Journal of Signal and Information Processing, 2013, 4, 58-61
doi:10.4236/jsip.2013.43B010 Published Online August 2013 (http://www.scirp.org/journal/jsip)
Performance Comparison of Three Algorithms Applied to
UM2000 Signal Demodulation
Zhichao Qiao, Fuping Wang
Department of Electrical Engineering, Tsinghua University, Beijing, China.
Received April, 2013.
ABSTRACT
UM2000 signal is a type of multi-audio frequency-modulated signal which is widely used for railway blocking. Princi-
ples of three typical demodulating algorithms are presented in details in this paper. Bit error rates of the three methods
at different SNRs are achieved by Monte Carlo simulation experiments. Among the three algorithms, the quadrature
demodulation has the best performance at the real working environment. However, the three methods have the same
problem of phase hopping when noise is too strong.
Keywords: UM2000 Signal; Differential Frequency Detection; Zero-Crossing Detection; Quadrature Demodulation
1. Introduction
With the rapid development of high-speed railway in the
world, some of the old track circuits have been unable to
meet the requirements in terms of speed and safety. So
the upgrading and updating of these old track circuits is
getting more and more urgent. UM2000 joint-less track
circuit is a new type of digital coding track circuit apply-
ing in high-speed railways. UM2000 signal is a type of
multi-audio frequency modulated signal, whose modu-
lated signal contains 28 sinusoidal waves. But the adja-
cent frequency interval is as small as 0.64 Hz. So its de-
modulation turns complicated and time-consuming. Then
the research of demodulating methods plays a vital role
in the railway system.
According to communication theory, coherent de-
modulation and non-coherent demodulation are the two
traditional demodulating approaches of frequency-
modulated signals. We can get the instantaneous phase of
the FM signal by coherent demodulation, and directly
obtain the instantaneous frequency by the non-coherent
demodulation. And that is the difference of the two ap-
proaches. From this point, the performances of the fol-
lowing three methods are compared. The three algo-
rithms are differential frequency detection, zero-crossing
detection and the quadrature demodulation.
2. Three Demodulation Algorithms
2.1. Model of UM2000 Signal
The UM2000 signal is frequency-modulated, which can
be expressed as
() sin[2π()d ]
cf
s
tA ftKxtt
 (1)
where
A
is the amplitude, c
f
is the carrier frequency,
and {1700, 2000, 2300,0}260
c
f

, f
K
is the FM con-
stant, ()
x
tis the low-frequency modulating signal.()
x
t
can be shown as
27
1
2828 28
() sin(2π)
sin(2π)
iii i
i
xt Aft
Aft






 (2)
where i
A
is the amplitude of every sinusoidal wave,
i

is the phase. The former 27 frequencies are used to
transfer the corresponding information, fori

=0, 1. And
the frequencies are fi=0.88+0.64× (i-1) Hz, i=1,2,…,27;
and f28 =25.68 Hz.
As we all know, the goal of demodulation is to obtain
the modulating signal ()
x
t from the modulated sig-
nal ()
s
t. Then we can get the 28 bits codes transmitted
between the station and the cab.
2.2. Differential Frequency Detection
As is described in the "Communication Theory"[1], the
algorithm of differential frequency detection is the
non-coherent demodulation of FM signals. The fre-
quency detector is the key part of this method, which is
cascaded by the ideal differentiator and envelope detector.
The principle of this method will be elaborated in the
next paragraphs [2].
Firstly we apply differentiator to the receiving sig-

Performance Comparison of Three Algorithms Applied to UM2000 Signal Demodulation 59
nal ()
s
t. We get its differential,()
d
s
t, which is noted as
() [2π()]
cos[2π()d]
dcf
cf
stA fKxt
f
tK xtt


 (3)
After the differential, the FM signal turns to be the
signal modulated by amplitude and frequency. From
Equation (3), we can easily see that the envelope of
()
d
s
t contains the information of()
x
t.
Then we can get its envelope by Hilbert Transform,
that is
ˆ() [2π()]
sin[2π()d]
dcf
cf
stA fKxt
f
tK xtt


 (4)
Getting the square root of ()
d
s
tand ˆ()
d
s
t as
22
[2π()]
ˆ() ()
d
cf
d
EvAfKx t
s
tst

 (5)
By removing the DC component by a filter, we get the
modulating signal()
x
t. So far, the demodulation of the
UM2000 signal has been achieved according to the algo-
rithm of differential frequency detection.
2.3. Zero-Crossing Detection
The algorithm of zero-crossing detection [3], also known
as the counting method, is the easiest approach to meas-
ure the instantaneous frequency. The principle is effec-
tive for the UM2000 signal demodulation because the
zero-crossing sequence directly reflects the signal’s pe-
riod. For the UM2000 signal, its instantaneous frequency
can be noted as
()
2π
f
c
K
I
Ff xt (6)
The relationship of modulating signal ()
x
tand the in-
stantaneous frequency
I
Fis clearly shown in Equation
(6). Then we can get the instantaneous frequency by de-
tecting the zero-crossing sequence. The specific steps are
clearly elaborated below.
Firstly, get the zero-crossing sequence. Then
the intervals sequence can be obtained as
()zero i
() [(1)()]/
s
intervalizero izero if (7)
where
s
f is the sampling frequency. Because the inter-
vals represent the signal’s half-cycle, we can get
1/[2( )]
I
Finterval i (8)
According to Equation (6), we get
2π
() ()
c
f
xtIFf
K
 (9)
At last, filtering and interpolation are necessary to ob-
tain the real modulating signal()
x
t. So far, the process of
demodulation by the method of zero-cross detection has
been completed.
2.4. Quadrature Demodulation
A common ground of the former two methods shown in
section 2.2 and 2.3 is to obtain the instantaneous fre-
quency directly. Whereas the quadrature demodulation
[4], its core step is to get the signal’s phase,
()d
f
K
xt t  . The principle will be elaborated later.
We make the carrier signal and ()
s
t to be the inputs
of the multiplier. We can get
()() cos(2π)
sin[4π()d ]
2
sin[()d]
2
Ic
cf
f
st stft
A
f
tK xtt
AKxtt





(10)
()() sin(2π)
cos[4π()d ]
2
cos[()d]
2
Qc
cf
f
st stft
A
f
tK xtt
AKxtt

 



(11)
Then a low pass filter is designed to remove the high-
frequency components. So we have the in-phase compo-
nent and the quadrature-phase component of the phase
signal as follows.
()sin[()d ]
2f
A
I
tKxtt (12)
()cos[()d ]
2f
A
QtKxt t (13)
Then we use anti-trigonometric functions to obtain the
phase signal()d
f
K
xt t  . Thus, the modulating signal
()
x
t can be derived as
d
()[ ()/]
df
x
tt
t
 K
s
(14)
Therefore, the demodulating has been achieved by
quadrature demodulation.
3. Simulations
In order to compare demodulation performance of the
three algorithms objectively[5], we chose the same envi-
ronment and parameters when simulated in MATLAB.
The sampling frequency is set as Hz. The
sampling time is
16384
s
f
3.125
d
T

. The carrier frequency is
2000
c
f

Hz. The message matrix of UM2000 signal
is . The sig-
nal-to-noise ratio is set as SNR=20dB. Their simulation
results are shown in the next parts.
=[0011110001011110011110 1110]Delta

Performance Comparison of Three Algorithms Applied to UM2000 Signal Demodulation
60
In accordance with the principles described in the
former part, the simulations are carried out in MATLAB.
Results are shown in the three figures below, where the
blue line represents the original modulating signal and
the red line represents the demodulated signal. These
three algorithms proved to be correct and effective.
0.5 11.5 22.5 3
-10
-5
0
5
10
15
20
Time(s)
Amplitude(V)
Figure 1. Differential Frequency Detec tion.
Figure 1 is the result of the algorithm of differential
frequency detection. When the Gaussian-White-Noise is
added to the signal, an amplitude limiter has to be placed
before the differentiator, in order to get rid of the para-
sitic amplitude modulation. And the design of differential
filter is also one step needed to be improved.
0.5 11.522.5 3
-10
-5
0
5
10
15
20
Time(s)
A mpl i t ude(V )
Figure 2. Zero-crossing Detection.
Figure 2 is the result of the algorithm of zero-crossing
detection. The performance of this method depends
largely on the sampling frequency. In order to raise the
sampling frequency, we usually take measures of inter-
polation. However, the computing time becomes longer
at the same time.
0.5 11.5 22.5 3
-10
-5
0
5
10
15
20
Time(s)
A m pl itude(V )
Figure 3. Quadrature Demodulation.
Figure 3 is the result of the algorithm of quadrature
demodulation. It is a type of PM demodulation algorithm
to obtain the phase information of the signals first.
However, the periodic character of the phase function
and the influence of phase noise, in some way, can cause
the phase hopping at demodulation. Unwrapping method
can remove the phase hopping caused by its periodic
character.
4. Performance Comparison
The evaluation of the performance of communication
receivers is most commonly used as BER (bit error rate).
The transmission channel interference was simulated
with additive Gaussian noise. The signal power is set as 1,
and the noise was added in-band. Among the parameters,
the message matrixwas generated randomly. Then
the simulations were achieved through Monte Carlo
experiments. And the relationship of BER-to-SNR was
shown in Figure 4.
Delta
4
10
As is clearly displayed in the figure, the BER of the
three algorithms at high SNR was almost zero. However,
with the reduction of the SNR, the BER became higher
suddenly. Among the three algorithms, the quadrature
demodulation has the best performance at the real work-
ing environment, i.e. at SNR > 20 dB. However, when
SNR is less than 15dB, the performance of all the meth-
ods turns very bad.
In addition to the bit-error-rate, the computing time is
another standard to evaluate the performance of algo-
rithms. Due to the high demands of real-time in
high-speed railway system, the decoding algorithm must
respond quickly in short time. Among them, the method
of zero-crossing detection takes longer time because of
the applying of mathematical interpolation.

Performance Comparison of Three Algorithms Applied to UM2000 Signal Demodulation
61
10 152025
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
S NR(d B )
B i t Error Rate
BER---zero
BER----IQ
BER---diff
Figure 4. BER of Three algorithms.
5. Conclusions
In this paper, principles of three algorithms of demodula-
tion were clearly elaborated and simulations were done
to prove their feasibility. As UM2000 is widely used in
railway system, the performances of its demodulation
methods were compared. And we have some conclusions
as below.
1) At real working environment (SNR > 20 dB), the
Quadrature Demodulation has the best BER performance
among the three demodulation algorithms. At SNR = 20
dB, its error rate is close to 10-5, while the error rates of
the two other methods are near 10-4.
2) When the power of the noise increases (SNR < 15
dB), the performance of all the algorithms turns very bad.
It is the same problem of all the demodulation algorithms.
The underlying of reasons may have something to do
with the phase hopping caused by the noise. The further
research of phase noise is still needed in the future.
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[2] L. Zhu and S. Wu, “Digital Demodulation Method for
Multi-tone FM Signal in Track Circuit System,” China
Railway Science, Vol. 26, No. 5, 2005, pp. 91-95.
[3] G. Hu, “Digital Signal Processing,” 2nd Edition,
Tsinghua University Press, Beijing, 2003.
[4] L. Nan, “Brief Introduction of Communication Princi-
ples,” Tsinghua University Press, Beijing, 2000.
[5] F. Wang, “Study on the Decoding Arithmetic of the
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