phase-difference of two noise FM
jamming. Deergha Rao. K. [9] presented an approach
based on jammer instantaneous frequency estimation for
suppression of frequency modulated jammers in spread
spectrum systems. [10] Focus on Subspace Projection
Technique for suppression of jamming in narrowband
FM jammers, however, NFM interference is a wideband
interference that this technique in [10] cannot be applied.
[11] presented performance analysis of subspace projec-
tion array processing techniques for suppression of fre-
quency modulated (FM) jammers in GPS receivers, and
based on this [12] made the approach applied to AM-FM
jammers as well, however, the subspace projection tech-
niques are not available under some radar receivers. [13]
offered a method against NFM based on Square Trans-
formation, however, it is only described in the applica-
tion of Pseudo-random Coded Fuze and analog circuits.
Above all, these research es made big progress in finding
solutions against NFM, but the methods cannot totally
resolve the problem in the radar systems.
Based on all the previous researches, a method is pro-
posed to eliminate NFM in this paper. It multiply the
mixed signal by two different reference signals two times
and with followed signal processing the needed signal
can be obtai ned from the output.
The paper is organized as follows. In Section 2, the
echo signal model and NFM interference model are de-
scribed in detail. Section 3 depicts how the new method
supposed here excise NFM interference and some key
factors of the method are analyzed. Section 4 gives the
performance analysis of the method. And some conclu-
sions are given in the last section.
2. Signal Model
Noise FM is a commonly used method for jamming
wireless communication systems such as Radar systems,
GPS etc. It has a strong suppress to the needed signal and

294 C. Y. JIANG ET AL.
 
its bandwidth is much wider than the needed signal. The
noise-FM is modeled as1



0
cos
NFM i ci
t
s
tAtkf d



ci
 (1)
where Ai is the amplitude of NFM interference,

is
the carrier frequency of NFM interference, and k is the
FM slope. The bandwidth of the NFM interference is
BWi.
The echo signal from the target is defined as

cos
use u

2
c0
s
tAtkt  
c
(2)
where Au is the amplitude of the echo signal,

is the
carrier frequency of the echo signal, and k0 is the FM
slope (k0=0 when the signal suse(t) is CW and k0≠0 when
the signal suse(t) is chirp ). The bandwidth of the echo
signal is BW. It is known that in order to make the inter-
ference more effective,ci c

 , iu
A
A
i
BW BW
 
use
and
must be satisfied. Thus it is hard to obtain
the needed signal suse(t) neither from time domain nor
frequency domain.
Without loss of generality, mixed signal which enters
the radar receiver is defined as

NFM
s
tstst
aab
bab
aab
(3)
where sNFM(t) is defined in Equation (1), suse(t) is defined
in Equation (2).
3. Nfm Excision
3.1. Basic Concept
This part simply shows what the new method derivate
from. It is supposed that two variables, “a” and “b” are
here. How to change each other’s value without any
other variable? A simple description of solving this ques-
tion is shown below.
First, let
(4)
Now the value of variable “a” becomes sum of “a”
and “b”, the value of variable “b” remains the same.
Second, let
(5)
then the value of variable “a” remains the same, the
value of variable “b” becomes the value of “a” which is
before Equation (4).
Last, let
(6)
And the aim of changing values of “a” and “b” is
reached.
Similarly, if two signals are mixed together, it is pos-
sible to separate them in the same way above.
3.2. Principle of the New Method
As is known to all, it is easy to get two signals added
with each other in the frequency domain just by multi-
plying each other. Two signals multiplied with each
other in the time domain means that their frequencies are
added with each other in the frequency domain. In this
way the new method contains two steps which mainly
consist of two multiplications, so it is called “dou-
ble-multiplication” method in the next chapters.
3.2.1. The First Step of Double-Mul tiplication Method
The first step of double-multiplication method can be
seen from Figure 1. It contains a multiplication, a low
pass filter and DC blocked module. The multiplication is




0M
s
tstst (7)
And all parts obtained after this multiplication are as
follows,
 direct current:


22
/2 /2
DCu i
stA A
 
(8)
 low frequency part:


2
10
0
cos t
Miu cic
tAAkf dtkt    
 (9)
s
 the part whose carrier frequency is nearly twice as
large as c

:






2
01 /2 cos2 Mu c
s
tA t


  
(10)


2
02 0
/2 cos 22t
Mi ci
s
tA tkfd

 

 
(11)


2
03 0
0
cos t
Miucic
tAAtkf dkt   
 (12)
s
After sM0(t) goes through a low pass filter and DC
blocked module, signals described in Equation (8), (10),
(11), (12) are filtered and only sM1(t) is left.
3.2.2. The Second Step of Double-Multiplication
Method
The second step of double-multiplication method can be
seen from Figure 1. It contains a multiplication, a band
pass filter. The second multiplication is






21MM
ststst (13)
And all the parts obtained are as follows.
 The parts whose carrier frequency is nearly the
same with c

:

 

22
210 0
cos 22t
Muicci
s
tAAtktkf d

  
 (14)

C. Y. JIANG ET AL. 295


C opyright © 2009 SciRes. WSN
 

2
22 cos Mu i0
t
ci
s
tAAtkfd

 

 (15)




22
0uc23 cos Mi
s
tAAtkt  
 
(16)
 


2
24 0
cos 22t
Miucic 2 0
s
tAAtk  
f dkt
  
g10( /)
iu
(17)
It is obvious that sM23(t) is the needed signal which
just only has a different amplitude with suse(t). Let sM2(t)
go through a band pass filter (BPF) which has a center
frequency of fc and a bandwidth of BW. As is known
that Ai>>Au, sM21(t) and sM22(t) can be omitted compared
to sM23(t). What’s more, as BWi>>BW and sM24(t) has a
bandwidth of 2BWi, sM24(t) left little after the band pass
filter. Thus the needed signal is obtained.
The whole process of the method is shown in Figure 1.
3.3. Analysis of Ke y Facto rs in Double -
Multiplicati on Method
The output signal, sout(t), from the process of dou-
ble-multiplication method contains four parts which are
described in Equation (14), (15), (16) and (17). Usually
the higher the interference to signal ratio (ISR) is, the
more effectivel y the in terf erence works ; and the wider the
bandwidth of NFM interference is, the more effectively
the interference works. So the two factors, ISR and the
bandwidth of NFM interference, are analyzed as follows.
3.3.1. Interference to Signal Ratio
1) Relationship between ISR and SIR
The interference to signal ratio (ISR) is defined as
20lo
I
SR A A (18)
From Equation (18) it is known that the higher the
ISR is, the bigger the Ai/Au is. According to Equation
(15), (16) and (17), among the output signal sM2(t) the
needed signal to interference ratio is
 









23 22
22
10log10 /
20log10 /
20log10 1///
MM
iuui i
uii
SIRPstP st
AAAA AA
AABWBW










24
2/
M
u i
P st
BWBW






(19)
For a certain bandwidth of NFM interference, the
BW/BWi is a constant. As ISR increases, Ai/Au also in-
creases, thus SIR described in Equation (19) increases, too.
Hence a conclusion is obtained: the higher the ISR is,
+
+

st

st LPF
DC
blocked

2
st
M
delay
BPF

out
s
t
BC D
The first stepThe second step
A

0M
st

1M
st

Figure 1. Structure of double-multiplication method.
the bigger the SIR is, which means that the higher the
ISR is, the more efficient the new method is.
2) Relationship between ISR and low pass filter
Within the first step of double-multiplication method,
after multiplication the power of sM02(t) to sM1(t) ratio is



02 120log10/2 MMu i
(20)
s
sRAA
c
Although the carrier frequency of sM02(t) is nearly
twice as large as

and sM02(t) is out of the passband
of LPF, if the stopband attenuation of LPF is smaller
than sM021sM1R, the interference signal sM02(t) may not be
filtered from sM1(t) by the low pass filter. So the design
of stopband attenuation of LPF must be bigger than
sM021sM1R dB. Hence another conclusion is obtained: the
higher the ISR is, the bigger the stopband attenuation of
LPF must be.
Above all, two conclusions related to ISR are ob-
tained as follows.
 The higher the ISR is, the more efficient the dou-
ble-multiplication method is. The higher the ISR is,
the bigger the stopband attenuation of LPF must be.
3.3.2. Bandwidth of NFM Interference
For a certain ISR, the Au/Ai is a constant. As BWi, the
bandwidth of NFM increases, SIR described in Equation
(19) increases, too. So the bigger the bandwidth of NFM
interference is, the h igher the SIR is, which means that the
more efficient the double-multiplication method is.
However, the bandwidth of NFM interference is un-
known under most conditions. Thu s the stopband of the
low pass filter cannot be decided. If the stopband of the
LPF is smaller than the bandwidth of NFM interference,
the output of the first step, i.e. sM1(t), may not be cor-
rectly obtained. There are two ways to solve this prob-
lem: 1) Measuring the bandwidth of NFM interference
if the receiver system is capable of this; 2) Designing
the LPF with a high stopband as possible as the receiver
system can.
Above all, conclusions related to bandwidth of NFM
interference are drawn as follows.
 The bigger the bandwidth of NFM interference is,
the more efficient the new method is.
 When bandwidth of NFM interference is un-
known, it is better to measure the bandwidth of
NFM interference, otherwise to design the LPF
with a high stopband as possible as the receiver
system can.
4. Performance Analysis
Without loss of generality, considering the echo signal is
CW signal and A
use=1, fc=100.2MHz. And simulation
results are depicted as follows.

296 C. Y. JIANG ET AL.
It is supposed that the bandwidth of NFM interference
is known as 20MHz and ISR is 40dB. Simulation results
can be seen from Figure 2 and Figure 3. In Figuer 2 the
graph above is the spectrum of the mixed signal which
contained the echo signal and the NFM interference, the
graph below shows the spectrum of the signal which is
the output (at dot “B” in Figure 1) after the first step. In
Figure 3 the graph above is the spectru m of signal which
is the output (at dot “C” in Figure 1) after the second
multiplication, the graph below shows the spectrum of
signal which is the output (at dot “D” in Figure 1) after
the whole process of double-multiplication method.
From the graph above in Figure 2 it is obvious that the
echo signal and NFM interference are overlapped with
each other and the echo signal cannot be distinguished
from the interference. However, the graph below in Fig-
ure 3 shows that the output signal is mainly the echo
signal after the process of double-multiplication method.
80100 120140 160 180200
0
1
2
3x 10
5
The spectrum of mi x ed si gnal (M Hz )
010 20 304050 6070 8090
2x 10
5
100
0
0. 5
1
1. 5
The s pectrum of s i gnal aft er t he firs t s tep. (MHz)
Figure 2. Spectrum of signals at different time.
80100 120140 160 180
15 x 10
7
200
0
5
10
X: 100.2
Y: 1.038e+008
The s pectrum of s i gnal after t he second m ultiplication. (M Hz)
80100 120140 160 180
6x 10
7
200
0
2
X: 100.2
Y: 5.179e+007
4
The s pectrum of out put signal. (M Hz)
Figure 3. Spectrum of signals at different time.

C. Y. JIANG ET AL. 297
100
010 2030 405060708090100
-20
0
20
40
60
80
ISR (dB)
SIR (dB)
Figure 4. SIR at different ISR.
4.1. Simulation of ISR
As mentioned above, when the ISR increases the
stopband attenuation of LPF increases and the SIR
increase. These two relationships are simulated as
follows.
4.1.1. The Relationship between ISR and SIR
It is supposed that the ISR varies from 0~100 dB, the
bandwidth of NFM interference is known as 20 MHz,
and the bandwidth of band pass filter (BPF) is 1 MHz.
Figure 4 shows the SIR at different ISR. It is obvious
that the larger the ISR is, the larger the SIR is, which
confirms the conclusion obtained above.
4.1.2. Design o f Sto pband Attenuation o f L PF
Consider the ISR varies from 0~100 dB, the stopband
attenuation of LPF are 20 dB and 100 dB. The graph
below in Figure 5 shows the results when the stopband
attenuation of is 20dB and the graph above shows the
results when the stopband attenuation of is 100 dB. It is
obvious that a small stopband attenuation of LPF will
cause errors to the output and high ISR needs large stop-
band attenuation of LPF, which also confirms the con-
clusion above.
4.2. Bandwidth of NFM Interference
Consider the bandwidth of NFM interference varies from
2~40 MHz, ISR is 40 dB.
4.2.1. Bandwidth of NFM Interference is Known
As the bandwidth of NFM interference is known, the
stopband of LPF is bigger than all the bandwidth of
NFM. Figure 6 shows the frequency of output signal
with different bandwidth of NFM interference. And a
conclusion is obtained: if the stopband of LPF is larger
than the bandwidth of NFM interference, the needed
signal can be got correctly.
4.2.2. Bandwidth of NFM Interference is Unknown
As the bandwidth of NFM interference is unknown, it is
supposed that it is 2MHz and 20MHz. Figure 7 shows
the obtained frequency when the stopband of LPF is
2MHz and Figure 8 shows the obtained frequency when
the stopband of LPF is 20MHz.
From Figure 7 and Figure 8, it is known that when
the bandwidth of NFM interference is unknown, to de-
sign the stopband of LPF as big as possible will help to
make the method more efficient.
010 2030 4050 60 7080 90 100
99
100
101
102
(MHz)
ISR ( dB)
Frequency
100. 3
010 2030 4050 60 7080 90 100
100
100. 1
100. 2
ISR ( dB)
Frequency (MHz )
Figure 5. Frequency of output at different ISR.
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298 C. Y. JIANG ET AL.
05 10 1520 25 30 3540
99
99. 5
100
100. 5
101
101. 5
Ba ndwi dth of NFM (M Hz)
Frequen c y (M Hz)
Figure 6. Frequency of output signal.
05 10 15 20 25303540
99. 6
99. 7
99. 8
99. 9
100
100. 1
100. 2
100. 3
100. 4
100. 5
100. 6
B andwi dth of NFM (M Hz )
Frequency (MHz )
Figure 7. Frequency of output signal.
0510 15202530 35 40
99
99.5
100
100. 5
101
101. 5
B andwidth of NFM (M Hz)
Frequenc y (MHz )
04.
06.
Figure 8. Frequency of output signal.
5. Conclusion
NFM interference can suppress the useful signal both in
the time domain and in the frequency domain. The new
method supposed in this paper can eliminate the effect of
the NFM interference. Some conclusions are obtained:
 The higher the ISR is, the more efficient the dou-
ble-multiplication method is.
 The higher the ISR is, the bigger the stopband
attenuation of LPF must be.
 The bigger the bandwidth of NFM interference is,
the more efficient the double-multiplication
method is.
 When bandwidth of NFM interference is un-
known, it is better to measure the bandwidth of
NFM interference if possible, otherwise to design
the LPF with a high stopband as possible as the
receiver system can.
Further studies will focus on the signal model for
SAR/ISAR and the real application on radar systems or
other communication systems.
6. References
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